Comparison Examples in Math

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

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 how two quantities relate in terms of size or value, using the symbols $<$ , $>$ , or $=$ .

Which is bigger? Which is smaller? Are they the same? Comparison answers these questions with precision.

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: Comparison decides how two values relate and records it with $<$ , $>$ , or $=$ .

Common stuck point: The procedure for comparison is the easy part; the trap is pointing the symbol the wrong way. Asking "Am I relating two values with one symbol, with the open end facing the larger?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I relating two values with one symbol, with the open end facing the larger?

Worked Examples

Example 1

easy

Compare

\dfrac{5}{8}

and

\dfrac{3}{5}

. Which is greater?

Answer

\dfrac{5}{8} > \dfrac{3}{5}

First step

Find a common denominator:

\text{lcm}(8,5) = 40

Full solution

2
Convert: $\dfrac{5}{8} = \dfrac{25}{40}$ and $\dfrac{3}{5} = \dfrac{24}{40}$ .
3
Since $25 > 24$ , we have $\dfrac{25}{40} > \dfrac{24}{40}$ , so $\dfrac{5}{8} > \dfrac{3}{5}$ .

To compare fractions with different denominators, rewrite them with a common denominator, then compare numerators directly. The fraction with the larger numerator is the greater fraction.

Example 2

medium

Place

-\dfrac{7}{3}

-2.4

-\dfrac{5}{2}

, and

-2

in order from least to greatest.

Example 3

easy

You have 3 cookies. Your friend has 5 cookies. Who has more?

Example 4

easy

🟦🟦🟦 and 🟥🟥🟥. Are there more blue blocks or red blocks?

Example 5

medium

Lily has 2 balloons. Sam has 4 balloons. Who has fewer balloons?

Example 6

easy

Anna counted 7 shells. Ben counted 10 shells. Who has more shells?

Example 7

easy

Which number is bigger, 6 or 9?

Example 8

medium

A tower of 9 blocks and a tower of 7 blocks stand on the floor. Which tower is taller?

Example 9

easy

Compare

14

and

14

using

<

>

, or

=

Example 10

easy

Order from least to greatest:

11

7

15

Example 11

hard

Three plants are measured. Plant A is 18 cm, Plant B is 9 cm, and Plant C is 15 cm. Order them from shortest to tallest using

<

Example 12

easy

Compare

605

and

650

using

<

>

, or

=

Example 13

easy

Two libraries report their books: Maple Library has

478

books and Birch Library has

487

books. Which library has more books?

Example 14

hard

Three classes counted their box-top collections: Class A has

309

, Class B has

390

, and Class C has

93

. Use

<

to order the totals from least to greatest, and name the class with the most.

Practice Problems

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

Example 1

easy

Insert

<

>

, or

=

between each pair: (a)

0.75

and

\dfrac{3}{4}

, (b)

\dfrac{2}{3}

and

\dfrac{3}{4}

Example 2

medium

Without a calculator, determine which is larger:

\sqrt{50}

7.1

Example 3

easy

Fill in the blank with

<

>

, or

=

7 \;\square\; 4

Example 4

easy

Fill in:

3 \;\square\; 3

Example 5

easy

Fill in:

-1 \;\square\; -10

Example 6

easy

Fill in:

0.5 \;\square\; 0.50

Example 7

easy

Fill in:

\frac{1}{3} \;\square\; \frac{1}{5}

Example 8

easy

Fill in:

25 \;\square\; 19

Example 9

easy

Which symbol makes it true:

0.7 \;\square\; 0.65

Example 10

easy

Fill in:

1000 \;\square\; 999

Example 11

medium

Compare

\frac{3}{4}

and

\frac{5}{8}

using a common denominator.

Example 12

medium

Compare

\frac{2}{3}

and

\frac{3}{5}

by cross-multiplying.

Example 13

medium

Compare

-\frac{3}{4}

and

-\frac{2}{3}

Example 14

medium

Compare

0.\overline{3}

(repeating) and

\frac{1}{3}

Example 15

medium

Which is larger:

\frac{7}{8}

0.9

Example 16

medium

Order using

<

: place

\frac{5}{6}, 0.8, \frac{4}{5}

in increasing order.

Example 17

medium

Two ropes are

\frac{3}{8}

m and

\frac{2}{5}

m. Which is longer?

Example 18

medium

\frac{a}{b} = \frac{c}{d}

when

a=3,b=4,c=9,d=12

? Justify with cross products.

Example 19

challenge

For which positive integers

n

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

Example 20

challenge

Without converting to decimals, decide which is larger:

\frac{17}{18}

\frac{18}{19}

Example 21

challenge

Numbers

a

and

b

satisfy

a < b

. Compare

\frac{a+b}{2}

with

a

and with

b

Example 22

medium

Compare

\frac{4}{9}

and

\frac{5}{11}

by cross-multiplying.

Example 23

easy

🐟🐟 or 🐟🐟🐟🐟. Which group has more fish?

Example 24

easy

🍓🍓🍓 or 🍓. Which group has fewer strawberries?

Example 25

easy

🐶🐶🐶🐶 or 🐱🐱. Are there more dogs or more cats?

Example 26

medium

⭐⭐⭐⭐⭐ or ⭐⭐⭐. Which group has more stars?

Example 27

hard

You have 4 stickers. Your sister has 4 stickers. Who has more?

Example 28

easy

A blue pencil is 6 cubes long. A red pencil is 9 cubes long. Which pencil is longer?

Example 29

easy

Mia is 8 blocks tall. Jay is 7 blocks tall. Who is taller?

Example 30

easy

A green ribbon is 5 cubes long. A yellow ribbon is 3 cubes long. Which ribbon is shorter?

Example 31

medium

Compare 4 and 8. Which is smaller?

Example 32

medium

Maya has 5 hair clips. Jen has 5 hair clips. Who has more?

Example 33

easy

Fill in with

<

>

, or

=

12 \;\square\; 17

Example 34

easy

Fill in with

<

>

, or

=

19 \;\square\; 9

Example 35

easy

Fill in with

<

>

20 \;\square\; 18

Example 36

medium

Fill in with

<

>

, or

=

16 \;\square\; 13

Example 37

medium

Jose has 17 marbles. Kim has 12 marbles. Use

<

>

, or

=

to compare their counts:

17 \;\square\; 12

Example 38

easy

Fill in with

<

>

, or

=

342 \;\square\; 324

Example 39

easy

Fill in with

<

>

, or

=

487 \;\square\; 512

Example 40

easy

Fill in with

<

>

, or

=

239 \;\square\; 239

Example 41

medium

Order from least to greatest:

356

365

336

Example 42

medium

Order from greatest to least:

712

721

127

← Back to Comparison Formula Explained Practice Mode

Related Concepts

More and Less Inequalities Ordering Numbers

Background Knowledge

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

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