Mixed Numbers Examples in Math

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

A mixed number combines a whole number and a proper fraction, such as $3\frac{1}{4}$ , representing the sum of the whole part and fractional part: $3 + \frac{1}{4} = \frac{13}{4}$ .

You ate 2 whole pizzas and $\frac{3}{4}$ of a third pizza—that's $2\frac{3}{4}$ pizzas.

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 mixed number names an amount greater than one using whole units and a fractional part.

Common stuck point: The procedure for mixed numbers is the easy part; the trap is reading $2\frac{3}{5}$ as $2 \times 3/5$ . Asking "Is the amount best read as whole units plus a fraction of one more unit?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is the amount best read as whole units plus a fraction of one more unit?

Worked Examples

Example 1

easy

Add

1\frac{2}{5} + 2\frac{1}{5}

The fractional parts of 1²/₅ and 2¹/₅ — same denominator, add the shaded sections

Answer

3\frac{3}{5}

First step

Add the whole number parts:

1 + 2 = 3

Full solution

2
Add the fraction parts (same denominator): $\frac{2}{5} + \frac{1}{5} = \frac{3}{5}$ .
3
Combine: $3 + \frac{3}{5} = 3\frac{3}{5}$ .

When adding mixed numbers with like denominators, add the whole numbers and the fractions separately, then combine the results. This works because a mixed number is simply a whole number plus a fraction.

Example 2

medium

Subtract

4\frac{1}{3} - 1\frac{3}{4}

Example 3

medium

Multiply

2\frac{1}{3} \times 1\frac{1}{2}

Example 4

medium

Multiply

3\frac{1}{2}\times 2\frac{2}{3}

Example 5

medium

Convert

7\frac{3}{10}

to a decimal.

Example 6

medium

Subtract

7-2\frac{3}{8}

Practice Problems

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

Example 1

easy

A recipe needs

2\frac{3}{4}

cups of flour and

1\frac{1}{4}

cups of sugar. How many cups of dry ingredients are needed in total?

Fractional parts of 2³/₄ and 1¼ combine to make exactly 1 extra cup

Example 2

hard

Add

3\frac{5}{6} + 2\frac{3}{4}

Example 3

easy

Convert

2\frac{3}{4}

to an improper fraction.

Example 4

easy

Convert

\frac{7}{3}

to a mixed number.

Example 5

easy

What does

3\frac{1}{2}

mean as a sum?

Example 6

easy

Convert

1\frac{2}{5}

to an improper fraction.

Example 7

easy

Convert

\frac{9}{4}

to a mixed number.

9/4 = 2 full groups of 4 with 1 left over — the shaded piece is the ¼ remainder

Example 8

easy

Which is larger,

2\frac{1}{4}

2\frac{3}{4}

Same whole number (2), different fractional parts — compare the shaded regions

Example 9

easy

What whole number does

4\frac{4}{4}

equal?

Example 10

easy

Convert

5\frac{1}{3}

to an improper fraction.

Example 11

medium

Add

1\frac{1}{2}+2\frac{1}{4}

Fractional parts of 1½ and 2¼ — rewrite ½ as 2/4 then add to get 3/4

Example 12

medium

Add

2\frac{2}{3}+1\frac{2}{3}

Example 13

medium

Subtract

3\frac{1}{4}-1\frac{3}{4}

Since 1/4 < 3/4, you must borrow before subtracting

Example 14

medium

Convert

\frac{23}{5}

to a mixed number.

Example 15

medium

Add

2\frac{1}{2}+1\frac{1}{3}

Example 16

medium

A board is

4\frac{1}{2}

feet long. You cut off

1\frac{3}{4}

feet. How much remains?

Example 17

challenge

Multiply

1\frac{1}{2}\times 2\frac{2}{3}

Example 18

challenge

A recipe needs

2\frac{1}{4}

cups of flour per batch. How much for 3 batches?

Example 19

challenge

Divide

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

Example 20

medium

Add

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

Add the fractional parts of 3¼ and 2¼ — the shaded sum 2/4 simplifies to ½

Example 21

medium

Subtract

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

Fractional parts of 4²/₃ and 2⅓ — 2/3 minus 1/3 needs no borrowing

Example 22

medium

Compare

2\frac{2}{3}

and

2\frac{3}{5}

. Which is larger?

Example 23

easy

Convert

5\frac{2}{3}

to an improper fraction.

Example 24

easy

Convert

\frac{19}{6}

to a mixed number.

Example 25

easy

Add

2\frac{1}{6}+1\frac{2}{6}

Fractional parts of 2¹/₆ and 1²/₆ — shaded sections combine to 3/6 = ½

Example 26

medium

Subtract

5\frac{1}{4}-2\frac{3}{4}

Since ¼ < ¾, borrow one whole from 5 before subtracting

Example 27

medium

Divide

4\frac{1}{2}\div 1\frac{1}{2}

Example 28

easy

Convert

4\frac{3}{8}

to an improper fraction.

Example 29

medium

Sara ran

2\frac{3}{4}

miles Monday and

3\frac{1}{2}

miles Tuesday. How many miles total?

Example 30

medium

A board is

6\frac{1}{4}

feet long. A

2\frac{1}{2}

foot piece is cut off. How long is the remaining piece?

Example 31

medium

Add

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

Example 32

hard

Multiply

2\frac{3}{5}\times 3\frac{1}{4}

Example 33

hard

A bag holds

4\frac{1}{2}

pounds of rice. If you use

\frac{3}{4}

pound per serving, how many full servings can you make?

Example 34

easy

Order from least to greatest:

1\frac{1}{2}

1\frac{3}{4}

1\frac{1}{4}

Example 35

medium

A jug holds

3\frac{1}{4}

cups of juice. Three jugs are filled. Total juice?

Example 36

hard

Add

4\frac{5}{6}+2\frac{7}{8}

Example 37

medium

Multiply

5\times 1\frac{2}{5}

Example 38

hard

A bookshelf is

6\frac{1}{2}

feet tall. Each shelf takes

1\frac{1}{8}

feet. How many full shelves fit?

Example 39

challenge

Compute

\left(1\frac{1}{2}\right)^2+\left(2\frac{1}{3}\right)^2

← Back to Mixed Numbers Formula Explained Practice Mode

Related Concepts

Fractions Mixed-Improper Conversion Adding Fractions with Unlike Denominators

Background Knowledge

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

fractions