# Simplify & Find Equivalent Ratios

## Simplifying Ratios

Being able to simplify ratios is a very important skill to posses. Simplifying ratios is very similar to simplifying fractions. There is a long and a short method.
The long method is to find any common factors of both of the numbers and divided them by it. This
has been done in the first part of the example on the right. However, if we would have used the short
method, we could have left out the steps which are marked in red. The short method involves finding
the highest common factor. In the first part of the example, this would have been 8. Dividing both
number by eight would have allowed us to get to 1:2 in one step. In the other two parts of the
example, we have also used the short method. Once there are no common factors remaining, the
ratio has been fully simplified. Here are a couple more examples.
Finding Equivalent Ratios
Finding equivalent ratios means finding ratios that are different but have or express the same value.
We have already found a few equivalent ratios above when simplifying. Finding equivalent ratios is
quite simple. You can either do it by multiplying both numbers by the same number or by dividing
both numbers by the same common factor. On every row in the example on the right, the ratios are
equivalent. In the bottom and the top row, we have just multiplied the ratio by two and then we have
multiplied the new ratio by two again. In the middle row, we have multiplied the original ratio by two,
three and four. Using multiplication and division, you can easily find equivalent ratios. Underneath
you will find a few more example.
Working with Ratios
Now that you possess the basic skills required to work with ratios and solve problems, you should try to divide some ratios and solve some proportional
problems. Please share this page if you like it or found it helpful!
Example 1
In this example, we found that 2 was the highest
common factor and divided both numbers by it
to simplify the ratio.

Example 2
In this example, 5 was the highest common
factor. We divided both numbers by 5 to simplify
the ratio.

Example 1
In this example, we have divided the ratio
by common factors to find equivalent
ratios.

Example 2
In this example, we have multiplied the
ratio by two to find equivalent ratios.

Example 3
In this example, we have again multiplied
the ratio by two to find equivalent ratios.

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Chapter 9.1: Learning Outcomes
Students will be able to simplify ratios!
Students will be able to find equivalent ratios!

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