Compare and Order Fractions

Fractions tell you how many equal parts of a whole you have. To compare or order fractions, you need a fair way to line them up. When the bottoms (denominators) match, the comparison is simple. When they do not match, rewrite the fractions so they share a common denominator first.

Same Denominator — Compare the Top

• If two fractions have the same denominator, the bigger numerator wins: 5/8 > 3/8.
• The pieces are the same size, so the fraction with more pieces is greater.
• Equal numerators with equal denominators means the fractions are equal: 3/8 = 3/8.

Same Numerator — Compare the Bottom

• When the numerators match, the fraction with the smaller denominator is greater: 3/4 > 3/8.
• A smaller denominator means each piece is bigger.
• Think of pizza: 3 of 4 slices is more food than 3 of 8 slices.

Different Denominators — Find a Common Denominator

1. Find a common multiple of both denominators (the least common multiple is easiest).
2. Rewrite each fraction with that common denominator by multiplying the top and bottom by the same number.
3. Compare the new numerators just like before.
4. Example: 2/3 vs 3/4. Common denominator 12. Rewrite as 8/12 vs 9/12. So 2/3 < 3/4.

Use 1/2 as a Benchmark

• A fraction equals 1/2 when the numerator is exactly half the denominator (3/6, 4/8, 5/10).
• A fraction is less than 1/2 when the numerator is less than half the denominator (2/8, 1/3).
• A fraction is greater than 1/2 when the numerator is more than half the denominator (5/8, 3/4).
• Comparing each fraction to 1/2 first can quickly tell you which side of the number line it sits on.