Practice Adding Fractions with Like Denominators in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

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 2

challenge

For positive integer

n

, simplify

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

in closed form.

Example 3

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 4

medium

Add

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

Example 5

medium

Express

\frac{4}{20}+\frac{6}{20}

in lowest terms.

Example 6

easy

Add

\frac{1}{6}+\frac{4}{6}

One sixth plus four sixths fills five of the six equal parts in the result bar.

Example 7

challenge

Express

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

as a single fraction and as a decimal.

Example 8

medium

Find the missing numerator:

\frac{4}{13}+\frac{\square}{13}=\frac{11}{13}

Example 9

medium

Add

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

and write the result as a mixed number.

Example 10

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 11

medium

Add

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

Example 12

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 13

easy

Worked example: add

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

and show why the denominator does not change.

Example 14

medium

Compute

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

and write as a mixed number.

Example 15

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 16

hard

Find all positive integers

n\le 10

such that

\frac{n}{12}+\frac{n}{12}

simplifies to a unit fraction

\frac{1}{k}

Example 17

easy

True or false:

\frac{3}{10}+\frac{2}{10}=\frac{5}{20}

Example 18

easy

Add

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

Two fourths fill exactly half the bar, showing why 2/4 simplifies to 1/2.

Example 19

challenge

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

and

a=2b

, find

a

and

b

Example 20

easy

A jug contains

\frac{2}{7}

litre of water. You pour in another

\frac{3}{7}

litre. How much water is in the jug?

The jug starts with 2 seventh-parts and gains 3 more, for a total of 5 out of 7.

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Related Concepts

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