2. Equivalent fractions — Learner Route

Fractions · Step 2

Same amount, different fractions

A fraction can look different without changing how much we have. Let’s see why.

Look first

Can these all show the same amount?

Choose a fraction. The shaded amount stays the same, but the whole is cut into more pieces.

Try it

Cut every piece in half

Start with one half. Then cut every piece in half again.

1/2
Notice: more pieces does not mean more amount. The pieces have become smaller.
Another example

Two thirds can become four sixths

Cut each third into two equal pieces. Nothing is added and nothing is taken away.

2/3 = 4/6
They cover the same amount. In 4/6, each third has been split into two equal sixths.
What have we discovered?

Equivalent fractions

Fractions that name the same amount are called equivalent fractions.

1/2 = 2/4 = 4/8 2/3 = 4/6 3/4 = 6/8
What has to change together?

Start with 3/4 and scale by 2.

Both change by the same factor
3 ×2 4 ×2
→
68
3/4
6/8 = 3/4
Each quarter is split into two eighths, so the number of selected pieces doubles as well. The amount stays the same.

Optional: explore what can go wrong.

To make an equivalent fraction, multiply the numerator and denominator by the same number.
Interactive lab

Match equivalent fractions

Choose the missing number. When you are right, the second picture slides over the first so you can compare the amounts.

Picture style: strip
Choose the missing number.
Method Trainer

Same amount or different amount?

Try five new examples. Your answers feed into your Practice Lab log on this device. For Yes/No questions, select a button to check your answer.

Question 1 of 5 · 0 answered

You have learned

The same amount can be named by different fractions. Equivalent fractions appear when we split every piece into the same number of smaller equal pieces.

Next: what happens when we put familiar fraction pieces together?