Ordering Numbers Examples in Math

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

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

Concept Recap

Ordering numbers is the process of arranging numbers in sequence from smallest to largest (ascending order) or largest to smallest (descending order). To order numbers, compare them using place value, common denominators, or convert to the same form (e.g. all decimals).

Numbers live on a line—you can always put them in order from left to right.

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: Ordering numbers arranges three or more values into a full ascending or descending sequence.

Common stuck point: The procedure for ordering numbers is the easy part; the trap is ordering fractions by denominator size. Asking "Am I sequencing three or more numbers into a full ordered list (not just comparing two)?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I sequencing three or more numbers into a full ordered list (not just comparing two)?

Worked Examples

Example 1

easy

Arrange from least to greatest:

\frac{1}{2}

0.3

\frac{3}{4}

0.65

Answer

0.3 < \frac{1}{2} < 0.65 < \frac{3}{4}

First step

Convert all to decimals:

\frac{1}{2} = 0.5

0.3 = 0.3

\frac{3}{4} = 0.75

0.65 = 0.65

Full solution

2
Order the decimals: $0.3 < 0.5 < 0.65 < 0.75$ .
3
In original form: $0.3 < \frac{1}{2} < 0.65 < \frac{3}{4}$ .

To order a mixed set of fractions and decimals, convert everything to the same format (decimals are easiest) and compare. Then translate back to the original representations for the answer.

Example 2

medium

Order from greatest to least:

-\frac{1}{2}

-0.6

0

-\frac{1}{3}

Example 3

medium

Order from least to greatest:

\frac{3}{8}

0.4

\frac{1}{3}

0.375

Example 4

easy

You see 3 toy cars, 1 toy car, and 5 toy cars. Put the piles in order from smallest to biggest.

Example 5

easy

Three kids have apples. Sam has 1, Pat has 4, Lou has 2. Order them smallest to biggest.

Example 6

medium

You have 5 blocks, 3 blocks, and 1 block in three piles. Put the piles in order from smallest to biggest.

Example 7

easy

Maya has 4 stickers, Noah has 9, and Ella has 6. Order them from least to greatest.

Example 8

easy

Order from least to greatest:

10, 4, 7, 2

Example 9

medium

Liam picked these number cards:

8, 3, 10, 5

. Put them in order from least to greatest.

Example 10

easy

Four friends caught fish: Sam

13

, Lily

6

, Max

20

, Ana

15

. Order their catches from least to greatest (ascending).

Example 11

easy

Order from greatest to least:

17, 3, 11, 14

Example 12

medium

Four students scored on a test:

18, 12, 16, 9

. Put the scores in descending (greatest to least) order.

Example 13

easy

Four classrooms have these book counts:

128, 182, 218, 138

. Order them from least to greatest.

Example 14

easy

A pet shop has

215

fish,

251

fish,

125

fish, and

152

fish in four tanks. Put the tanks in descending order (greatest to least).

Example 15

medium

Four cities have populations

812, 281, 218, 128

. Order them from least to greatest, then state the difference between the greatest and least.

Practice Problems

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

Example 1

easy

Write three integers in order such that each is exactly 5 less than the previous.

Example 2

medium

Insert a rational number between

\frac{2}{5}

and

\frac{3}{5}

Example 3

easy

Order from least to greatest:

7, 3, 9, 1

Example 4

easy

Order from greatest to least:

4, 8, 2, 6

Example 5

easy

Place

-2

correctly: order

-2, 1, -5, 3

from least to greatest.

Example 6

easy

Where does

0

go? Order

-3, 0, 2, -1

from least to greatest.

Example 7

easy

Order the decimals from least to greatest:

0.3, 0.7, 0.1

Example 8

easy

Order from least to greatest:

\frac{1}{2}, \frac{1}{4}, \frac{3}{4}

Example 9

easy

Order from greatest to least:

15, 5, 25, 10

Example 10

easy

Which list is in correct ascending order: (A)

2,1,3

(B)

1,2,3

(C)

3,2,1

Example 11

medium

Order from least to greatest:

0.5, \frac{1}{4}, 0.3

Example 12

medium

Order from least to greatest:

-1.5, -1, -2, 0

Example 13

medium

Order from greatest to least:

\frac{2}{3}, \frac{1}{2}, \frac{5}{6}

Example 14

medium

Insert

\frac{1}{3}

into the ordered list

0.2, 0.5, 0.8

Example 15

medium

Order from least to greatest:

0.09, 0.1, 0.099

Example 16

medium

A list reads

3, 7, 5, 9, 1

. After sorting ascending, what is the 3rd value?

Example 17

medium

Order from least to greatest:

-\frac{1}{2}, \frac{1}{4}, -\frac{3}{4}, 0

Example 18

medium

Order from greatest to least:

1.2, \frac{6}{5}, 1.25

Example 19

medium

Sort ascending and report the median of

8, 2, 5, 11, 3

Example 20

challenge

Five distinct numbers are placed in ascending order. The largest is

20

, the smallest is

4

, and the middle (3rd) is

12

. If the 2nd value is the average of the 1st and 3rd, find the 2nd value.

Example 21

challenge

You must order

\frac{a}{7}

and

\frac{a}{9}

for an unknown positive

a

. Which is larger, and does the answer depend on

a

Example 22

challenge

Three numbers

x, x+3, 2x-1

are listed and happen to already be in ascending order with no ties. What inequalities must

x

satisfy?

Example 23

easy

Put these in order from smallest to biggest:

3, 1, 2

Example 24

easy

Order from smallest to biggest:

4, 2, 5

Example 25

easy

Put these in order from smallest to biggest:

2, 5, 3

Example 26

medium

Order from smallest to biggest:

5, 1, 4

Example 27

hard

You have 3 ducks, 5 ducks, and 4 ducks in three ponds. Put the ponds in order from smallest to biggest.

Example 28

easy

Order from least to greatest:

7, 3, 9

Example 29

easy

Order from least to greatest:

6, 2, 10, 8

Example 30

easy

Order from least to greatest:

5, 8, 1

Example 31

medium

Order from least to greatest:

9, 3, 6, 8

Example 32

medium

Order from least to greatest:

5, 2, 9, 6

Example 33

easy

Order from least to greatest:

14, 7, 19, 11

Example 34

easy

Order from greatest to least (descending):

5, 18, 12, 9

Example 35

easy

Order from least to greatest:

16, 8, 12, 4

Example 36

medium

Order from least to greatest using

<

19, 13, 18, 15

Example 37

medium

Order from least to greatest:

11, 1, 20, 9

Example 38

easy

Order from least to greatest:

342, 234, 432, 324

Example 39

easy

Order from greatest to least:

507, 705, 570, 750

Example 40

easy

Order from least to greatest using

<

463, 436, 643, 634

Example 41

medium

Order from least to greatest:

309, 390, 393, 339

Example 42

medium

Order from greatest to least:

608, 680, 686, 668

← Back to Ordering Numbers Formula Explained Practice Mode

Related Concepts

More and Less Inequalities Number Line

Background Knowledge

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

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