# Three equivalent ratios ## Equivalent Ratios

Recall that ratios are comparisons. They are used to compare two quantities.

Sometimes it is useful to write a ratio in another way. For example, there are 8 cups of strawberries added to a fruit salad for every 16 cups of other fruits. This is an 8:16 ratio of strawberries to other fruits. However, it can also be represented as 1 :2. So if we add one cup of strawberries we can add two cups of other fruits and keep the same mixture in a smaller amount.

We can get equivalent ratios by scaling upor scaling down.

1.) This is an example of scaling up by a scale factor of 3. The ratio 2 : 3 is the same as the ratio of 6 : 15.

2.) This is an example of scaling down by a scale factor of 5. The ratio 8 to 11 is the same as the ratio 40 : 55.

3.) Here, we scaled up by a factor of 8 to create two equivalent ratios.

We can make a string of equivalent ratios by continuing to scale up or scale down.

1 : 3 = 2 : 6 = 3 : 9 = 4 : 12 = 5 : 15 = 6 : 18 = 7 : 21....

All of these ratios show the same relationship.

Simplifying ratios to the simplest form can be helpful when solving problems that deal with ratios. You can simplify a ratio the same way that you simplify a fraction. This is basically just scaling down until you can no longer scale down anymore.

Examples.

1.) 14 : 18 = 7 : 9

2.) 25 : 500 = 5 : 100 = 1 : 20

3.) 18 : 60 = 9 : 30 = 3 : 10

Let's take a look at how scaling up and scaling down can be helpful with a couple of word problems.

1. At East Ridge Middle School, the ratio of boys to girls is 3 to 2. There are 600 students at the school. How many are boys?

Solution: We have been given the whole. So let's write a ratio that compares the boys to the whole. 3 : 5 is the part-to-whole relationship. Now we can scale up from 5 to 600. 5 x 120 = 600, so 3 x 120 = 360. There are 360 boys at the school.

2. For every 3 parts of yellow, 5 parts red have been mixed to make a particular shade of orange. If there are 80 gallons of orange made, how many gallons of red were added in?

Solution: The 80 gallons is the whole mixture of paint. So we need a part to whole ratio comparing red to the whole. This would be 5 : 8. Now we can scale up 5 : 8 = 50 : 80. Therefore, 50 gallons of red were used to make the 80 gallons of orange paint.

Math
What is a Ratio?
What is a proportion?
Unit Rates
Ratios
Fractions
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## Equivalent Ratios

Learn about equivalent ratios to get the clear concept on ratio. We know that we use ratios to compare numbers.

How do we find two equivalent ratios by using multiplication and division?

To get a ratio equivalent to a given ratio we multiply or divide both the terms of the given ratio by the same non-zero number. We will learn how to find the equivalent ratios of a given ratio by writing the ratio as a fraction and then compare by using multiplication and division.

Solved examples to find two equivalent ratios:

1. Give two equivalent ratios of 8 : 18.

Solution:

We will find the first equivalent ratio of 8 : 18 by using multiplication.

So, first we need to write the given ratio as fraction,

= 8/18

= (8 × 2)/(18 × 2)

= 16/36

= 16 : 36 (one equivalent ratio),

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

Now we will find another equivalent ratio of 8 : 18 by using division.

Similarly, first we need to write the given ratio as fraction,

= 8/18

= (8 ÷ 2)/(18 ÷ 2)

= 4/9

= 4 : 9 (another equivalent ratio)

So, 4 : 9 is an equivalent ratio of 8 : 18.

Therefore, the two equivalent ratios of 8 : 18 are 16 : 36 and 4 : 9.

2. Frame two equivalent ratios of 4 : 5.

Solution:

To findtwo equivalent ratios of 4 : 5 we need to apply multiplication method only to get the answer in integer form.

First we need to write the given ratio as fraction,

= 4/5

= (4 × 2)/(5 × 2)

= 8/10

= 8 : 10 is one equivalent ratio,

Similarly again, we need to write the given ratio 4 : 5 as fraction to get another equivalent ratio;

= 4/5

= (4 × 3)/(5 × 3)

= 12/15 is another equivalent ratio

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

Note: In this question we can’t apply division method to get the answer in integer form because the G.C.F. of 4 and 5 is 1. That means, 4 and 5 cannot be divisible by any other number except 1.

