Fractions for Kids: Comparing and Understanding Fractions
By the Duck Math team ·
Fractions are where many children first feel math get harder. The way through is to see a fraction as a real amount, then compare amounts with a few reliable strategies.
What a fraction means
A fraction shows equal parts of a whole. In 3/4 the denominator (bottom number) says the whole is cut into 4 equal parts. The numerator (top number) says you have 3 of them.
Same denominator: compare the tops
When the parts are the same size, more parts is more. 5/8 is bigger than 3/8 because 5 eighths is more than 3 eighths.
Same numerator: compare the bottoms
When you have the same number of parts, smaller parts mean less. 1/3 is bigger than 1/5, because cutting a whole into 3 pieces gives bigger pieces than cutting it into 5.
Use 1/2 as a benchmark
Ask whether each fraction is more or less than one half. 3/7 is less than 1/2 because half of 7 is 3.5. 5/9 is more than 1/2 because half of 9 is 4.5. If one fraction is below 1/2 and the other above it, you are done.
Cross-multiplying for tricky pairs
To compare 3/5 and 4/7, multiply across: 3 × 7 = 21 and 4 × 5 = 20. The bigger product sits on the side of the bigger fraction, so 3/5 is bigger than 4/7.
Practise with a game
Fraction Feast shows two fractions with bar models and asks which is bigger. The early rounds share a denominator, and later rounds mix denominators up to 12.
Questions
Why is a bigger denominator a smaller piece?
Because the whole is split into more equal parts, each part is smaller. Splitting a pizza into 8 slices gives smaller slices than splitting it into 4.
When do children learn to compare fractions?
Most curricula introduce comparing fractions around grades 3 and 4 (ages 8 to 10), but the exact timing depends on your country and school.