Comparing Fractions Which is Bigger

When two fractions have the same denominator, the one with the BIGGER numerator is bigger. 3/8 is bigger than 2/8 because 3 is bigger than 2. When denominators are different, it is trickier: 1/2 is bigger than 1/4 even though 2 is smaller than 4. Why? Because dividing into fewer pieces makes each piece bigger.

Think of a pizza. If you cut it into 2 pieces (halves), each piece is huge. If you cut it into 8 pieces (eighths), each piece is tiny. So 1/2 of a pizza is bigger than 1/8. When the TOP number is 1, the fraction with the SMALLER denominator is bigger. When denominators are equal, just look at the top number.

Same denominator: 3/5 vs 4/5 — 4/5 is bigger. 2/7 vs 5/7 — 5/7 is bigger. Same numerator, different denominator: 1/3 vs 1/5 — 1/3 is bigger (bigger pieces). 2/3 vs 2/9 — 2/3 is bigger. Trick: when in doubt, convert both fractions to the same denominator.

To compare fractions with different denominators, find a common denominator. Example: 1/2 vs 2/3. Convert both to sixths: 1/2 = 3/6, 2/3 = 4/6. Now compare: 4/6 is bigger than 3/6, so 2/3 is bigger than 1/2. This is called the cross-multiply trick or the common denominator method.