What are the main strategies for comparing two fractions?

Three common approaches: convert to equivalent fractions with a common denominator, use cross-multiplication, or convert both to decimals.

How does cross-multiplication work for comparing?

For a/b vs c/d, compare a × d vs b × c. If a × d > b × c, then a/b > c/d.

When two fractions have the same numerator, the one with the smaller denominator is larger. For example, 3/5 > 3/8.

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Name:Date:Class:

2

\frac{7}{10}

\frac{1}{2}

\frac{1}{3}

\frac{3}{2}

\frac{19}{10}

2

\frac{17}{12}

\frac{3}{2}

1

\frac{1}{7}

\frac{3}{8}

\frac{7}{4}

\frac{4}{5}

2

\frac{3}{2}

\frac{1}{2}

\frac{7}{4}

10.

\frac{9}{8}

\frac{2}{11}

11.

\frac{1}{5}

\frac{2}{5}

12.

\frac{5}{6}

2

13.

\frac{18}{11}

\frac{1}{8}

14.

1

\frac{9}{5}

15.

2

\frac{1}{3}

16.

\frac{4}{9}

2

17.

\frac{11}{8}

\frac{5}{11}

18.

\frac{3}{4}

\frac{13}{12}

19.

\frac{8}{5}

\frac{1}{4}

20.

\frac{1}{5}

\frac{5}{9}

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Problem: Compare 5/6 and 7/9 using cross-multiplication.

Cross-multiply: 5 × 9 = 45.— Multiply the numerator of the first by the denominator of the second.
7 × 6 = 42.— Multiply the numerator of the second by the denominator of the first.
45 > 42, so 5/6 > 7/9.— The product on the side of 5/6 is larger, so 5/6 is the greater fraction.

Answer: 5/6 > 7/9