3. For the following ratio find the two equivalent ratios of 11 : 13.

Solution:

To find two equivalent ratios of 11 : 13 first we need to write the given ratio as fraction,

11/13

= (11 × 2)/(13 × 2)

= 22/26

= 22 : 26 is one equivalent ratio

Similarly again, to get another equivalent ratio of 11 : 13;

11/13

= (11 × 4)/(13 × 4)

= 44/52

= 44 : 52 is another equivalent ratio

Therefore, the two equivalent ratios of 11 : 13 are 22 : 26 and 44 : 52.

Note: If a : b and x : y are two equivalent ratios, we write a/b = x/y.

Solved example to find three equivalent ratios:

4. Find three equivalent ratios of 3 : 8.

Solution:

3 : 8 = 3/8 = (3 × 2)/(8 × 2), [Multiply both numerator and denominator by 2]

= 6/16

= 6 : 16 is the first equivalent ratio.

3 : 8 = 3/8 = (3 × 4)/(8 × 4), [Multiply both numerator and denominator by 4]

= 12/32

= 12 : 32 is the second equivalent ratio.

3 : 8 = 3/8 = (3 × 6)/(8 × 6), [Multiply both numerator and denominator by 6]

= 18/48

= 18 : 48 is the third equivalent ratio.

Therefore, the three equivalent ratios of 3 : 8 are 6 : 16, 12 : 32 and 18 : 48.

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## Ratio Calculator

### What is a Ratio?

A contrast, which exists between two particular numbers, is defined as ratio. Our ratio calculator is developed to compute this contrast and find out the relationship between these numbers.

### Using the Ratio Calculator

Resort to the help of this amazing ratio calculator when you have you settle ratio/proportion problems and check equivalent fractions. Despite the fact that you cannot enter a ratio of 4/5 into this calculator, it accepts values such as 4:5, for example, 4/3 should be written as 4:3. Moreover, our ratio calculator is also able to write down the list of equivalent ratios and process decimal numbers.

### How to Calculate Ratios

In order to keep numbers in direct relation you should first divide or multiply, which depends on your task, them in the ratio. Therefore, a ratio of 8/6 is an equivalent ratio of 4/3: in that particular ratio calculation, you should just multiply 4, as well as 3, by 2.

You may also want to try our Aspect Ratio Calculator.

Sours: https://goodcalculators.com/ratio-calculator/
Equivalent Ratios

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## Ratios three equivalent

Hint: First write the ratio 12 to 9 in the fractional form with 12 as the numerator and 9 as the denominator. Now, cancel the common factors (if present) and get the simplest form of the fraction. This simplest form obtained will be an equivalent fraction. To find more equivalent fractions multiply the numerator and the denominator of the simplest form with the same numerical value. Choose a different numerical value each time and get the answer. Write them in the ratio form to get the answer.

Here we are provided with the ratio 12 to 9 and we are asked to write its three equivalent ratios. First let us find its equivalent fractions which can be converted into the ratios easily.
The ratio 12 to 9 can be written in fractional form by considering 12 as the numerator and 9 as the denominator as $\dfrac{12}{9}$. Let us see if it has common factors, so we get,
\begin{align} & \Rightarrow \dfrac{12}{9}=\dfrac{3\times 4}{3\times 3} \\ & \Rightarrow \dfrac{12}{9}=\dfrac{4}{3} \\ \end{align}
Therefore, the simplest form of the fraction $\dfrac{12}{9}$ is $\dfrac{4}{3}$.
Now, two or more fractions are said to be equivalent if their simplest forms are equal. So, $\dfrac{4}{3}$ is an equivalent fraction of $\dfrac{12}{9}$. To find equivalent fractions we multiply the numerator and the denominator with the same numerical value other than 0. So let us find two more equivalent fractions.
\begin{align} & \left( i \right)\dfrac{4}{3}=\dfrac{4\times 5}{3\times 5}=\dfrac{20}{15} \\ & \left( ii \right)\dfrac{4}{3}=\dfrac{4\times 6}{3\times 6}=\dfrac{24}{18} \\ \end{align}
Therefore, $\dfrac{4}{3}$,$\dfrac{20}{15}$ and $\dfrac{24}{18}$ are the three equivalent fractions of $\dfrac{12}{9}$. We know that a fraction of the form $\dfrac{a}{b}$ is written in the ratio form as $a:b$. Hence, we have $4:3,20:15$ and $24:18$ as the three equivalent ratios of $12:9$.

Note: You must remember the definition of equivalent fraction to solve the above question. Do not multiply the numerator and denominator with 0 otherwise you will get the fraction undefined as the denominator of a fraction cannot be 0. So other than 0 you may choose any real number whether positive or negative, decimal or natural. There can be infinite equivalent ratios of a given ratio.
Equivalent Ratios Lesson

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