Comparing Fractions Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Comparing Fractions.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Determining which of two fractions is greater, less, or equal using common denominators, benchmarks, or cross-multiplication.

To compare $\frac{3}{4}$ and $\frac{5}{6}$ , rewrite them with the same denominator so the numerators can be compared directly.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A fraction comparison is only fair when both fractions refer to the same whole.

Common stuck point: The procedure for comparing fractions is the easy part; the trap is choosing the fraction with the larger denominator automatically. Asking "Am I judging size rather than combining amounts?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I judging size rather than combining amounts?

Worked Examples

Example 1

easy

Compare

\frac{4}{7}

and

\frac{3}{7}

using the

<

>

, or

=

symbol.

Which bar shows more? Compare 4/7 and 3/7.

Answer

\frac{4}{7} > \frac{3}{7}

First step

The denominators are the same (

7

), so the pieces are the same size.

Full solution

2
Compare the numerators: $4 > 3$ .
3
Therefore $\frac{4}{7} > \frac{3}{7}$ .

When two fractions have identical denominators, they represent the same size pieces. The fraction with the larger numerator is greater because it contains more of those equal-sized pieces.

Example 2

medium

Compare

\frac{5}{9}

and

\frac{7}{12}

using a common denominator.

Example 3

medium

Use cross-multiplication to compare

\frac{7}{10}

and

\frac{5}{8}

Example 4

medium

Compare

\frac{4}{5}

and

\frac{5}{6}

by thinking about how far each is from

1

Example 5

hard

For which integer values of

n

from

1

20

\frac{n}{15} > \frac{2}{3}

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

Compare

\frac{2}{3}

and

\frac{3}{4}

using cross-multiplication.

Example 2

hard

Without finding a common denominator, use benchmark reasoning to compare

\frac{11}{20}

and

\frac{8}{15}

Example 3

easy

Which is greater,

\frac{3}{5}

\frac{2}{5}

Compare 3/5 and 2/5 using the bar models.

Example 4

easy

Which is greater,

\frac{1}{3}

\frac{1}{4}

Locate 1/3 and 1/4 on the number line. Which is greater?

Example 5

easy

Compare

\frac{1}{2}

and

\frac{3}{4}

using the benchmark

\frac{1}{2}

The benchmark 1/2 is marked. Where does 3/4 fall?

Example 6

easy

Which is greater,

\frac{5}{8}

\frac{3}{8}

Compare 5/8 and 3/8 using the bar models.

Example 7

easy

\frac{2}{3}

greater or less than 1?

Is 2/3 greater or less than 1?

Example 8

easy

Which is greater,

\frac{4}{7}

\frac{4}{9}

Both fractions have numerator 4. Which is greater?

Example 9

easy

Compare

\frac{2}{5}

\frac{1}{2}

using a benchmark.

Use the benchmark 1/2. Is 2/5 greater or less?

Example 10

easy

Are

\frac{2}{4}

and

\frac{1}{2}

equal?

Do 2/4 and 1/2 shade the same amount?

Example 11

medium

Which is greater,

\frac{3}{4}

\frac{5}{7}

? Use cross-multiplication.

Example 12

medium

Which is greater,

\frac{5}{6}

\frac{7}{9}

? Use a common denominator.

Example 13

medium

Order

\frac{3}{8}

and

\frac{2}{5}

from least to greatest.

Example 14

medium

Which is greater,

\frac{7}{12}

\frac{1}{2}

Is 7/12 greater or less than the benchmark 1/2?

Example 15

medium

Compare

\frac{9}{10}

and

\frac{11}{12}

. Which is closer to 1?

Example 16

medium

Two pies of the same size: one has

\frac{2}{3}

left, the other

\frac{3}{5}

left. Which has more?

Example 17

challenge

For which whole values of

n

\frac{n}{12} < \frac{1}{2}

Example 18

challenge

Order

\frac{5}{8}

\frac{2}{3}

\frac{7}{12}

from least to greatest.

Example 19

challenge

Insert a fraction strictly between

\frac{1}{3}

and

\frac{1}{2}

Example 20

medium

Which is greater,

\frac{4}{5}

\frac{5}{6}

? Use cross-multiplication.

Example 21

medium

Which is greater,

\frac{3}{7}

\frac{1}{2}

Is 3/7 greater or less than 1/2?

Example 22

medium

Which is greater,

\frac{7}{10}

\frac{2}{3}

? Use a common denominator.

Example 23

easy

Compare

\frac{5}{6}

and

\frac{4}{6}

using

<

>

, or

=

Compare 5/6 and 4/6 using the bar models.

Example 24

easy

Use the benchmark

1

to compare

\frac{7}{8}

and

\frac{9}{8}

Use the benchmark 1. Which fraction is greater?

Example 25

medium

Compare

\frac{3}{8}

and

\frac{5}{12}

by finding a common denominator.

Example 26

medium

Compare

\frac{9}{14}

and

\frac{2}{3}

using cross-multiplication.

Example 27

easy

Compare

\frac{6}{9}

and

\frac{2}{3}

Do 6/9 and 2/3 shade the same length?

Example 28

medium

Using the benchmark

\frac{1}{2}

, compare

\frac{7}{15}

and

\frac{9}{16}

Use the benchmark 1/2. Which side does each fraction fall on?

Example 29

medium

Order from greatest to least:

\frac{2}{3},\ \frac{5}{8},\ \frac{7}{12}

Order 2/3, 5/8, and 7/12 from greatest to least.

Example 30

medium

Anna ate

\frac{3}{8}

of a pizza. Ben ate

\frac{2}{5}

of an identical pizza. Who ate more?

Example 31

hard

Without computing a common denominator, compare

\frac{99}{100}

and

\frac{100}{101}

Example 32

hard

A jar contains

\frac{3}{10}

cup of honey. A second jar contains

\frac{2}{7}

cup. Which jar has more honey?

Example 33

hard

Compare

\frac{7}{12}

and

\frac{11}{18}

Example 34

hard

Compare

-\frac{3}{5}

and

-\frac{4}{7}

Example 35

medium

Two students simplify

\frac{12}{18}

and

\frac{10}{15}

. Are the simplified fractions equal?

Do 12/18 and 10/15 shade the same fraction of the bar?

Example 36

hard

A recipe calls for

\frac{3}{4}

cup of flour. You measured

\frac{11}{16}

cup. Do you have enough, and if not, how much more do you need?

Example 37

challenge

Find a fraction in lowest terms that lies strictly between

\frac{5}{12}

and

\frac{1}{2}

Example 38

medium

Order from least to greatest:

\frac{3}{4},\ \frac{7}{10},\ \frac{4}{5}

Order 3/4, 7/10, and 4/5 from least to greatest.

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Related Concepts

Fractions Equivalent Fractions Ordering Fractions

Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsequivalent fractions