# Simplify & Find Equivalent Fractions

## Simplifying Fractions

When answering a fractional problem, we tend to give the answer (if it is fractional) in its simplest form. To do this, we must simplify or reduce the fraction. This involves finding a common factor of the numerator and the denominator and then dividing both numbers by it. Always ensure to find the highest common factor when simplifying as otherwise you have to repeat the procedure multiple times until there are not common factors anymore. If the numerator and the denominator do not have a common factor, then they are fully simplified. The bigger the number is, the more difficult it will be for you to simplify it as the common factors are not always as obvious as in the two examples above. After you have simplified a fraction, always make sure that you can’t make it any simpler as otherwise it will not be seen as fully simplified. When moving on to calculating with fractions, you will learn an even easier way to simplify your result. Equivalent Fractions Equivalent fractions are different fractions that have the same value. The simplification problems above are a great example of equivalent fractions as simplifying is basically finding an equivalent fraction with smaller numerators and denominators. Although a fraction may look different, it can still have the same meaning (value) as another fraction.

### Graphic Examples

Underneath you can see some graphic examples of equivalent fractions.
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Example 1 This is the long method for simplifying. In this example, we can see that 8/16 are both factors of two and so we were able to simplify the fraction until we arrived at 1/2 since 2 is not a factor of 1. If you want to get around doing the procedure multiple times, you can just divide the numerator and denominator by their highest common factor. As a result you can get from 8/16 to 1/2 in one step. You should always try to use this method as it is faster.
Example 2 In this example, we are trying to simplify 9/27. In the first part of the example, we have used the long method by identifying 3 as a common factor. This works until we get to 1/3 as 3 is not a factor of 1. Since there is no common factor of 1 and 3, 1/3 is the fraction in its simplest form. In the second part of the example, we have used the short method again. by identifying that 9 is the highest common factor of 9 and 27, we were able to get from 9/27 to 1/3 in one step by dividing both the numerator and the denominator by 9.
Example 1 In this first example, you can see 5 fractions and all of them are equal to 1/4. The easiest way to find an equivalent fraction is to use multiplication or division. Just multiply or divide, both the numerator and denominator, by the same number and you should get an equivalent fraction.
Example 1 In the second example, there are again 5 equivalent fractions (all equal to 2/3). However, this time we have used a different method. Instead of always multiplying the fraction by 2, we have only taken the first fraction (2/3) and multiplied it by 2,3,4 and 5. This gives you different answers than just doubling the fraction every time.
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