# Equivalent Fractions

## What are equivalent fractions

Equivalent fractions means fractions with the same, equal denominators. It's important the fractions are equal when you want to add or subtract fractions.

Are the terms described here difficult? Have a look at the 'What Is a Fraction' page for more explanation first.

On this page you will find examples and exercices. For an extensive practice go to one of the 5-step plans.

### 5-step plans

### Example 1

Making the fractions 23 and 16 equivalent.

**Step 1. Determine which denominator this fraction can be made equal with.**

The new denominator is usually easiest to find by checking if the smallest denominator can be made the same as the largest. In this example the smallest denominator (3) can be made the same as the largest denominator (6) by multiplying the number by 2.

**Step 2. Make the denominators equal.**

Now the numerator and the denominator must be multiplied by 2 to make the fractions equal. You then get: 2 x 2 = 43 x 2 = 6.

You now have equivalent fractions. The answer is 46 and 16.

What if you can't make the smallest denominator the same as the largest denominator? Have a look at example 2 to see how you can solve this.

### Exercise 1:

Choose the number of sums and the time per sum and click start.

Tip: use tab to go to the next field

### Example 2

Making the fractions 13 and 35 equivalent.

**Step 1. Determine which denominator the equivalent fractions should have.**

The easiest way to find the new denominator is by making the smallest denominator the same as the largest denominator. If this isn't possible we try to multiply the largest denominator by 2 and see if that number can be divided by the smallest denominator. If multiplying by 2 doesn't work, try multiplying by 3, and if that doesn't work, multiply by 4, etcetera.

In this example the largest denominator is 5.

5 can't be divided by 3 (the smallest denominator). So we first try 5 x 2 = 10. 10 can't be divided by 3. Now we try 5 x 3 = 15. 15 can be divided by 3, because 15 divided by 3 is 5.

**Step 2. Make the denominators equal.**

To make equivalent fractions, the numerator and denominator of the fraction with the smallest denominator (13) need to be multiplied by 5. And the numerator and denominator of the fraction with the largest denominator (35) need to be multiplied by 3, so they both get the new denominator 15. The result is 515 and 915. You can also see this in the image below:

### Exercise 2:

Choose the number of sums and the time per sum and click start.

Tip: use tab to go to the next field