Make equivalent fractions

Keep the same whole

A denominator tells you how many equal parts make the whole. The numerator tells you how many parts you have.

Split each half into two equal pieces. One half becomes two quarters: 1/2 = 2/4. The whole and the shaded amount stay the same.

More parts, the same shaded amount.

12 ÷ 3 = 4

2 × 4 = 8

2/3 = 8/12

To write 2/3 with denominator 12, find the scale factor: 12 ÷ 3 = 4.

Multiply both numbers by 4. The numerator becomes 8 and the denominator becomes 12, so 2/3 = 8/12.

Compare close fractions

Compare cross-products using positive denominators. The larger cross-product identifies the larger fraction.

7/15 < 8/17; 7 × 17 = 119 < 120 = 8 × 15

Order close fractions

Compare exact cross-products for each adjacent pair, then read the fractions from smallest to largest.

7/15 < 8/17 < 9/19

7 × 17 = 119 < 120 = 8 × 15; 8 × 19 = 152 < 153 = 9 × 17

Mixed numbers

Convert each mixed number to an improper fraction, use a common denominator, then simplify.

2 3/4 + 1 1/2 = 11/4 + 6/4 = 17/4 = 4 1/4

Cancel across operations

Rewrite division as multiplication by the reciprocal. Cancel common factors across the numerator and denominator before multiplying.

6/5 × 5/2 ÷ 3/2 = 6/5 × 5/2 × 2/3

6/5 × 5/2 × 2/3 = 2/1 × 1/1 × 1/1 = 2

Each third is split into four equal pieces.

Complete 3/4 = ?/20. The whole stays the same, but each quarter is split into smaller equal pieces.

Find what multiplies 4 to make 20, then multiply 3 by that same number.

Three quarters of the same whole.

Which numerator completes 3/4 = ?/20?

Show the answer

4 × 5 = 20, so multiply the numerator by 5 too: 3 × 5 = 15. Thus 3/4 = 15/20.

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