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Mathematics LibreTexts

12.2: Navigating a Table of Equivalent Ratios

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Let's use a table of equivalent ratios like a pro.

Exercise \(\PageIndex{1}\): Number Talk: Multiplying by a Unit Fraction

Find the product mentally.

\(\frac{1}{3}\cdot 21\)

\(\frac{1}{6}\cdot 21\)

\((5.6)\cdot\frac{1}{8}\)

\(\frac{1}{4}\cdot (5.6)\)

Exercise \(\PageIndex{2}\): Comparing Taco Prices

Use the table to help you solve these problems. Explain or show your reasoning.

  • Noah bought 4 tacos and paid $6. At this rate, how many tacos could he buy for $15?
  • Jada’s family bought 50 tacos for a party and paid $72. Were Jada’s tacos the same price as Noah’s tacos?

Exercise \(\PageIndex{3}\): Hourly Wages

Lin is paid $90 for 5 hours of work. She used the table to calculate how much she would be paid at this rate for 8 hours of work.

clipboard_ede1ffa294d54829eacf2dcce3bc9eb3d.png

  • What is the meaning of the 18 that appears in the table?
  • Why was the number \(\frac{1}{5}\) used as a multiplier?
  • Explain how Lin used this table to solve the problem.
  • At this rate, how much would Lin be paid for 3 hours of work? For 2.1 hours of work?

Exercise \(\PageIndex{4}\): Zeno's Memory Card

In 2016, 128 gigabytes (GB) of portable computer memory cost $32.

  • Here is a double number line that represents the situation:

clipboard_e43a11971033777137066e60b23cdd5d5.png

One set of tick marks has already been drawn to show the result of multiplying 128 and 32 each by \(\frac{1}{2}\). Label the amount of memory and the cost for these tick marks.

Next, keep multiplying by \(\frac{1}{2}\) and drawing and labeling new tick marks, until you can no longer clearly label each new tick mark with a number.

  • Did you prefer the double number line or the table for solving this problem? Why?

Are you ready for more?

A kilometer is 1,000 meters because kilo is a prefix that means 1,000. The prefix mega means 1,000,000 and giga (as in gigabyte) means 1,000,000,000. One byte is the amount of memory needed to store one letter of the alphabet. About how many of each of the following would fit on a 1-gigabyte flash drive?

Finding a row containing a “1” is often a good way to work with tables of equivalent ratios. For example, the price for 4 lbs of granola is $5. At that rate, what would be the price for 62 lbs of granola?

Here are tables showing two different approaches to solving this problem. Both of these approaches are correct. However, one approach is more efficient.

  • Less efficient

clipboard_e97581642d0425969e479bb879df42183.png

  • More efficient

clipboard_e4e6aeb416b0ac973f921cc3a59aa6299.png

Notice how the more efficient approach starts by finding the price for 1 lb of granola.

Remember that dividing by a whole number is the same as multiplying by a unit fraction. In this example, we can divide by 4 or multiply by \(\frac{1}{4}\) to find the unit price.

Glossary Entries

Definition: Table

A table organizes information into horizontal rows and vertical columns . The first row or column usually tells what the numbers represent.

For example, here is a table showing the tail lengths of three different pets. This table has four rows and two columns.

Exercise \(\PageIndex{5}\)

Priya collected 2,400 grams of pennies in a fundraiser. Each penny has a mass of 2.5 grams. How much money did Priya raise? If you get stuck, consider using the table.

Exercise \(\PageIndex{6}\)

Kiran reads 5 pages in 20 minutes. He spends the same amount of time per page. How long will it take him to read 11 pages? If you get stuck, consider using the table.

Exercise \(\PageIndex{7}\)

Mai is making personal pizzas. For 4 pizzas, she uses 10 ounces of cheese.

  • How much cheese does Mai use per pizza?
  • b. At this rate, how much cheese will she need to make 15 pizzas?

Exercise \(\PageIndex{8}\)

Clare is paid $90 for 5 hours of work. At this rate, how many seconds does it take for her to earn 25 cents?

Exercise \(\PageIndex{9}\)

A car that travels 20 miles in \(\frac{1}{2}\) hour at constant speed is traveling at the same speed as a car that travels 30 miles in \(\frac{3}{4}\) hour at a constant speed. Explain or show why.

(From Unit 2.3.5)

Exercise \(\PageIndex{10}\)

Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. Complete the diagram to show smaller and larger batches that would taste the same as Lin's favorite blend.

clipboard_e2c62b77269a19070ed34370dd182dbd1.png

(From Unit 2.3.1)

Exercise \(\PageIndex{11}\)

Each of these is a pair of equivalent ratios. For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios.

  • \(600:450\) and \(60:45\)
  • \(60:45\) and \(4:3\)
  • \(600:450\) and \(4:3\)

(From Unit 2.2.3)

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Word Problems Involving Equivalent Ratio

An equivalent ratio is a ratio that has the same relationship between numbers as another ratio, but the numbers themselves may be different.

Word Problems Involving Equivalent Ratio

For example, the ratio 2:4 is equivalent to the ratio 4:8 because in both cases, the relationship between the numbers is the same (1:2).

Step-by-step guide to solving equivalent ratios word problems

To solve the equivalent ratio’s word problems, follow these steps: Step 1: Find the ratio given in the word problem. Step 2: Find the given value of one of the two values involved in the ratio Step 3: Divide the given value of step 2 by the corresponding value in the ratio from step 1. Step 4: Multiply both numbers in the original ratio by the number found in step 3 to construct the equivalent ratio.

Word Problems Involving Equivalent Ratio – Examples 1

If a box contains pink and green marbles in the ratio of 3:8 pink to green, how many pink marbles are there if 40 green marbles are in the box? Solution: Step 1: Write the ratios. \(\frac{3}{8}=\frac{x}{40}\) Step 2: Use cross multiplication. \(3×40=8×x⇒120=8x\) Step 3: Divide. \(x=\frac{120}{8}=15\)

Word Problems Involving Equivalent Ratio – Examples 2

Are these ratios equivalent? 10 books for 15 shelves, and 20 books for 25 shelves. Solution: Step 1: Write the ratios. \(\frac{10}{15}, \frac{20}{25}\) Step 2: Use cross multiplication. \(10×25=20×15⇒250≠300\) So these ratios are not equivalent.

by: Effortless Math Team about 1 year ago (category: Articles )

Effortless Math Team

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Basics on the topic Solving Problems with Equivalent Ratios

After this lesson, you will be able to visually solve real-world problems with equivalent ratios using tape diagrams.

The lesson begins by teaching you that ratio problems can be visualized and solved using tape diagrams. It leads you to learn how to solve ratio problems using tape diagrams and find the value of each piece of tape. It concludes with noting that visual representations can be efficient when solving problems with equivalent ratios.

Learn about solving ratio problems by helping Paul give the best care possible to his plant.

This video includes key concepts, notation, and vocabulary such as ratio (a relationship between two non-negative numbers, both of which are not zero); a tape diagram (a visual representation of a ratio); and equivalent ratios (two ratios that are equal).

Before watching this video, you should already be familiar with ratios and how to represent them visually using tape diagrams.

After watching this video, you will be prepared to learn how to solve unit rate problems, including those involving unit pricing and speed; how to find a percent of a quantity as a rate per 100; and how to use ratio reasoning to convert measurement units.

