Adding Fractions with Like Denominators Examples in Math

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

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

Concept Recap

Adding fractions that share the same denominator by adding the numerators and keeping the denominator.

If you have $\frac{2}{5}$ of a pie and get $\frac{1}{5}$ more, you now have $\frac{3}{5}$ —same size pieces, just count them up.

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: When denominators match, you are adding counts of the same unit fraction.

Common stuck point: The procedure for adding fractions with like denominators is the easy part; the trap is adding the denominators. Asking "Are the fractions counting the same-size pieces?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Are the fractions counting the same-size pieces?

Worked Examples

Example 1

easy

Add

\frac{3}{8} + \frac{4}{8}

Each bar is divided into 8 equal parts. Count the shaded pieces to see why the numerators add.

Answer

\frac{7}{8}

First step

The denominators are both

8

, so the pieces are the same size.

Full solution

2
Add the numerators: $3 + 4 = 7$ . Keep the denominator: $\frac{7}{8}$ .
3
Check: $\gcd(7, 8) = 1$ , so the fraction is already in simplest form.

Adding like-denominator fractions means combining the counts of equal-sized pieces. The denominator acts as a label (eighths) and stays unchanged — only the count of pieces (numerator) changes.

Example 2

medium

Add

\frac{5}{9} + \frac{7}{9}

and simplify fully.

Example 3

easy

Worked example: add

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

and show why the denominator does not change.

Example 4

medium

Worked example:

1\frac{3}{7}+2\frac{5}{7}

Example 5

medium

Worked example: explain why

\frac{3}{5}+\frac{4}{5}\ne\frac{7}{10}

Example 6

hard

Worked example: A garden is divided into 20 equal beds. Bed-by-bed,

\frac{6}{20}

are roses and

\frac{9}{20}

are tulips. What fraction of beds are neither, in lowest terms?

Practice Problems

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

Example 1

easy

A jug contains

\frac{2}{7}

litre of water. You pour in another

\frac{3}{7}

\frac{5}{8}+\frac{7}{8}

and write the result as a mixed number.

Example 12

medium

Add

\frac{2}{9}+\frac{4}{9}+\frac{1}{9}

Example 13

medium

\frac{3}{11}+\frac{?}{11}=\frac{10}{11}

. Find the missing numerator.

The result bar must reach 10 out of 11. How many more pieces (shown as ?) must the middle bar have?

Example 14

medium

Add

1\frac{2}{5}+\frac{4}{5}

Example 15

medium

Add

\frac{7}{15}+\frac{3}{15}

and simplify.

Ten of 15 equal parts are shaded in the result bar; dividing both by 5 gives the simplified answer 2/3.

Example 16

medium

Two ribbons are

\frac{3}{8}

m and

\frac{4}{8}

m. What is their total length?

Each bar represents one metre split into 8 equal sections. Joining the two ribbons fills 7 of those sections.

Example 17

medium

Add

\frac{9}{10}+\frac{3}{10}

and write as a mixed number.

Example 18

medium

Add

\frac{4}{15}+\frac{6}{15}

and simplify.

Ten of 15 parts shaded in the sum bar reduces to 2/3 after dividing numerator and denominator by 5.

Example 19

medium

Add

2\frac{3}{8}+1\frac{7}{8}

Example 20

challenge

A pizza is cut into 8 equal slices. Mia eats

\frac{2}{8}

, then

\frac{3}{8}

more. What fraction is left?

Example 21

challenge

\frac{a}{12}+\frac{b}{12}=\frac{9}{12}

and

a=2b

, find

a

and

b

Example 22

challenge

Express

\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}

as a single fraction and as a decimal.

Example 23

easy

Add

\frac{1}{9}+\frac{5}{9}

Example 24

easy

Add

\frac{2}{11}+\frac{6}{11}

Example 25

easy

A bowl has

\frac{4}{10}

kg of rice. You add

\frac{3}{10}

kg more. How much rice is in the bowl?

Example 26

easy

Add

\frac{2}{15}+\frac{4}{15}

and simplify.

Example 27

medium

Add

\frac{7}{12}+\frac{11}{12}

and write as a mixed number.

Example 28

medium

Add

\frac{3}{14}+\frac{5}{14}+\frac{6}{14}

and simplify.

Example 29

medium

Add

3\frac{2}{9}+1\frac{4}{9}

Example 30

medium

A runner completes

\frac{3}{10}

of a track, then another

\frac{4}{10}

. How much of the track is left?

Example 31

medium

Add

\frac{5}{16}+\frac{7}{16}

and simplify.

Example 32

medium

Three friends each ate

\frac{2}{12}

of a cake. How much of the cake did they eat together?

Example 33

medium

Compute

\frac{11}{20}+\frac{13}{20}

and write as a mixed number.

Example 34

medium

Two pitchers each hold water. Pitcher A holds

\frac{5}{8}

litre and pitcher B holds

\frac{6}{8}

litre. How much in total?

Example 35

hard

\frac{a}{9}+\frac{b}{9}=\frac{11}{9}

and

b=a+3

. Find

a

and

b

Example 36

hard

Bag A has

\frac{5}{12}

kg of flour, bag B has

\frac{7}{12}

kg, bag C has

\frac{11}{12}

kg. Total mass?

Example 37

hard

A recipe uses

\frac{7}{8}

cup oats in the morning and

\frac{5}{8}

cup oats in the afternoon. How many cups in total, and how many full cups can you make?

Example 38

challenge

Three distinct positive integers

a<b<c

satisfy

\frac{a}{15}+\frac{b}{15}+\frac{c}{15}=1

. How many such triples exist?

Example 39

challenge

For positive integer

n

, simplify

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

in closed form.

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Related Concepts

Fractions Addition Adding Fractions with Unlike Denominators Subtracting Fractions with Like Denominators

Background Knowledge

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

fractionsaddition