Equivalent Ratios Worksheet, Definition, Examples

Here’s how to find Equivalent Ratios

Equivalent ratios are a fundamental concept in mathematics that allow us to compare two or more quantities. They are used to identify the relationship between different quantities and are often used in real-world applications such as cooking, engineering, and finance. Ratios can be expressed in different ways, but equivalent ratios are ratios that have the same value.

One way to identify equivalent ratios is to determine if you can multiply or divide the corresponding parts of the ratio by the same amount. For example, the ratios 2:4 and 4:8 are equivalent because you can multiply the first ratio by 2 to get the second ratio. Equivalent ratios can be simplified by dividing the numerator and denominator by their greatest common factor. Simplifying ratios can help make them easier to work with and understand.

Understanding equivalent ratios is an important skill in mathematics that can help students solve problems involving proportions, rates, and percentages. In this article, we will explore what equivalent ratios are, how to find them, and some real-world applications. We will also provide examples and a free equivalent ratios worksheet to help you practice your skills.

What Are Ratios?

Ratios are a way of comparing two quantities or numbers. They are expressed as a fraction or a colon. For example, if there are 3 boys and 5 girls in a class, the ratio of boys to girls is 3:5 or 3/5. Ratios can be used to compare any kind of quantity, such as weight, height, or time.

Ratios can be multiplied or divided by the same number to obtain equivalent ratios. For example, if the ratio of boys to girls is 3:5, then multiplying both sides by 2 gives the equivalent ratio of 6:10 or 3/5. This is because both ratios represent the same relationship between the numbers, just on a different scale.

Ratios are made up of two parts: the numerator and the denominator. The numerator represents the number of parts of the first quantity, while the denominator represents the number of parts of the second quantity. For example, in the ratio 3:5, the numerator is 3 and the denominator is 5.

Ratios can also be expressed as fractions. The numerator of the ratio becomes the numerator of the fraction, while the denominator becomes the denominator of the fraction. For example, the ratio 3:5 can be expressed as the fraction 3/5.

Ratios are used to compare quantities in a variety of contexts, from cooking to finance to sports. They are an important tool for understanding the relationship between different numbers and quantities.

Equivalent Ratios Definition

Equivalent ratios are two or more ratios that have the same value when simplified. In other words, ratios are equivalent if they express the same relationship between two quantities. This means that if we multiply or divide both parts of a ratio by the same number, we will get an equivalent ratio.

For example, the ratios 2:3 and 4:6 are equivalent because we can divide both sides of the second ratio by 2 to get the first ratio. Similarly, the ratios 1:2 and 3:6 are equivalent because we can multiply both sides of the first ratio by 3 to get the second ratio.

To simplify ratios, we need to find the highest common factor (HCF) of the two numbers in the ratio. The HCF is the largest number that divides both numbers without leaving a remainder. We can then divide both parts of the ratio by the HCF to get the simplest form of the ratio.

There are several methods to simplify ratios. One way is to list the factors of the two numbers and find the highest common factor. Another way is to use a ratio calculator or a ratio simplifier tool online.

Equivalent ratios are used in many different types of problems, such as proportion problems, missing value problems, and others. For example, if we know that two ratios are equivalent, we can use this information to find a missing value in one of the ratios.

It is important to note that ratios can be expressed as whole numbers, decimals, or fractions. When simplifying ratios with decimal values, we need to convert them to fractions first. We can do this by placing the decimal over a power of 10 and simplifying the resulting fraction.

Overall, understanding equivalent ratios is an essential concept in mathematics. It allows us to compare and relate quantities in a simple and meaningful way.

Solving Equivalent Ratios Examples

Equivalent ratios are ratios that have the same value. For example, 2:3 and 4:6 are equivalent ratios because they both represent the same quantity. In other words, if you multiply or divide both terms of one ratio by the same number, you will get the other ratio. Here are some examples of equivalent ratios:

• 1:2 and 2:4 are equivalent ratios because you can multiply the terms of the first ratio by 2 to get the second ratio.
• 3:4 and 6:8 are equivalent ratios because you can multiply the terms of the first ratio by 2 to get the second ratio.
• 5:7 and 10:14 are equivalent ratios because you can multiply the terms of the first ratio by 2 to get the second ratio.