Common Core Standard(s) in focus: 6.RP.A.1 and 6.RP.A.3 A video intended for math students in the 6th grade Recommended for students who are 11 - 12 years old

Transcript Solving Problems with Equivalent Ratios

Today we're visiting Paul's plant shop. Paul loves and cares for all his plants, but he has a particular affinity for his Dionaea muscipula, aka, his venus fly trap. This is because his venus fly trap, affectionately named Deon, wave hello, Deon, is a little plant with dreams of being a Broadway star. To give Deon the best care possible, Paul needs to solve problems with equivalent ratios. Deon, like all venus fly traps, needs a specific amount of light each day. 1 hour of light to 2 hours of darkness is the ideal ratio for Deon. We can represent this visually with a tape diagram that shows the parts of the ratio. Notice the one rectangle of light to two rectangles of darkness. With the tape diagram the ratio always remains the same. Therefore, using equivalent ratios, we can find out the number of hours of light that Deon needs per day. We all know there are 24 hours in a day, so during a 24-hour period, how long should Deon be exposed to light and how long should he spend in darkness? To find this solution, we divide the total hours, 24, by the total number of rectangles in the tape diagram. In this case, 3. Therefore, each rectangle represents 8 hours. This shows that, each day, Deon needs 8 hours of light and 16 hours of darkness. Wow! Looks like that sunlight has been good for Deon. To keep growing strong he needs some really good soil. Using a tape diagram, we can represent the soil mixture ideal for venus fly traps. Deon's soil should contain 5 parts peat moss, 3 parts silica sand, and 2 parts perlite. We need to know how much of each part of the soil will fit in Deon's 20-gallon flower pot. To solve we should count the total number of rectangles. There are 10 total rectangles. Dividing we see that each rectangle represents 2 gallons. Looks like we need 10 gallons of peat moss, 6 gallons of silica sand, and 4 gallons of perlite to fit the 20 gallon flower pot. Only the best for Deon! What nutrients Deon doesn't get through light and soil, he makes up for by trapping insects. For every 3 flies Deon catches, he eats 7 ants. This fall, Deon ate 48 more ants than flies. How many of each insect did he eat? This problem is a little bit different because we don't know how many insects Deon ate in total, but don't worry, we'll figure it out! We know that Deon ate 48 MORE ants than flies. The tape diagram for ants is 4 rectangles longer than the tape diagram for flies. So, these 4 more rectangles must represent the 48 MORE ants! To find the value of each rectangle, we divide the 48 by 4, and find that each rectangle equals 12 insects. Which means Deon ate 84 ants and 36 flies this fall. Is that right? Let's check. 84 minus 36 is 48 So there were 48 more ants. Too bad Deon's diet doesn't include breath mints. There are a few steps we should summarize about solving problems with equivalent ratios. First, create a tape diagram with given ratio. Tape diagrams help us visualize and solve ratios problems. Tape diagrams show the rectangles, or units, in a ratio and help us figure out their numeric value. If you know the overall total, like the 24 hours in the light example, divide this number by the total number of rectangles, to find the value of each rectangle. This gives us the solution for each part of the ratio. We use the same steps of creating a tape diagram from given information. Except, if you know the difference between two quantities in a ratio, like the 48 more ants than flies, count how many MORE rectangles one tape diagram has compared to the other. Then, divide the difference between the quantities by the difference in the number of rectangles to find the value of each rectangle. This, again, gives us the solution for each part of the ratio. Paul has taken great care of Deon. Therefore, Deon has been able to develop quite an impressive vocal range! He's packed his bags and is off to Broadway.

Solving Problems with Equivalent Ratios exercise

Use tape diagrams and equivalent ratios to solve problems..

Given the ratio between different quantities and the total number of those quantities combined, we can use tape diagrams to find out how much of each quantity we have.

For example:

  • Suppose we are given the ratio of Peanuts to Walnuts: $P:W=3:2$.
  • We are also given a total of $P+W=30$ nuts in total.
  • We know there are $3+2=5$ rectangles in total.
  • That means each rectangle represents $\frac{30}{5}=6$ nuts.
  • Since Peanuts have $3$ rectangles, there are $3\times6=18$ Peanuts.
  • Since Walnuts have $2$ rectangles, there are $2\times6=12$ Walnuts.

We can use tape diagrams to solve problems involving three quantities. Suppose that in a restaurant, the ratio of Chairs to Tables to Stools is $3:2:1$. And suppose there are $42$ pieces of furniture total. How many of each type of furniture are in the restaurant?

  • There are $6$ total rectangles.
  • $\frac{42}{6}$ gives us $7$ pieces of furniture per rectangle.
  • The number of Chairs is $3\times7=21$.
  • The number of Tables is $2\times7=14$.
  • The number of Stools is $1\times7=7$.
  • We can check our answer by adding: $21+14+7=42$ pieces of furniture.
  • Draw rectangles to represent the ratio between different quantities.
  • Find the total number of rectangles.
  • Divide the total of the quantities by the total rectangles to get the quantity per rectangle.
  • Then multiply to find how much of each quantity you've got.

Because the ratio $P:C:D$ is $5:2:3$ , Phalaenopsis gets $5$ rectangles, Cattleya gets $2$, and Dendrobium gets $3$. There are $10$ rectangles in total. Because there are $100$ orchids in the shop, we divide $100$ by $10$ to give us $10$ orchids per rectangle. Because Phalaenopsis has $5$ rectangles, there are $5\times10=50$ plants of this type. Because Cattleya has $2$ rectangles, there are $2\times10=20$ plants of this type. Dendrobium has $3$ rectangles and so there are $3\times10=30$ plants of this type.

Use tape diagrams to solve the given ratio problem.

Given a ratio, we can determine how many more rectangles are assigned to one quantity over another.

  • Suppose we are give that the ratio of Cars to Trucks at a car dealership is $C:R=14:11$.
  • We are also given that there are $12$ more Cars than Trucks.
  • Cars have $14$ rectangles and Trucks have $11$.
  • Cars have $14-11=3$ more rectangles than Trucks.
  • Because there are $12$ more Cars than Trucks and that's represented by $3$ rectangles, each rectangle represents $\frac{12}{3}=4$ automobiles.
  • So there are $14\times4=56$ Cars and $11\times4=44$ Trucks.
  • We can confirm our answer by subtracting the number of Trucks from the number of Cars: $56-44=12$.

Given a ratio and the difference between the quantities, we can find the amount of each quantity:

  • Assign rectangles to each quantity based on the given ratio.
  • Subtract the number of rectangles of one quantity from that of the other.
  • Divide the given difference between the quantities by the number of rectangles from the last step. This gives you the quantity per rectangle.
  • Multiply the number of rectangles for each quantity times the quantity per rectangle to get the value for each quantity.

Suppose the ratio of a quantity $A$ to a quantity $B$ is $8:5$, and the difference $A-B=30$. What's quantity of $A$ and the quantity of $B$?

  • $\frac{30}{3}=10$.
  • The quantity of $A$ is $8\times10=80$.
  • The quantity of $B$ is $5\times10=50$.
  • We can check our answer: $80-50=30$, the difference given in the original problem.
  • The ratio of Blueberries to Raspberries is $4$ to $7$.
  • There are $27$ more Raspberries than Blueberries.
  • Write the ratio in proper notation:
  • Subtract to find the difference in the number of rectangles assigned to each quantity:
  • Divide to find the number of berries per rectangle:
  • $\frac{27}{3}=9$ berries per rectangle.
  • Multiply to find the number of Blueberries and Raspberries:
  • $4\times9=36$ Blueberries, and $7\times9=63$ Raspberries.
  • Subtract these values to check your answer:
  • $63-36=27$.

Determine the total number of Venus fly traps and roses in Paul's shop.

Suppose the ratio of Road Bikes to Mountain Bikes in a bike shop is $R:M=5:7$, and there are 12 more Mountain bikes than Road bikes in the shop.

  • The tape diagram will show $2$ more rectangles for $M$ than $R$.
  • Those $2$ rectangles represent $12$ bikes.
  • So each rectangle represents $\frac{12}{2}=6$ bikes.
  • Because we have $5+7=12$ rectangles, we have $12\times6=72$ bikes in total.

