Equivalent fractions: how to find and exercises

equivalent fractions relate to a property of the fractions, representatives of the set of rational numbers. This property shows that there is an infinite number of fractions representing the same amount, that is, express the same number.

In math, when we say that two elements are equivalent is the same as saying that they are equal. So when we say that A is equivalent to B, we can represent them by:

A = B

Know more: Fraction and Mathematical Operations: Learn How to Solve Them

What are fractions?

fraction is a way of representing parts of one or more integers. For example, when dividing a pizza into 8 slices, we will have that each part corresponds to one eighth of the total. Check the picture:

That is, if we add all the parts, we will get an integer, see:

The number found in the top part of the fraction we call numerator, and the number that is in the bottom we call denominator. So, in the previous example, the number 1 is the numerator and the number 8 is the denominator.

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What are equivalent fractions?

Equivalent fractions are those that represent the same amount or the same number. See the example:

Looking at these images, we can find some equivalences, for example: consider 6/24 is the same as considering 1/4. That is:

We can also say that 12/24 is the same as considering 1/2. That is:

Or, for example, consider 18/24 is the same as considering 1/3.

These fractions are all equivalent as they represent the same amount. Also notice that if the we simplify we will find other equivalent fractions.

Let’s say two fractions are equivalent when the multiplicamos crosswise and the result of equality is true. See the next example:

Check that the 18/24 and 3/4 fractions are equivalent.

Since the equality is true, the fractions are equivalent.
Since the equality is true, the fractions are equivalent.

Read more: Fraction reduction to the same denominator

How to find equivalent fractions?

Equivalence between fractions is the possibility of representing the same quantity in different fractions.
Equivalence between fractions is the possibility of representing the same quantity in different fractions.

To find the equivalent fraction or fractions, simply divide or multiply the numerator and denominator of the fraction by the same non-zero number. When we perform the division operation, we are simplifying the fraction.

Let’s determine some fractions equivalent to 2/8.

solved exercises

question 1 – Check if the following fractions are equivalent:

Resolution

question 2 – Knowing that these fractions are equivalent, determine the value of x:

Resolution

by Robson Luiz
Maths teacher

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