Equivalent ratios can also be expressed as fractions. For example, 2:3 can be written as 2/3, and 4:6 can be written as 4/6 or simplified to 2/3. Here are some more examples:

• 3:5 is equivalent to 6/10 or 9/15 or 12/20.
• 4:9 is equivalent to 8/18 or 12/27 or 16/36.

Equivalent Ratios Non Examples

It’s important to note that not all ratios are equivalent. Here are some examples of non-equivalent ratios:

• 2:3 and 3:4 are not equivalent ratios because you can’t multiply or divide one ratio by the same number to get the other ratio.
• 5:6 and 7:8 are not equivalent ratios because you can’t simplify one ratio to get the other ratio.
• 1:2 and 3:4 are not equivalent ratios because you can’t multiply or divide one ratio by the same number to get the other ratio.

In conclusion, equivalent ratios are ratios that have the same value and can be expressed as fractions. Non-equivalent ratios are ratios that can’t be simplified or multiplied by the same number to get the other ratio.

How to Find Equivalent Ratios with 3 Simple Ways

Finding equivalent ratios is an important concept in mathematics that involves determining ratios that represent the same quantity. There are several methods to find equivalent ratios, including multiplying or dividing by the same number, reducing fractions to their simplest form, and using the cross multiplication method.

Multiplying or Dividing by the Same Number

One way to find equivalent ratios is to multiply or divide the corresponding parts of the ratio by the same number. For example, if the ratio is 2:3, multiplying both parts by 2 gives the equivalent ratio of 4:6. Similarly, dividing both parts by 3 gives the equivalent ratio of 2/3:1.

Reducing Fractions to Their Simplest Form

Another way to find equivalent ratios is to convert the given ratio into fraction form and then reduce the fraction to its simplest form. To do this, find the greatest common factor (GCF) of the numerator and denominator and divide both by it. For example, the ratio 8:12 can be converted to the fraction 8/12, which can be reduced to 2/3 by dividing both parts by 4.

Using the Cross Multiplication Method

The cross multiplication method is a quick and easy way to find equivalent ratios. To use this method, multiply the numerator of one ratio by the denominator of the other ratio and set them equal to each other. Then, solve for the missing value. For example, to find the equivalent ratio of 3:4 to 6:8, cross-multiply to get 3 x 8 = 4 x 6. Solving for the missing value gives the equivalent ratio of 9:12.

In conclusion, there are several methods to find equivalent ratios, including multiplying or dividing by the same number, reducing fractions to their simplest form, and using the cross multiplication method. By understanding these methods, learners can solve a variety of problems involving ratios and proportions with ease.

How to Solve Equivalent Ratios Practice Problems

Applications of Equivalent Ratios

Real-Life Examples

Equivalent ratios are used in a variety of real-life situations, from cooking and baking to construction and engineering. In cooking, equivalent ratios are used to scale recipes up or down depending on the number of servings needed. For example, if a recipe calls for 2 cups of flour and serves 4 people, an equivalent ratio would be 1 cup of flour for 2 people.

In construction and engineering, equivalent ratios are used to determine the correct proportions of materials needed for a project. For example, if a building requires 10 bags of cement for every 20 bags of sand, an equivalent ratio would be 5 bags of cement for every 10 bags of sand.

Miles Per Hour

Equivalent ratios are also commonly used to calculate speed, such as miles per hour. Miles per hour is a unit of measure used to express the speed of an object in miles traveled per hour. For example, if a car travels 60 miles in 1 hour, its speed would be 60 miles per hour.

To calculate miles per hour, equivalent ratios can be used to convert between miles and hours. For example, if a car travels 120 miles in 2 hours, an equivalent ratio would be 60 miles per hour. This is because 120 miles divided by 2 hours equals 60 miles per hour.