Suppose the ratio of Burritos to Tacos at a Mexican food truck is given as $B:T=5:9$, and there are $20$ more Tacos than Burritos.

  • The tape diagram will show $4$ more rectangles for $T$ than $B$.
  • Those $4$ rectangles represent $20$ food items.
  • So each rectangle represents $\frac{20}{4}=5$ food items.
  • Because we have $5+9=14$ rectangles, we have $14\times5=70$ food items in total.

At Paul’s plant shop there are $5$ Venus Fly Traps for every $8$ Roses. Paul has $90$ more Roses than Venus Fly Traps. How many Venus Fly Traps and Roses does Paul’s plant shop have?

  • The ratio of Venus Fly Traps to Roses is given as $V:R=5:8$.
  • The tape diagram has $8$ rectangles on top and $5$ on the bottom, so the top represents Roses and the bottom represents Venus Fly Traps.
  • There are $3$ more rectangles for Roses than for Venus Fly Traps.
  • Those $3$ rectangles represent $90$ plants.
  • So each rectangle represents $\frac{90}{3}=30$ plants.
  • There are $5+8=13$ rectangles in total, so there are $13\times30=390$ plants in total.

Calculate the solution to the following problems using tape diagrams.

Suppose the ratio of Planets to Moons around a star is $11:14$. There are $100$ celestial bodies in total associated with the star. How many more Moons than Planets are there?

  • All the celestial bodies are represented by $25$ rectangles.
  • Each rectangle represents $\frac{100}{25}=4$ celestial bodies.
  • There are $14-11=3$ more rectangles for Moons than for Planets.
  • Those $3$ rectangles represent $3\times4=12$ Moons.

Suppose the ratio of Football teams to Basketball teams in a town is $4$ to $5$. There are $3$ more Basketball teams than Football teams. How many teams are there in total?

  • The difference in rectangles is $1$.
  • This rectangle represents $3$ teams.
  • There are $4+5=9$ rectangles in total.
  • There are $9\times3=27$ teams in total.

Suppose the ratio of Plates to Cups in a kitchen is $7$ to $10$, and there are $12$ more Cups than Plates. How many Plates are there?

  • There are $10-7=3$ more rectangles for Cups than Plates.
  • Those $3$ rectangles represent $12$ pieces of dinnerware.
  • Each rectangle represents $\frac{12}{3}=4$ pieces of dinnerware.
  • There are $7 \times 4=28$ Plates.

A clothing store features Shirts and Pants in the ratio of $3:6$. There are $42$ more Shirts than pairs of Pants. How many articles of clothing in total are in the store?

  • $6-3=3$ more rectangles for Shirts than Pants.
  • $\frac{42}{3}=14$ articles of clothing per rectangle.
  • $3+6=9$ rectangles in total.
  • $9\times 14 =126$ articles of clothing in the store.
  • $11-7=4$ more rectangles for Cubist works.
  • $\frac{24}{4}=6$ works of art per rectangle.
  • $7 \times 6 = 42$ Impressionist works.
  • There is $1$ more rectangle for Raisins than Peanuts.
  • This rectangle represents $2$ Raisins.
  • There are $10\times2=20$ Raisins in total.
  • There are $9+7=16$ rectangles in total.
  • These rectangles represent $32$ songs in total.
  • Each rectangle represents $\frac{32}{16}=2$ songs.
  • There are $9-7=2$ more rectangles for the Eighties than the Nineties.
  • That represents $2\times2=4$ songs.

Create a tape diagram to represent the given ratios.

If the ratio $A:B=25:10$, we can reduce this ratio by dividing each value by $5$:

  • $\frac{25}{5}=5$
  • $\frac{10}{5}=2$

If the ratio $A:B=7:3$, we can say that the ratio $B:A=3:7$.

Given the following ratios, we can combine them into a single ratio statement involving three values:

  • Therefore: $A:B:C=5:7:4$

The given ratios are $P:M=12:8$ and $T:M=15:30$.

  • $P:M=12:8$ can be reduced.
  • Dividing each value by $4$ gives us $P:M=3:2$.
  • $T:M=15:30$ can also be reduced.
  • Dividing each value by $2$ gives us $T:M=1:2$.
  • If $T:M=1:2$, then $M:T=2:1$.
  • Therefore, $P:M:T=3:2:1$.
  • In the tape diagram, $P$ gets $3$ rectangles, $M$ gets $2$, and $T$ gets $1$.

Confirm or correct the solution to each word problem.

Remember, with ratios, order matters. If the ratio of Cups to Bowls is $3:10$, we must be careful to assign $3$ rectangles to Cups, and $10$ rectangles to Bowls, not the other way around.

Remember, we have used two different methods to find the quantity per rectangle:

  • Given $A:B=2:7$,
  • And there are $45$ more of $A$ than $B$, we compute:
  • $\frac{45}{5}=9$ units per rectangle.
  • And there are $45$ units in total , we compute:
  • $\frac{45}{9}=5$ units per rectangle.

If we can find the values of two quantities, we can compute a reduced ratio between them. For example:

  • Given $A=400$ and $B=1400$,
  • $A:B=400:1400$.
  • We can reduce this by dividing each value by $200$:

A scout troop is selling boxes of cookies. The ratio of boxes of Chocolate Chip to boxes of Sugar cookies is $5$ to $6$. There are $33$ boxes of cookies in total. Chocolate Chip cookies are represented by $5$ rectangles, and Sugar by $6$ rectangles. There are $\frac{33}{11}=3$ boxes per rectangle. This gives us $5\times 3=15$ boxes of Chocolate Chip, and $6\times 3=18$ boxes of Sugar cookies.

A grove of trees has Spruce trees and Fir trees such that $S:F=6:3$. There are $90$ more Spruce trees than Fir trees. There are $3$ more rectangles for Spruce than for Fir. So there are $\frac{90}{3}=30$ trees per rectangle. That means there are $6\times30=180$ Spruce trees and $3\times30=90$ Fir trees.

A fruit table at a marathon features Apples, Oranges, and Bananas. There are $48$ more Bananas than Oranges. The ratio $O:B=6:8$. There are $264$ Apples and Oranges. What is the ratio of Apples to Oranges?

There are $2$ more rectangles for Bananas than for Oranges. This means there are $\frac{48}{2}=24$ pieces of fruit per rectangle. There are $6$ rectangles for Oranges, so there are $6\times 24=144$ Oranges. Since there are $264$ Apples and Oranges, there must be $264-144=120$ Apples. The ratio of Apples to Oranges is $120:144$ which reduces to $5:6$.

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Associated Ratios and the Value of a Ratio

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Tens and Ones

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Representing Proportional Relationships by Equations

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Unit Rates with Fractions

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Conditions for a Unique Triangle

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What is a Ratio? (Using Ratio Language)

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Equivalent Ratios – Definition with Examples

What are equivalent ratios, what is the standard form of ratio, how to identify equivalent ratios, visual representation of equivalent ratios, solved examples on equivalent ratios, practice problems on equivalent ratios, frequently asked questions on equivalent ratios.

Two ratios that turn out to be the same in comparison are known as equivalent ratios. In order to check whether the given ratios are equivalent or not, we will have to simplify them or reduce them to their simplest form.

Example: Consider the ratios as 1:2, 2:4. 3:6. 

If you reduce 3:6 to its  simplest form, you get 1:2.

If you reduce 2:4 to its simplest form, you get 1:2.

Thus, these are equivalent ratios.

Equivalent ratios visual

Related Games

Are the Fractions Equivalent Game

What Is a Ratio?

Ratio is defined as the quantitative relation or comparison between two different quantities of the same kind and same unit. In mathematics, the symbol “:” is used to express ratio, where a ratio is anything that compares two quantities of the same kind. 

