Ever wondered if 2 big pieces can equal 4 small ones?

Tunde breaks his chocolate bar into 3 equal pieces and eats 2. Aisha breaks the same size bar into 6 pieces and eats 4. Who ate more? Neither — they ate exactly the same amount!

📒 Equivalent Fractions: lesson notes

Discover why 12, 24 and 48 are the same amount, then simplify and compare fractions with confidence.

Tunde breaks his chocolate bar into 3 equal pieces and eats 2. Aisha breaks the same size bar into 6 pieces and eats 4. Who ate more? Neither — they ate exactly the same amount!

Same amount, different names

Equivalent fractions are fractions that are worth the same amount, like 23 and 46.

If you cut every piece of 23 into 2 smaller pieces, you get 6 pieces in the whole and 4 of them are shaded. The amount shaded has not changed.

That is why we multiply the top and the bottom by the same number. Doing this to 23 gives 46 (× 2), 69 (× 3) and 812 (× 4).

🔑 Key idea: Multiply (or divide) the top AND bottom by the same number — the value stays the same.

Simplifying: lowest terms

Going the other way, we divide the top and bottom by the same number to simplify: 1218 ÷ 6 on top and bottom gives 23.

Divide by the HCF of the top and bottom to reach the lowest terms in one step. A fraction is in lowest terms when the top and bottom have no common factor except 1.

Careful: adding the same number to top and bottom does NOT give an equivalent fraction. 12 and 23 are not equal.

🔑 Key idea: Lowest terms: divide top and bottom by their HCF.

Comparing fractions

To compare 34 and 56, change both to the same denominator. The LCM of 4 and 6 is 12.

34 = 912 and 56 = 1012. Now the pieces are the same size, so just compare the numerators: 1012 is bigger.

So 56 > 34.

🔑 Key idea: Same denominator → compare numerators.

Worked example

Find the missing number: 16 = ? / 30

Step 1: Find the multiplier
6 × 5 = 30
Step 2: Multiply the top by the same number
1 × 5 = 5
16 = 530
Why? Multiplying top and bottom by the same number cuts the same amount into more, smaller pieces — the value does not change.

Answer: 5

Summary

Equivalent fractions are worth the same amount: 12 = 24 = 48.
Multiply or divide the top and bottom by the SAME number.
Adding the same number to top and bottom changes the value.
Simplify to lowest terms by dividing by the HCF.
To compare fractions, give them a common denominator first.

Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.