Equivalent Fractions

Fractions that are equal in overall value are called equivalent fractions. They can appear to be different numbers but a closer look would show that they are the same.

Take a look at the pictures below to see how fractions with different numbers can have the same value.

In the image above, you can see that one-fourth (

^{1}/

_{4} ) is equals to two-eighths (

^{2}/

_{8} ) and to four-sixteenths (

^{4}/

_{16} ). Even if they have different number representations, they are all equal to the same part or section of the pizza.

Finding equivalent fractions is very useful in adding and subtracting fractions. Since fractions need to have the same bottom numbers or denominators before you can add or subtract them, you will find yourself converting fractions into their equivalents when adding and subtracting fractions.

Let's take our example above and convert

^{1}/

_{4} into a fraction with 8 (a factor of 4) as the denominator.

^{1}/_{4} = ^{A}/_{8}

To find the equivalent denominator, we divide the new denominator (8) by the original denominator (4), and multiply it by the original numerator (1).

### (8 **รท** 4) x 1 = A

### (2) x 1 = A

### 2 = A

^{1}/_{4} = ^{2}/_{8}

To check if this is correct, we can cross multiply the top and bottom numbers of our equivalent fractions. This means that we multiple the numerator with the denominator of the first fraction with the second, and vice versa.

Here's how the equation would look:

Let's take one of our examples above and check if it is they are really equal by cross multiplying them:

^{1}/_{4} = ^{4}/_{16}

1 x 16 = 4 x 4

16 = 16