Ratio of a to $b = a : b = \frac{a}{b}$ 

The first quantity of the ratio is called antecedent, whereas the second quantity of the ratio is called consequent. In the above example, 1 is the antecedent and 3 is the consequent. 

Antecedent and consequent in a ratio

So, what are equivalent ratios? Let’s see an example.

Example: The ratio of the number of oranges to the number of apples in the fruit basket is 2:3 or $\frac{2}{3}$. Can you guess how many apples and oranges are there in the basket? 

Here’s the interesting part! Note that this does not mean that there are 2 oranges and 3 apples in the basket. It means that the number of oranges will be some multiple of 2 and the number of apples will be the multiple of 3 with respect to the same number. 

What are the possibilities then?

A visual example of equivalent ratios using oranges and apples

And so on, of course.

Here, the ratios 2:3, 4:6, 6:9 are equivalent ratios since they ultimately get reduced to the same value, 2:3.

Related Worksheets

Circle Equivalent Fractions Worksheet

Equivalent Ratios: Definition

Two ratios are said to be equivalent if they represent the same value when reduced to the simplest form.

Examples of equivalent ratios:

  • 1:2 , 2:4, 3:6
  • 3:7, 6:14, 9:21
  • 4:3, 8:6, 20:15

The standard form of the ratio can be given as a:b, where a is the antecedent and b is the consequent. 

When a ratio is expressed in the form of a fraction it can be written as a/b or $\frac{a}{b}$. Here, a is the numerator and b is the denominator.

We can use two methods. The first method is the cross multiplication method and the second method is the Highest Common Factor (HCF) method. Let us understand both of these methods with the help of examples.

Cross Multiplication Method

This method is convenient to use when the numbers involved are small. 

Check whether 12:18 and 10:15 are equivalent ratios or not using the cross multiplication method.

Step 1: Write the given ratios in the fractional form that is numerator by denominator form.

$12:18 = \frac{12}{18}$ and $10:15 = \frac{10}{15}$

Step 2: Cross multiply.

$12 \times 15 = 180$

$18 \times 10 = 180$

Step 3: If both products turn out to be equal, it would mean that the given ratios are equivalent ratios. 

Here, $12 \times 15 = 18 \times 10 = 180$.

Therefore, the given ratios (12:18 and 10:15) are equivalent ratios.

Let’s use the same example.

Step 1: We will find the HCF of the antecedent and consequent of both the given ratios. 

HCF $(12,18) = 6$

HCF $(10,15) = 5$

Step 2: Next, divide both the antecedent and consequent terms of both ratios by their respective HCF. So, we will get

$(12 \div 6) :(18 \div 6) = 2:3$

$(10 \div 5) :(15 \div 5)=2:3$

Step 3: If the reduced forms of both the given ratios are equal, it means that the given ratios are equivalent. 

Here, $12:18 = 10:15$.

How to Find Equivalent Ratios?

If one of the ratios can be expressed as a multiple of the other given ratio, then they are said to be equivalent ratios. Thus, creating equivalent ratios is simple.

As is the case for equivalent fractions, we can easily find an equivalent ratio by multiplying the given ratio (both antecedent and consequent) with the same natural number. 

Example: Find equivalent ratios of 1:4.

Finding equivalent ratios

Equivalent ratios of 1:4 are 

2:8  … multiply 1:4 by 2

3:12 … multiply 1:4 by 3

4:16 … multiply 1:4 by 4

Table of Equivalent: Ratios 

As we discussed earlier, we can easily find an equivalent ratio by multiplying the given ratio (both antecedent and consequent) with the same number. This number could be any natural number. We can find an infinite number of equivalent ratios for a given ratio. 

These equivalent ratios for a given ratio, when combined together and presented in a tabular format, gives us the required “Equivalent Ratios Table.” 

Let us make our own Equivalent Ratio Table when the given ratio is 5:3. All we have to do is to think of any natural number and then multiply both the terms of the given ratio with that number to obtain a unique equivalent ratio. 

$5:3 = (5 \times 2) :(3 \times 2) = 10:6$

$5:3 = (5 \times 3) : (3 \times 3) = 15:9$

$5:3 = (5 \times 4) : (3 \times 4) = 20:12$

$5:3 = (5 \times 5) : (3 \times 5) = 25:15$

Equivalent Ratio Table for the ratio 5:3 can thus be represented as,

Finding equivalent ratios of 5:3

When we represent the equivalent ratios visually, the shaded area (and thus the unshaded area) is the same for each ratio.

Example:  1: 3

     2 : 6

     4 : 12

Visual representation of equivalent ratios

  • The quantities that are to be compared using ratios should be of the same kind. 
  • The quantities that are to be compared using ratios should have the same unit.
  • Not only can we multiply the terms of the ratio to get an equivalent ratio, but we can also divide both the terms with the same natural number. 

In this article, we learned about equivalent ratios definition and meaning in mathematics, what ratios are, what the standard form of ratio is, and how to find equivalent ratios. We also understood how to make the equivalent ratios table for a given ratio.

1. Find one equivalent ratio of 3:22.

Solution: We will first write the given ratio in the form of a fraction.

$3 :22 \Rightarrow \frac{3}{22}$

Now we will multiply both the numerator and denominator by 2

$\frac{3 \times 2}{22 \times 2} = \frac{6}{44} = 6 : 44$

So, 8 :44 is an equivalent ratio of 3 :22.

2. Find any two equivalent ratios of 14 :21 .

Solution:  

We will first write the given ratio in the form of a fraction.

$14:21 \Rightarrow \frac{14}{21}$

Now we will multiply both the numerator and denominator by 3, to get the first equivalent fraction.

$= \frac{14}{21}$

$= \frac{14 \times 3}{21 \times 3}$

$= \frac{42}{63}= \frac{14}{21}$

Again, multiply and divide 1421 by another natural number, such as 5, as given below:

$= \frac{14 \times 5}{21 \times 5}$

$= \frac{70}{105} = \frac{14}{21}$

Hence, the two equivalent ratios of 14 :21 are 42 :63 and 70 :105.

3. Find any four equivalent ratios of 2:9. Present them with the help of the Equivalent Ratios Table.

Solution: 

$2:9 = (2 \times 2) : (9 \times 2) = 4:18$

$2:9 = (2 \times 3) : (9 \times 3) = 6:27$

$2:9 = (2 \times 4) : (9 \times 4) = 8:36$

$2:9 = (2 \times 5) : (9 \times 5) = 10:45$

Equivalent Ratio Table for ratio 2:9 can thus be represented as:

Equivalent ratios of 2:9

4. Are the ratios 18:10 and 63:35 equivalent?

Let’s use the HCF method.

HCF $(18,10) = 2$

HCF $(63:35) = 7$

$\frac{18 \div 2}{10 \div 2} = \frac{9}{5}$ and $\frac{63 \div 7}{35 \div 7} = \frac{9}{5}$

Both ratios in their reduced form are equal.

Thus, the ratios 18:10 and 63:35 are equivalent.

5. What will be the value of x if 2:5 is equivalent to 12:x ?

It is given that $2 :5 = 12:x$. 

In fraction form, we write $\frac{2}{5} = \frac{12}{x}$

By cross multiplying, we get

$2x = 12 \times 5$

Equivalent Ratios - Definition with Examples

Attend this quiz & Test your knowledge.

The ratios 5:3 and 30:x are equivalent. Find x.

Equivalent ratios have the same ______________., which of the following ratios are not equivalent with 5:10, find the odd one out..

What are fractions?

Fraction means a part of the whole.

What is proportion?

Proportion is defined as the equality between two ratios.

What is HCF?

