Equivalent Fractions Explained (With Pictures)
By the TimesTable.co team · Updated · 3 min read
Equivalent fractions are the key that unlocks almost everything else in fractions: comparing them, adding them and simplifying them all depend on it. The idea is simple once children can see it. Cut a pizza into 4 slices or 8 slices, and half the pizza is still half the pizza. Only the number of pieces has changed.
What are equivalent fractions?
Two fractions are equivalent when they are the same size. Picture a bar cut into 2 equal parts with 1 shaded. Now cut each part in half again: there are 4 parts and 2 are shaded. Cut again and it's 4 out of 8. The shaded amount never changed, so:
1/2 = 2/4 = 4/8 = 8/16
Try it on the fraction visualiser at 2/4: it shows the fraction as pie slices and a bar, and tells you when a fraction can be written in a simpler way.
How do you find equivalent fractions?
Multiply the numerator (top) and the denominator (bottom) by the same number. Multiplying both by the same number is really multiplying by 1 (2/2, 3/3 and so on), which is why the amount stays the same.
| Start with | Multiply both by | Equivalent fraction |
|---|---|---|
| 2/3 | 2 | 4/6 |
| 2/3 | 3 | 6/9 |
| 2/3 | 4 | 8/12 |
| 3/5 | 10 | 30/50 |
Notice that the tops of 2/3's family are the 2 times table and the bottoms are the 3 times table. Children who know their times tables find equivalent fractions much easier, because they can spot the patterns straight away.
How do you simplify a fraction?
Simplifying goes the other way: divide the top and bottom by the same number. Keep going until no number (other than 1) divides into both. This is called writing the fraction in its simplest form.
- 12/16: both divide by 4, giving 3/4.
- 18/24: both divide by 6, giving 3/4. (Dividing by 2 and then by 3 works too.)
- 10/15: both divide by 5, giving 2/3.
The biggest number that divides into both is called the highest common factor. Children don't need to find it in one go: dividing by any common factor, then again, gets to the same answer.
How do you check if two fractions are equivalent?
Two quick methods. Simplify both: 6/8 and 9/12 both simplify to 3/4, so they're equivalent. Or cross-multiply: multiply each numerator by the other fraction's denominator.
- 6/8 and 9/12: 6 × 12 = 72 and 8 × 9 = 72. Equal, so equivalent.
- 2/3 and 3/4: 2 × 4 = 8 and 3 × 3 = 9. Not equal, so not equivalent (3/4 is bigger).
What mistakes do children commonly make?
- Adding instead of multiplying: 1/2 becoming 2/3 by adding 1 to both. Draw both to show they're different sizes.
- Only changing one number: 1/2 becoming 2/2. Remind them it's "whatever you do to the top, do to the bottom".
- Thinking bigger numbers mean a bigger fraction: 4/8 looks bigger than 1/2 but is the same size.
- Stopping too early when simplifying: 8/12 to 4/6 instead of 2/3. Ask, "Can you divide again?"
Why do equivalent fractions matter?
They're the tool for everything that follows. To compare 2/3 and 3/4, write both in twelfths: 8/12 and 9/12, so 3/4 is bigger. To add fractions with different denominators, you rewrite them as equivalent fractions first; see adding fractions with different denominators. And equivalent fractions with a denominator of 100 turn straight into percentages: 3/4 = 75/100 = 75%, as explained in how fractions, decimals and percentages connect.
How can you practise equivalent fractions at home?
- Fold paper strips into halves, quarters and eighths and line them up.
- Share out food: "Is 2 slices of 4 the same as 4 slices of 8?"
- Explore on the fraction visualiser: change the top and bottom numbers and watch the pie.
- Print a fractions worksheet or try the step-by-step fraction workouts.
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Frequently asked questions
What are equivalent fractions?
Fractions that are the same amount written with different numbers, such as 1/2, 2/4 and 3/6. The whole is cut into more pieces, but the same share is shaded.
How do you find an equivalent fraction?
Multiply the numerator and the denominator by the same number. 2/3 × 4/4 gives 8/12, so 2/3 and 8/12 are equivalent.
How do you check if two fractions are equivalent?
Cross-multiply: for 3/4 and 9/12, work out 3 × 12 = 36 and 4 × 9 = 36. The results match, so the fractions are equivalent.
What does simplifying a fraction mean?
Writing it as the equivalent fraction with the smallest possible numbers, by dividing the top and bottom by a number that goes into both. 6/8 simplifies to 3/4.
Why can't you add the same number to the top and bottom?
Adding changes the size of the fraction. 1/2 plus 1 on top and bottom gives 2/3, which is bigger than a half. Only multiplying or dividing both by the same number keeps the amount the same.
When do children learn equivalent fractions?
In England, equivalent fractions are introduced with diagrams in Year 3 and developed through Years 4 and 5. In the US they are part of Grade 3 and Grade 4 (standard 4.NF.A.1).