Fractions Examples in Math

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

A fraction is a number of the form $\frac{a}{b}$ where $a$ (the numerator) counts how many equal parts you have and $b$ (the denominator, which must not be zero) tells how many equal parts the whole is divided into.

A pizza cut into 4 slices—eating 1 slice means you ate $\frac{1}{4}$ of the pizza.

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 only makes sense after you know what one whole is.

Common stuck point: The procedure for fractions is the easy part; the trap is counting parts before naming the whole. Asking "What is one whole, and are the parts equal?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: What is one whole, and are the parts equal?

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Fractions Mistakes

Worked Examples

Example 1

easy

Add

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

Adding like-denominator fractions: 2/5 + 1/5 = 3/5

Answer

\frac{3}{5}

First step

Check that the denominators are the same: both fractions have denominator

5

Full solution

2
Since denominators match, add the numerators directly: $\frac{2 + 1}{5} = \frac{3}{5}$ .
3
Simplify: $\gcd(3, 5) = 1$ , so $\frac{3}{5}$ is already in lowest terms.

When fractions share the same denominator, you simply add the numerators and keep the denominator unchanged. Always check whether the result can be simplified.

Example 2

medium

Which is larger:

\frac{3}{7}

\frac{5}{11}

Example 3

medium

Add

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

Example 4

medium

Add

\frac{1}{6} + \frac{3}{8}

Example 5

medium

Multiply

\frac{2}{3} \times \frac{9}{14}

Example 6

medium

Divide

\frac{3}{5} \div \frac{6}{25}

Example 7

medium

Find a fraction equivalent to

\frac{4}{7}

with denominator

35

Example 8

hard

Compute

\frac{2}{3} + \frac{1}{4} - \frac{1}{6}

Example 9

hard

\frac{3}{5}

of a number is

24

, what is the number?

Example 10

hard

Simplify

\frac{\frac{1}{2}}{\frac{3}{8}}

Example 11

challenge

A tank is

\frac{2}{3}

full. After

\frac{1}{4}

of the current contents is drained, what fraction of the full tank remains?

After draining, 1/2 of the full tank remains

Practice Problems

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

Example 1

easy

Add

\frac{4}{9} + \frac{2}{9}

4/9 + 2/9 = 6/9 = 2/3

Example 2

medium

Arrange

\frac{2}{3}

\frac{5}{8}

, and

\frac{7}{12}

in order from least to greatest.

Example 3

easy

A pizza is cut into 8 equal slices. You eat 3 slices. What fraction of the pizza did you eat?

3 out of 8 equal pizza slices

Example 4

easy

\frac{5}{9}

, which number is the numerator?

Example 5

easy

Write 'three fourths' as a fraction.

Example 6

easy

A chocolate bar has 6 equal squares. You have 6 of them. What fraction of the bar is that?

All 6 squares shaded: 6/6 = 1 whole

Example 7

easy

Which is a larger piece:

\frac{1}{3}

of a cake or

\frac{1}{5}

of the same cake?

Comparing 1/3 and 1/5 of the same-size cake

Example 8

easy

A bag has 10 marbles; 4 are red. What fraction of the marbles are red?

4 out of 10 marbles are red: 4/10 = 2/5

Example 9

easy

Express

\frac{1}{2}

with a denominator of 8.

1/2 and 4/8 shade the same amount — they are equivalent

Example 10

easy

Reduce

\frac{9}{12}

to lowest terms.

9/12 shaded — simplifies to 3/4

Example 11

medium

A class has 24 students.

\frac{3}{8}

of them walk to school. How many students walk?

3/8 of 24 students walk — how many is that?

Example 12

medium

Two pizzas are the same size. One is cut into 4 slices, the other into 6 slices. Is 1 slice of the first equal to 1 slice of the second? Explain with fractions.

One slice of a pizza cut in 4 vs one slice of a pizza cut in 6

Example 13

medium

Of 30 books,

\frac{2}{5}

are fiction and the rest are nonfiction. How many are nonfiction?

Example 14

medium

A recipe needs

\frac{2}{3}

cup of sugar. You make half the recipe. How much sugar do you use?

Example 15

medium

Which is larger,

\frac{3}{4}

\frac{7}{10}

? Rewrite with a common denominator.

Comparing 3/4 and 7/10 — which is larger?

Example 16

medium

A wall is

\frac{5}{6}

painted. What fraction is still unpainted?

5/6 of the wall is painted — what fraction remains?

Example 17

medium

A number line from 0 to 1 is split into 5 equal parts. A point sits at the 2nd tick after 0. What fraction is it?

Example 18

challenge

A jar of

\frac{3}{4}

liter of juice is shared equally among 6 friends. How much does each get?

Example 19

challenge

Three quarters of a class are present. If 6 students are absent, how many students are in the class?

Example 20

challenge

Why does

\frac{2}{3}

equal

\frac{8}{12}

? Justify using equal parts.

2/3 and 8/12 shade the same region — they are equal

Example 21

medium

Simplify

\frac{18}{24}

to lowest terms.

Example 22

medium

What fraction of an hour is 45 minutes? Simplify.

45 minutes out of 60 = 3/4 of an hour

Example 23

easy

Simplify

\frac{12}{18}

12/18 shaded — simplify to lowest terms

Example 24

easy

Subtract

\frac{7}{10} - \frac{3}{10}

7/10 − 3/10: the difference is the extra shading in the top bar

Example 25

easy

Convert

\frac{9}{4}

to a mixed number.

Example 26

easy

Convert

3\frac{2}{5}

to an improper fraction.

Example 27

easy

24

apples,

\frac{3}{8}

are green. How many green apples are there?

3/8 of 24 apples are green — how many?

Example 28

medium

Subtract

\frac{5}{6} - \frac{1}{4}

Example 29

medium

Sara reads

\frac{2}{5}

of a book on Monday and

\frac{1}{4}

on Tuesday. What fraction is left to read?

Example 30

medium

What is

\frac{2}{3}

\frac{3}{4}

Example 31

medium

Order from least to greatest:

\frac{3}{5}, \frac{2}{3}, \frac{7}{10}

Example 32

medium

A board

\frac{7}{8}

m long is cut into pieces

\frac{1}{16}

m long. How many pieces are there?

Example 33

hard

Compute

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

Example 34

hard

A recipe needs

\frac{3}{4}

cup of milk for one batch. How many cups for

2\frac{1}{2}

batches?

Example 35

hard

On a road trip,

\frac{2}{5}

of the distance was driven by Ana and

\frac{1}{3}

by Ben. What fraction was left for Cara?

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Related Concepts

Division Equal Equivalent Fractions Decimals Ratios

Background Knowledge

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

divisionequal