The full form of HCF is the Highest Common Factor. It is the greatest factor that divides the given two or more numbers. For example, 4 is the HCF of 4 and 16.

What is LCM?

The full form of LCM is the least common multiple. For example, LCM of 16 and 24 will be $2 \times 2 \times 2 \times 2 \times 3 = 48$, where 48 is the smallest common multiple for numbers 16 and 24.

What is the unit of ratio?

Ratio is a number, so it has no unit.

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Equivalent Ratios

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not. For example, 1:2 and 2:4 are equivalent ratios.

In other words, we can say, two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number. This method is similar to the method of finding equivalent fractions .

Let us learn in this article how to find the equivalent ratios with examples. But before we proceed, first we need to understand about ratios and their quantities.

What is Ratio?

In Mathematics, a ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

A ratio is usually expressed with the symbol ‘:’. The comparison or simplified form of two quantities of the same kind is referred to as ratio.

Numerator and Denominator

We can also express the ratio as a fraction. If a:b, is a ratio, then a/b is its fraction form. Thus, we can easily compare two or more equivalent ratios in the form of equivalent fractions.

Standard Form of Ratio

The standard form of the ratio is given below:

How to Find Equivalent Ratios?

As we know, two or more ratios are equivalent if their simplified forms are the same. Thus, to find a ratio equivalent to another we have to multiply the two quantities, by the same number.

Another way to find equivalent ratios is to convert the given ratio into fraction form and then multiply the numerator and denominator by the same number to get equivalent fractions. Then again we can write the resulting fraction as an equivalent ratio.

Also, if we have to compare any two equivalent ratios, then we can divide the two quantities by the highest common factor and get the simplest form of ratio. Hence, we can compare them.

The examples of equivalent ratios are:

  • 2 : 4 :: 4 : 8
  • 10 : 20 :: 20 :40
  • 1 : 2 :: 2 : 4
  • 0.5 : 1 :: 2:4

Solved Examples

Q.1: Find the equivalent ratios of 8 : 18.

Solution: Let us first write the given ratio as a fraction.

8:18 ⇒ 8/18

Now multiply the numerator and denominator by 2

= (8 × 2)/(18 × 2)

Or we can write, the above fraction as a ratio;

So, 16 : 36 is an equivalent ratio of 8 : 18.

Q.2. Find any two equivalent ratios of 4 : 5.

Now multiply the numerator and denominator by 2, to get the first equivalent fraction.

= (4 × 2)/(5 × 2)

Again, multiply and divide ⅘ by another natural number, such as 3, as given below:

= (4 × 3)/(5 × 3)

4:5 = 12:15

Hence, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

Q.3. Compare the given ratios if they are equivalent or not.

14:21, 2:3, 1:1.5, 6:9

Solution: Let us write the given ratios as fractions.

14:21 ⇒ 14/21

1:1.5 ⇒ 1/1.5

Now, we have to find the common factors that divide the numerator and denominator evenly and hence we get the simplified form of fractions.

14/21 = ⅔ (HCF = 7)

⅔ = ⅔ (Already simplified form)

1/1.5 = 10/15 = ⅔ (HCF = 5)

6/9 = ⅔ (HCF = 3)

Thus, we can see all the above fractions are equivalent since their simplified forms are the same. Therefore, the given ratios are also equivalent to each other.

Q.4: A bag contains 4 red balls and 9 white balls. What is the ratio of red balls to the white balls?

Solution: Number of red balls = 4

Number of white balls = 9

Therefore, the ratio of red balls to the white balls is 4:9.

Frequently Asked Questions on Equivalent Ratios

What are equivalent ratios.

When the comparison of two different ratios is same, the such ratios are called equivalent ratios. For example, 1:2 and 3:6 are equivalent.

How can we find the equivalent ratio of 6:4?

To find the equivalent ratio of 6:4, convert the ratio into fraction and then multiply and divide the fraction by a common factor. 6:4 = 6/4 x (2/2) = 12/8 Thus, 12/8 is equivalent to 6:4.

Are 30 : 20 and 24 : 16 equivalent ratios?

30:20 and 24:16 are equivalent ratios, since the lowest form of both ratios is 3:2.

What is the simplest form of 14:21?

The simplest form of 14:21 is ⅔.

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Illustrative Mathematics Unit 6.2, Lesson 14: Solving Equivalent Ratio Problems

Learning Targets:

  • I can decide what information I need to know to be able to solve problems about situations happening at the same rate.
  • I can explain my reasoning using diagrams that I choose.

Related Pages Illustrative Math Grade 6

Lesson 14: Solving Equivalent Ratio Problems

How to solve equivalent ratio problems?

Illustrative Math Unit 6.2, Lesson 14 (printable worksheets)

Lesson 14 Summary

The following diagram shows how to solve equivalent ratio problems.

Equivalent Ratio Problems

14.1 What Do You Want to Know?

Here is a problem: A red car and a blue car enter the highway at the same time and travel at a constant speed. How far apart are they after 4 hours? What information would you need to solve the problem?

Scroll down the page for the solution to the number of cats and dogs.

14.2 - Info Gap: Hot Chocolate and Potatoes

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If your teacher gives you the problem card:

  • Read your card silently and think about what you need to know to be able to answer the questions.
  • Ask your partner for the specific information that you need.
  • Explain how you are using the information to solve the problem.
  • Solve the problem and show your reasoning to your partner.

If your teacher gives you the data card:

  • Read your card silently.
  • Ask your partner “What specific information do you need?” and wait for them to ask for information. If your partner asks for information that is not on the card, do not do the calculations for them. Tell them you don’t have that information.
  • Have them explain “Why do you need that information?” before telling them the information.
  • After your partner solves the problem, ask them to explain their reasoning, even if you understand what they have done. Both you and your partner should record a solution to each problem.

14.3 - Comparing Reading Rates

  • Lin read the first 54 pages from a 270-page book in the last 3 days.
  • Diego read the first 100 pages from a 320-page book in the last 4 days.
  • Elena read the first 160 pages from a 480-page book in the last 5 days. If they continue to read every day at these rates, who will finish first, second, and third? Explain or show your reasoning.

Are you ready for more?

cats and dogs

Lesson 14 Practice Problems

  • A chef is making pickles. He needs 15 gallons of vinegar. The store sells 2 gallons of vinegar for $3.00 and allows customers to buy any amount of vinegar. Decide whether each of the following ratios correctly represents the price of vinegar. a. 4 gallons to $3.00 b. 1 gallon to $1.50 c. 30 gallons to $45.00 d. $2.00 to 30 gallons e. $1.00 to 2/3 gallon
  • A caterer needs to buy 21 pounds of pasta to cater a wedding. At a local store, 8 pounds of pasta cost $12. How much will the caterer pay for the pasta there? a. Write a ratio for the given information about the cost of pasta. b. Would it be more helpful to write an equivalent ratio with 1 pound of pasta as one of the numbers, or with $1 as one of the numbers? Explain your reasoning, and then write that equivalent ratio. c. Find the answer and explain or show your reasoning.
  • Lin is reading a 47-page book. She read the first 20 pages in 35 minutes. a. If she continues to read at the same rate, will she be able to complete this book in under 1 hour? b. If so, how much time will she have left? If not, how much more time is needed? Explain or show your reasoning.
  • Diego can type 140 words in 4 minutes. a. At this rate, how long will it take him to type 385 words? b. How many words can he type in 15 minutes? If you get stuck, consider creating a table.
  • A train that travels 30 miles in 1/2 hour at a constant speed is going faster than a train that travels 20 miles in 1/2 hour at a constant speed. Explain or show why.

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Equivalent Ratio Worksheets

Equivalent ratio worksheets are used to give students a good understanding of how to deal with ratio and proportion problems. The questions in these worksheets range from simple interpretation sums to word problems that require analysis.