Equivalent ratios can also be used to convert between different units of measure. For example, if a car travels 60 miles per hour, an equivalent ratio would be 96.56 kilometers per hour. This is because 1 mile is equal to 1.609 kilometers.

Reduced Form

Equivalent ratios can also be expressed in reduced form, which means that the ratio is simplified to its lowest terms. To reduce a ratio, both the numerator and denominator are divided by their greatest common factor. For example, the ratio 6:9 can be reduced to 2:3 by dividing both the numerator and denominator by 3.

Reducing ratios to their lowest terms makes them easier to work with and compare. It also helps to avoid errors when calculating equivalent ratios.

Types of Equivalent Ratios Worksheets

Equivalent ratios worksheet are an essential tool for students to practice their understanding of ratios. These worksheets help students learn how to identify if two ratios are equivalent and solve for unknown variables. They also help students fill in a given table for a given ratio.

Equivalent ratios worksheet are appropriate for students in 5th, 6th, and 7th grades. These worksheets are designed to help students understand the concept of ratios and how to apply them in real-world situations. They are also a great way to reinforce the concept of equivalent ratios, which is a critical aspect of understanding ratios.

One of the most common types of equivalent ratios worksheet is the part-to-part ratio worksheet. These worksheets require students to count how many of one thing there is as compared to another and express it as a ratio. These worksheets are perfect for students who are just starting to learn about ratios and are looking for a simple and straightforward way to practice.

Another type of equivalent ratio worksheet is the finding equivalent ratios worksheet. These worksheets require students to find an equivalent ratio given one number or select equivalent ratios from a set of ratios. These worksheets are perfect for students who are looking to challenge themselves and apply their knowledge of ratios in more complex situations.

Overall, equivalent ratios worksheet are an excellent tool for students to practice their understanding of ratios. They are designed to help students understand the concept of equivalent ratios and how to apply them in real-world situations. With the help of these worksheets, students can develop a strong foundation in ratios that will serve them well throughout their academic and professional careers.

FAQ about Equivalent Ratios

How do I find equivalent ratios?

To find equivalent ratios, you need to divide or multiply both the antecedent and consequent of the given ratio by the same number. This is because equivalent ratios have the same value, but different numbers. For example, if you have the ratio 2:3, you can multiply both the antecedent and consequent by 2 to get 4:6, which is an equivalent ratio.

How do you create equivalent ratios?

You can create equivalent ratios by multiplying or dividing both the antecedent and consequent of a given ratio by the same number. This will give you a new ratio that has the same value as the original ratio but with different numbers. For example, if you have the ratio 3:4, you can multiply both the antecedent and consequent by 2 to get 6:8, which is an equivalent ratio.

What are some examples of equivalent ratios with solutions?

Some examples of equivalent ratios with solutions include:

• 2:3 and 4:6 (multiply both by 2)
• 5:7 and 10:14 (multiply both by 2)
• 4:9 and 8:18 (multiply both by 2)
• 3:8 and 6:16 (multiply both by 2)

What is the equivalent ratio of 10:3?

To find the equivalent ratio of 10:3, you need to multiply both the antecedent and consequent by the same number. For example, if you multiply both by 2, you get the equivalent ratio of 20:6.

How can you find equivalent ratios?

You can find equivalent ratios by dividing or multiplying both the antecedent and consequent of a given ratio by the same number. This will give you a new ratio that has the same value as the original ratio but with different numbers.

Are the ratios 2:3 and 1:2:18 equivalent?

No, the ratios 2:3 and 1:2:18 are not equivalent. The first ratio has two numbers, while the second ratio has three numbers. Equivalent ratios have the same value but different numbers.

Which ratio is equivalent to 14 1:2?

To find the ratio that is equivalent to 14 1:2, you need to convert the mixed number to an improper fraction. This gives you 29/2. You can then divide both the antecedent and consequent by the same number to find an equivalent ratio. For example, if you divide both by 2, you get the equivalent ratio of 14 1:2 : 1.

How many equivalent ratios can be written?

