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Equivalent Fractions and Simplest Form (Mathematics Lesson)

What Are Equivalent Fractions?

Equivalent fractions are fractions that show the same part of the whole, even though they look different.

Examples of Equivalent Fractions

The following fractions are all equivalent to 1/2 (one half):



They represent the same part of the whole, but have a different top number (called the numerator) and a different bottom number (called the denominator).

How to Find Equivalent Fractions

You can make equivalent fractions by multiplying or dividing the numerator and denominator by the same number.



In our example above, equivalent fractions of ½ are found by multiplying both the numerator and denominator by 2.

Simplifying (or Reducing) Fractions

Just as equivalent fractions can be found by multiplying both top and bottom by the same number, equivalent fractions can also be found by dividing top and bottom by the same number.

This is called cancelling. It simplifies (or reduces) fractions.



In our example above, equivalent fractions are found by dividing both the numerator and denominator by 2.

Read more about simplifying fractions

Simplest Form

A fraction is in its simplest form if the top and bottom numbers cannot be made any smaller by cancelling (while still being whole numbers).

The simplest form of a fraction is the equivalent fraction with the smallest possible numbers.

More About Equivalent Fractions and Simplest Form

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Here's a third test on equivalent fractions.
Note

What Is a Fraction?

A fraction is a part of a whole number.

Fractions consist of a numerator and a denominator.

There are three different types of fractions:

Visualizing Equivalent and Simplest Fractions

Fractions can be visualized as a cake cut into equal slices.

Using this method, equivalent fractions can be visualized. The three fractions below are equivalent:



The top cake shows the simplest fraction, as there are the fewest slices.

What Is a Multiple?

A multiple is the result of multiplying a number by an integer.

For example, the multiples of 3 are:

What Is a Factor?

A factor is a number or symbol which divides exactly into another number.

For example, the factors of 10 are:

What Is the Greatest Common Factor?

The greatest common factor is the largest factor that is common to two or more numbers.