Benefits of Equivalent Ratio Worksheets

Equivalent ratios are used very frequently in daily life. It is good for young minds to have a clear foundation of this concept. By solving the problems in equivalent ratio worksheets, children can increase their speed and accuracy. Questions are structured in a way to improve a student's logical and analytical abilities. The worksheets are provided with answer keys with step-by-step solutions to help students in case they get stuck while solving a question.

Read More :- Topic-wise Math Worksheets

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Ratio problem solving

Here you will learn about ratio problem solving, including how to set up and solve problems. You will also look at real life ratio word problems.

Students will first learn about ratio problem solving as part of ratio and proportion in 6 th grade and 7 th grade.

What is ratio problem solving?

Ratio problem solving is a collection of ratio and proportion word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem.

A ratio is a relationship between two or more quantities. They are usually written in the form a : b where a and b are two quantities. When problem solving with a ratio, the key facts that you need to know are:

  • What is the ratio involved?
  • What order are the quantities in the ratio?
  • What is the total amount / what is the part of the total amount known?
  • What are you trying to calculate ?

As with all problem solving, there is not one unique method to solve a problem. However, this does not mean that there aren’t similarities between different problems that you can use to help you find an answer.

The key to any problem solving is being able to draw from prior knowledge and use the correct piece of information to allow you to get to the next step and then the solution.

Let’s look at a couple of methods you can use when given certain pieces of information.

When solving ratio word problems, it is very important that you are able to use ratios. This includes being able to use ratio notation.

For example, Charlie and David share some sweets in the ratio of 3 : 5. This means that for every 3 sweets Charlie gets, David receives 5 sweets.

Charlie and David share 40 sweets, how many sweets do they each get?

You use the ratio to divide 40 sweets into 8 equal parts.

40 \div 8=5

Then you multiply each part of the ratio by 5.

3\times 5:5\times 5=15 : 25

This means that Charlie will get 15 sweets and David will get 25 sweets.

There can be ratio word problems involving different operations and types of numbers.

Here are some examples of different types of ratio word problems:

What is ratio problem solving?

Common Core State Standards

How does this relate to 6 th grade math?

  • Grade 6 – Ratios and Proportional Relationships (6.RP.A.3) Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • Grade 7 – Ratio and Proportional Relationships (7.RP.A.2) Recognize and represent proportional relationships between quantities.

How to do ratio problem solving

In order to solve problems including ratios:

Identify key information within the question.

Know what you are trying to calculate.

Use prior knowledge to structure a solution.

[FREE] Ratio Check for Understanding Quiz (Grade 6 and 7)

[FREE] Ratio Check for Understanding Quiz (Grade 6 and 7)

Use this quiz to check your 6th and 7th grade students’ understanding of ratios. 10+ questions with answers covering a range of 6th and 7th grade ratio topics to identify areas of strength and support!

Ratio problem solving examples

Example 1: part:part ratio.

Within a school, the total number of students who have school lunches to packed lunches is 5 : 7. If 465 students have a school lunch, how many students have a packed lunch?

Within a school, the number of students who have school lunches to packed lunches is \textbf{5 : 7} . If \textbf{465} students have a school lunch, how many students have a packed lunch?

Here you can see that the ratio is 5 : 7, where the first part of the ratio represents school lunches (S) and the second part of the ratio represents packed lunches (P).

You could write this as:

Ratio Problem Solving Image 2 US

Where the letter above each part of the ratio links to the question.

You know that 465 students have school lunch.

2 Know what you are trying to calculate.

From the question, you need to calculate the number of students that have a packed lunch, so you can now write a ratio below the ratio 5 : 7 that shows that you have 465 students who have school lunches, and p students who have a packed lunch.

Ratio Problem Solving Image 3 US

You need to find the value of p.

3 Use prior knowledge to structure a solution.

You are looking for an equivalent ratio to 5 : 7. So you need to calculate the multiplier.

You do this by dividing the known values on the same side of the ratio by each other.

465\div 5 = 93

This means to create an equivalent ratio, you can multiply both sides by 93.

Ratio Problem Solving Image 4 US

So the value of p is equal to 7 \times 93=651.

There are 651 students that have a packed lunch.

Example 2: unit conversions

The table below shows the currency conversions on one day.

Use the table above to convert £520 \; (GBP) to Euros € \; (EUR).

Use the table above to convert \bf{£520} \textbf{ (GBP)} to Euros \textbf{€ } \textbf{(EUR)}.

The two values in the table that are important are \text{GBP} and EUR. Writing this as a ratio, you can state,

Ratio Problem Solving Image 7 US

You know that you have £520.

You need to convert GBP to EUR and so you are looking for an equivalent ratio with GBP=£520 and EUR=E.

Ratio Problem Solving Image 8 US

To get from 1 to 520, you multiply by 520 and so to calculate the number of Euros for £520, you need to multiply 1.17 by 520.

1.17 \times 520=608.4

So £520=€608.40.

Example 3: writing a ratio 1 : n

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the 500 \, ml of concentrated plant food must be diluted into 2 \, l of water. Express the ratio of plant food to water, respectively, in the ratio 1 : n.

Liquid plant food is sold in concentrated bottles. The instructions on the bottle state that the \bf{500 \, ml} of concentrated plant food must be diluted into \bf{2 \, l} of water. Express the ratio of plant food to water respectively as a ratio in the form 1 : n.

Using the information in the question, you can now state the ratio of plant food to water as 500 \, ml : 2 \, l. As you can convert liters into milliliters, you could convert 2 \, l into milliliters by multiplying it by 1000.

2 \, l=2000 \, ml

So you can also express the ratio as 500 : 2000 which will help you in later steps.

You want to simplify the ratio 500 : 2000 into the form 1:n.

You need to find an equivalent ratio where the first part of the ratio is equal to 1. You can only do this by dividing both parts of the ratio by 500 (as 500 \div 500=1 ).

Ratio Problem Solving Image 9 US

So the ratio of plant food to water in the form 1 : n is 1 : 4.

Example 4: forming and solving an equation

Three siblings, Josh, Kieran and Luke, receive an allowance each week proportional to their age. Kieran is 3 years older than Josh. Luke is twice Josh’s age. If Josh receives \$ 8 allowance, how much money do the three siblings receive in total?

Three siblings, Josh, Kieran and Luke, receive an allowance each week proportional to their ages. Kieran is \bf{3} years older than Josh. Luke is twice Josh’s age. If Luke receives \bf{\$ 8} allowance, how much money do the three siblings receive in total?

You can represent the ages of the three siblings as a ratio. Taking Josh as x years old, Kieran would therefore be x+3 years old, and Luke would be 2x years old. As a ratio, you have:

Ratio Problem Solving Image 10 US

You also know that Luke receives \$ 8.

You want to calculate the total amount of allowance for the three siblings.

You need to find the value of x first. As Luke receives \$ 8, you can state the equation 2x=8 and so x=4.

Now you know the value of x, you can substitute this value into the other parts of the ratio to obtain how much money the siblings each receive.

Ratio Problem Solving Image 11 US

The total amount of allowance is therefore 4+7+8=\$ 19.

Example 5: simplifying ratios

Below is a bar chart showing the results for the colors of counters in a bag.

Ratio Problem Solving Image 12 US

Express this data as a ratio in its simplest form.

From the bar chart, you can read the frequencies to create the ratio.

Ratio Problem Solving Image 13 US

You need to simplify this ratio.

To simplify a ratio, you need to find the highest common factor of all the parts of the ratio. By listing the factors of each number, you can quickly see that the highest common factor is 2.

\begin{aligned} & 12 = 1, {\color{red}2}, 3, 4, 6, 12 \\\\ & 16 = 1, {\color{red}2}, 4, 8, 16 \\\\ & 10 = 1, {\color{red}2}, 5, 10 \end{aligned}

HCF(12,16,10) = 2

Dividing all the parts of the ratio by 2, you get

Ratio Problem Solving Image 14 US

Our solution is 6 : 8 : 5.