There are an infinite number of equivalent ratios that can be written for a given ratio. This is because you can multiply or divide both the antecedent and consequent by any number and still get an equivalent ratio.

Watch the video explanation of our Equivalent Ratios Worksheet

Watch our free video on how to solve Ratios. This video shows how to solve problems that are on our free finding Equivalent Ratios worksheets that you can get by submitting your email above.

Watch the free Equivalent Ratios video on YouTube here: How to do Equivalent Ratios Video

Video Transcript:

This video is about answering the question what are equivalent ratios. You can get the Equivalent Ratios worksheet 6th grade used in this video for free by clicking on the link in the description below. Equivalent ratios 6th grade are ratios that contain the same relationship between the two ratios. Equivalent ratios can be found by multiplying either the numerator or the denominators by the same number. You can use multiplication or division to find missing numbers in equivalent ratios. In the case of this example that gives us two equivalent ratios we have six to a missing number is equal to 12 to 48. We can take these equivalent ratios and we can write them out as fractions in order to show you how to find the missing number.

The first ratio gives us 6 over our missing number which I’m going to use a question mark and that’s equal to the second ratio which is 12 over 48. In the case of this example, we’re going to use division. Now I know we’re going to use division because we have to find the relationship from the second ratio back to the first ratio. This is because we can’t use the first ratio to find the relationship because we’re missing a number in that ratio so we’re going to take the second ratio and we’re going to find the relationship of the numerator and the denominator to the relationship in the first ratio of the numerator and the denominator. In order to go from 12 to 6 you have to divide by 2. 12 divided by 2 is 6. Then you can use that same relationship to go backwards from 48 to get our missing number. We’re also going to do 48 divided by 2. 48 divided by 2 is 24. Now I know that our missing number has to be 24 because our equivalent ratios have to have the same relationship between the two ratios. In the case of this example the relationship is to divide by 2. Let’s do a couple practice problems on our equivalent ratios worksheet.

The first problem on our equivalent ratios worksheet gives us the ratio of 2 to 8 is equal to 6 to our missing number. The directions say to fill in the blank with a number that will make the ratios equivalent. We can take our ratios and we can write them out as fractions. 2 over 8 is equal to 6 over our missing number. We know that equivalent ratios have the same relationship between the two sets of ratios. We can use one ratio to determine the missing number in another ratio in the case of this example we’re going to use the first ratio to find the missing number in the second ratio. We have to determine the relationship to go from two to six. two times three is equal to six. We can use that same relationship of times three to fill in our missing number 8 times 3 is 24. I know that our missing number is 24 in this equivalent ratios 6th grade because in order for the ratios to be equivalent this number has to be 24. We know that the relationship between the two ratios is to multiply times three.

The next problem we’re going to complete on our equivalent ratios worksheet is number three. This problem gives us a blank number is 2 10 is equal to 4 over 5. We don’t know this number so we’re going to say question mark over 10 is equal to the ratio of 4 over 5. Again we have to fill in our missing number here by finding the relationship between the two equivalent ratios. We have to go from the second ratio back to the first ratio this time by using the denominator because we’re missing a number in the first ratio. We have to figure out how do we go from 5 to 10 and 5 times 2 is 10. I know that the relationship is to multiply times 2 and then 4 times 2 will give us our missing number which in this case is going to be eight. Our missing number in this equivalent ratio is eight.

The final problem we’re going to complete on our equivalent ratios worksheet is number eight this problem gives us 99 over nine is equal to 11 over our missing number again we need to find the relationship between the two ratios by going from one ratio to the other. In the case of this example, we have to figure out how do we go from 99 to 11 because we’re missing a number in the denominator. We have to use the two numbers in the numerator. 99 divided by 9 is 11.  Now we know the relationship is to divide by 9. We take that relationship and we also use it in the denominator nine divided by nine is equal to one. I know that our missing number has to be one. Hopefully you found this video helpful for answering the question what are equivalent ratios. Try the other practice problems by downloading all equivalent ratio worksheets above.