Example 6: combining two ratios

Glass is made from silica, lime and soda. The ratio of silica to lime is 15 : 2. The ratio of silica to soda is 5 : 1. State the ratio of silica:lime:soda.

Glass is made from silica, lime and soda. The ratio of silica to lime is \bf{15 : 2}. The ratio of silica to soda is \bf{5 : 1}. State the ratio of silica:lime:soda.

You know the two ratios

Ratio Problem Solving Image 15 US

You are trying to find the ratio of all 3 components: silica, lime and soda.

Using equivalent ratios you can say that the ratio of Silica:Soda is equivalent to 15 : 3 by multiplying the ratio by 3.

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You now have the same amount of silica in both ratios and so you can now combine them to get the ratio 15 : 2 : 3.

Ratio Problem Solving Image 17 US

Example 7: using bar modeling

India and Beau share some popcorn in the ratio of 5 : 2. If India has 75 \, g more popcorn than Beau, what was the original quantity?

India and Beau share some popcorn in the ratio of \bf{5 : 2} . If India has \bf{75 \, g} more popcorn than Beau, what was the original quantity?

You know that the initial ratio is 5 : 2 and that India has three more parts than Beau.

You want to find the original quantity.

Drawing a bar model of this problem, you have:

Ratio Problem Solving Image 18 US

Where India has 5 equal shares, and Beau has 2 equal shares.

Each share is the same value and so if you can find out this value, you can then find the total quantity.

From the question, India’s share is 75 \, g more than Beau’s share so you can write this on the bar model.

Ratio Problem Solving Image 19 US

You can find the value of one share by working out 75 \div 3=25 \, g.

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You can fill in each share to be 25 \, g.

Ratio Problem Solving Image 21 US

Adding up each share, you get

India=5 \times 25=125 \, g

Beau=2 \times 25=50 \, g

The total amount of popcorn was 125+50=175 \, g.

Teaching tips for ratio problem solving

  • Continue to remind students that when solving ratio word problems, it’s important to identify the quantities being compared and express the ratio in its simplest form.
  • Create practice problems for students using the information in your classroom. For example, ask students to find the ratio of boys to the ratio of girls using the total number of students in your classroom, then the school.
  • To find more practice questions, utilize educational websites and apps instead of worksheets. Some of these may also provide tutorials for struggling students. These can also be helpful for test prep as they are more engaging for students.
  • Use a variety of numbers in your ratio word problems – whole numbers, fractions, decimals, and mixed numbers – to give students a variety of practice.
  • Provide students with a step-by-step process for problem solving, like the one shown above, that can be applied to every ratio word problem.

Easy mistakes to make

  • Mixing units Make sure that all the units in the ratio are the same. For example, in example 6, all the units in the ratio were in milliliters. You did not mix ml and l in the ratio.
  • Writing ratios in the wrong order For example, the number of dogs to cats is given as the ratio 12 : 13 but the solution is written as 13 : 12.

Ratio Problem Solving Image 22 US

  • Counting the number of parts in the ratio, not the total number of shares For example, the ratio 5 : 4 has 9 shares, and 2 parts. This is because the ratio contains 2 numbers but the sum of these parts (the number of shares) is 5+4=9. You need to find the value per share, so you need to use the 9 shares in your next line of working.
  • Ratios of the form \bf{1 : \textbf{n}} The assumption can be incorrectly made that n must be greater than 1, but n can be any number, including a decimal.

Related ratio lessons

  • Unit rate math
  • Simplifying ratios
  • Ratio to fraction
  • How to calculate exchange rates
  • Ratio to percent
  • How to write a ratio

Practice ratio problem solving questions

1. An online shop sells board games and computer games. The ratio of board games to the total number of games sold in one month is 3 : 8. What is the ratio of board games to computer games?

GCSE Quiz True

8-3=5 computer games sold for every 3 board games.

2. The ratio of prime numbers to non-prime numbers from 1-200 is 45 : 155. Express this as a ratio in the form 1 : n.

You need to simplify the ratio so that the first number is 1. That means you need to divide each number in the ratio by 45.

45 \div 45=1

155\div{45}=3\cfrac{4}{9}

3. During one month, the weather was recorded into 3 categories: sunshine, cloud and rain. The ratio of sunshine to cloud was 2 : 3 and the ratio of cloud to rain was 9 : 11. State the ratio that compares sunshine:cloud:rain for the month.

3 \times S : C=6 : 9

4. The angles in a triangle are written as the ratio x : 2x : 3x. Calculate the size of each angle.

You should know that the 3 angles in a triangle always equal 180^{\circ}.

\begin{aligned} & x+2 x+3 x=180 \\\\ & 6 x=180 \\\\ & x=30^{\circ} \\\\ & 2 x=60^{\circ} \\\\ & 3 x=90^{\circ} \end{aligned}

5. A clothing company has a sale on tops, dresses and shoes. \cfrac{1}{3} of sales were for tops, \cfrac{1}{5} of sales were for dresses, and the rest were for shoes. Write a ratio of tops to dresses to shoes sold in its simplest form.

\cfrac{1}{3}+\cfrac{1}{5}=\cfrac{5+3}{15}=\cfrac{8}{15}

1-\cfrac{8}{15}=\cfrac{7}{15}

6. The volume of gas is directly proportional to the temperature (in degrees Kelvin). A balloon contains 2.75 \, l of gas and has a temperature of 18^{\circ}K. What is the volume of gas if the temperature increases to 45^{\circ}K?

The given ratio in the word problem is 2. 75 \mathrm{~L}: 18^{\circ} \mathrm{K}

Divide 45 by 18 to see the relationship between the two temperatures.

45 \div 18=2.5

45 is 2.5 times greater than 18. So we multiply 2.75 by 2.5 to get the amount of gas.

2.75 \times 2.5=6.875 \mathrm{~l}

Ratio problem solving FAQs

A ratio is a comparison of two or more quantities. It shows how much one quantity is related to another.

A recipe calls for 2 cups of flour and 1 cup of sugar. What is the ratio of flour to sugar? (2 : 1)

In middle school ( 7 th grade and 8 th grade), students transition from understanding basic ratios to working with more complex and real-life applications of ratios and proportions. They gain a deeper understanding of how ratios relate to different mathematical concepts, making them more prepared for higher-level math topics in high school.

The next lessons are

  • Properties of equality
  • Multiplication and division

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Equivalent Ratio Worksheets

Created: February 13, 2024

Last updated: February 13, 2024

If two ratios are identical when compared, they are equivalent. They may be compared to determine whether two or more ratios are comparable. A typical example of equivalent ratios are 2:3 and 4:6. When simplified, equivalent ratios still indicate the same value. A ratio’s equivalent is the same as a fraction’s equivalent. No matter how dissimilar two ratios seem, if their values are equal, they are identical. Keep reading to learn why equivalent ratio worksheets are essential to every child’s learning process.

How to Use Equivalent Ratio Worksheets

Equivalent ratio worksheets are a perfect educational choice for kids as they break the complex parts of the concept into units. These equivalent ratio tables worksheets introduce kids to the three distinct rules for expressing equivalent ratios.

  • Convert every ratio to a fraction. Put the two fractions side by side.
  • If the numerator of both fractions contains numbers, get the second by multiplying or dividing the first numerator by some number. Find the number that may be multiplied or divided by the first denominator to produce the second denominator if both fractions include numbers written in the denominator.
  • Using the same number from Step 2, multiply or divide the numerator or denominator.

Math for Kids

Why Should I Use an Equivalent Ratio Worksheet?

Ratio is a fundamental concept with numerous practical and sophisticated applications in mathematics; hence, learning it is crucial. Students develop their analytical and problem-solving abilities using equivalent ratio worksheets with answers as they learn about ratios and how to use them to connect various values.

Students with a firm grasp of equivalent ratios can better use proportional reasoning, understand equivalent fractions, manipulate percentages, and draw connections to various mathematical topics, including geometry, statistics, and functions.

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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VIDEO

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COMMENTS

  1. Equivalent ratio word problems (practice)

    Solving ratio problems with tables Ratio tables Equivalent ratios Equivalent ratios: recipe Equivalent ratios Equivalent ratio word problems Understanding equivalent ratios Interpreting unequal ratios Equivalent ratio word problems Google Classroom A fruit basket is filled with 8 bananas, 3 oranges, 5 apples, and 6 kiwis. Complete the ratio.

  2. Ratios and proportions

    part: whole = part: sum of all parts To write a ratio: Determine whether the ratio is part to part or part to whole. Calculate the parts and the whole if needed. Plug values into the ratio. Simplify the ratio if needed. Integer-to-integer ratios are preferred. [Example: Part to whole] [Examples: Simplifying ratios]

  3. 12.4: Solving Equivalent Ratio Problems

    Basic Math (Grade 6) 2: Introducing Ratios

  4. PDF Equivalent Ratios and Tables

    Sample Problem 1: Which among the following is an equivalent ratio of 3:5? Give all possible answers. a. d. 12:20 b. 9:10 e. 45:75 c. 6:10 SCALING DOWN A RATIO We scale down a ratio by a scale factor, which means dividing each term of the ratio by a given scale factor. Example: Give 3 equivalent ratios for 24:48. Sample Problem 2:

  5. Equivalent Ratios

    4.7K Share 525K views 3 years ago Ratios, Unit Rates, & Proportions Welcome to Equivalent Ratios with Mr. J! Need help with how to find equivalent ratios? You're in the right place! ...more...

  6. 12.2: Navigating a Table of Equivalent Ratios

    Here are tables showing two different approaches to solving this problem. Both of these approaches are correct. However, one approach is more efficient. ... For each pair, explain why they are equivalent ratios or draw a representation that shows why they are equivalent ratios. \(600:450\) and \(60:45\) \(60:45\) and \(4:3\)

  7. Word Problems Involving Equivalent Ratio

    For example, the ratio 2:4 is equivalent to the ratio 4:8 because in both cases, the relationship between the numbers is the same (1:2). Step-by-step guide to solving equivalent ratios word problems. To solve the equivalent ratio's word problems, follow these steps: Step 1: Find the ratio given in the word problem.

  8. Solving Problems by Finding Equivalent Ratios

    Videos and solutions to help Grade 6 students learn how to solve problems by finding equivalent ratios. New York State Common Core Math Grade 6, Module 1, Lesson 5. Grade 6, Module 1, Lesson 5. Lesson 5 Student Outcomes. Students use tape diagrams to find an equivalent ratio when given the part-to-part ratio and the total of those two quantities.

  9. Equivalent Ratios

    Step 1: Write both the ratios in fractional form ( numerator over denominator ). Step 2: Do the cross multiplication. Multiply 10 by 24 and 8 by 30. Step 3: If both products are equal, it means that they are equivalent ratios. Here 10 × 24 = 8 × 30 = 240. Therefore, they are equivalent ratios.

  10. Solving Problems with Equivalent Ratios

    There are a few steps we should summarize about solving problems with equivalent ratios. First, create a tape diagram with given ratio. Tape diagrams help us visualize and solve ratios problems. Tape diagrams show the rectangles, or units, in a ratio and help us figure out their numeric value. If you know the overall total, like the 24 hours in ...

  11. Equivalent ratio word problems (video)

    Equivalent ratio word problems Simplify a ratio from a tape diagram Equivalent ratios with equal groups Ratios and double number lines Create double number lines Ratios with double number lines Relate double number lines and ratio tables Math > 6th grade > Ratios > Visualize equivalent ratios

  12. Equivalent Ratios

    Ratio of a to b = a: b = a b The first quantity of the ratio is called antecedent, whereas the second quantity of the ratio is called consequent. In the above example, 1 is the antecedent and 3 is the consequent. So, what are equivalent ratios? Let's see an example.

  13. Equivalent Ratios (How to Find Equivalent Ratios)

    Numerator and Denominator We can also express the ratio as a fraction. If a:b, is a ratio, then a/b is its fraction form. Thus, we can easily compare two or more equivalent ratios in the form of equivalent fractions. Standard Form of Ratio The standard form of the ratio is given below: Ratio = a : b = Numerator : Denominator Or

  14. How to Solve Word Problems with Equivalent Ratios

    How to Solve Word Problems with Equivalent Ratios When a word problem expresses a ratio, follow these steps to find an equivalent ratio that solves the problem: Step 1: Identify the...

  15. Solving Equivalent Ratio Problems

    a. Write a ratio for the given information about the cost of pasta. b. Would it be more helpful to write an equivalent ratio with 1 pound of pasta as one of the numbers, or with $1 as one of the numbers? Explain your reasoning, and then write that equivalent ratio. c. Find the answer and explain or show your reasoning.

  16. Download Free Equivalent Ratio Worksheet PDFs

    By solving the problems in equivalent ratio worksheets, children can increase their speed and accuracy. Questions are structured in a way to improve a student's logical and analytical abilities. The worksheets are provided with answer keys with step-by-step solutions to help students in case they get stuck while solving a question.

  17. Equivalent ratios (practice)

    Solving ratio problems with tables Ratio tables Equivalent ratios Equivalent ratios: recipe Equivalent ratios Equivalent ratio word problems Understanding equivalent ratios Equivalent ratios in the real world Interpreting unequal ratios Understand equivalent ratios in the real world Equivalent ratios Google Classroom

  18. Solving Word Problems with Equivalent Ratios

    30. Jose fills 2 liters juice in 7 cups equally. How many cups are needed to fill 6 liters of juice equally? Answers: 21. 18. 25. 12. Practice Solving Word Problems with Equivalent Ratios with ...

  19. Ratio Problem Solving

    Ratio problem solving is a collection of word problems that link together aspects of ratio and proportion into more real life questions. This requires you to be able to take key information from a question and use your knowledge of ratios (and other areas of the curriculum) to solve the problem. ... Units and conversions are usually equivalent ...

  20. Ratio Problem Solving

    When problem solving with a ratio, the key facts that you need to know are: What is the ratio involved? What order are the quantities in the ratio? What is the total amount / what is the part of the total amount known? What are you trying to calculate? As with all problem solving, there is not one unique method to solve a problem.

  21. Solving ratio problems with tables (video)

    Solving ratio problems with tables Google Classroom About Transcript Equivalent ratios have the same relationship between their numerators and denominators. To find missing values in tables, maintain the same ratio. Comparing fractions is easier with common numerators or denominators.

  22. Free Equivalent Ratio Worksheets For Your Kids [PDFs] Brighterly.com

    If two ratios are identical when compared, they are equivalent. They may be compared to determine whether two or more ratios are comparable. A typical example of equivalent ratios are 2:3 and 4:6. When simplified, equivalent ratios still indicate the same value. A ratio's equivalent is the same as a fraction's equivalent.

  23. Ratio tables (practice)

    6th grade Course: 6th grade > Unit 1 Lesson 3: Equivalent ratios Ratio tables Solving ratio problems with tables Ratio tables Equivalent ratios Equivalent ratios: recipe Equivalent ratios Equivalent ratio word problems Understanding equivalent ratios Equivalent ratios in the real world Interpreting unequal ratios