Adding Fractions with Unlike 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 Unlike 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 with different denominators by first rewriting them with a common denominator (usually the LCD), then adding numerators.

You can't add thirds and fourths directly—it's like adding apples and oranges. Convert both to twelfths first, then add.

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: You cannot add fractions until both are renamed into equal-size pieces with a common denominator.

Common stuck point: The procedure for adding fractions with unlike denominators is the easy part; the trap is adding numerators and denominators straight across. Asking "Do the fractions have different denominators that must be matched before adding?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Do the fractions have different denominators that must be matched before adding?

Worked Examples

Example 1

easy

Add

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

1/3 + 1/4 = 7/12

Answer

\frac{7}{12}

First step

Find the LCD of 3 and 4:

\text{LCD} = 12

Full solution

2
Rewrite each fraction: $\frac{1}{3} = \frac{4}{12}$ and $\frac{1}{4} = \frac{3}{12}$ .
3
Add: $\frac{4}{12} + \frac{3}{12} = \frac{7}{12}$ .

To add fractions with unlike denominators, first convert them to equivalent fractions with a common denominator (the LCD), then add the numerators.

Example 2

medium

Subtract

\frac{5}{6} - \frac{3}{8}

Example 3

easy

Worked example: add

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

1/2 + 1/5 = 7/10

Example 4

medium

Worked example: add

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

and explain the LCD choice.

Example 5

medium

Worked example: add

\frac{5}{6}+\frac{7}{10}

Example 6

hard

Worked example: a chef uses

\frac{3}{8}

kg of butter on Monday,

\frac{1}{6}

kg Tuesday, and

\frac{5}{12}

kg Wednesday. Total used?

Practice Problems

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

Example 1

medium

Add

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

Example 2

hard

Compute

\frac{7}{10} + \frac{2}{15} - \frac{1}{6}

Example 3

easy

Add

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

1/2 + 1/4 = 3/4

Example 4

easy

Add

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

1/3 + 1/6 = 1/2

Example 5

easy

Add

\frac{1}{4}+\frac{1}{8}

1/4 + 1/8 = 3/8

Example 6

easy

Find the least common denominator of

\frac{1}{3}

and

\frac{1}{4}

Example 7

easy

Add

\frac{2}{5}+\frac{1}{10}

2/5 + 1/10 = 1/2

Example 8

easy

Add

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

1/2 + 1/3 = 5/6

Example 9

easy

Subtract

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

3/4 − 1/2: how much more is shaded in the top bar?

Example 10

easy

Add

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

and state whether you needed to rename.

1/6 + 1/6 = 2/6 = 1/3

Example 11

medium

Add

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

2/3 + 1/4 = 11/12

Example 12

medium

Add

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

Example 13

medium

Subtract

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

5/6 − 1/4: compare the two shaded amounts

Example 14

medium

Add

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

Example 15

medium

A jug holds

\frac{2}{3}

liter; you add

\frac{1}{4}

liter more. How much is in the jug?

Jug: 2/3 L + 1/4 L = 11/12 L

Example 16

medium

Add

\frac{4}{9}+\frac{1}{6}

4/9 + 1/6 = 11/18

Example 17

challenge

A walker covers

\frac{1}{3}

of a trail before lunch and

\frac{2}{5}

after. What fraction of the trail remains?

Example 28

medium

Add

\frac{5}{6}+\frac{2}{9}

Example 29

medium

Subtract

\frac{7}{12}-\frac{1}{8}

Example 30

medium

Add

\frac{1}{4}+\frac{1}{6}+\frac{1}{12}

Example 31

medium

A board is

\frac{3}{4}

m long. Another is

\frac{5}{6}

m. Total length end-to-end?

Example 32

medium

Subtract

\frac{11}{15}-\frac{1}{6}

Example 33

medium

Compute

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

Example 34

hard

Compute

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

Example 35

hard

Solve for

x

x-\frac{2}{9}=\frac{1}{6}

Example 36

hard

A tank is filled

\frac{2}{5}

by pump A and

\frac{1}{4}

by pump B. What fraction remains, in lowest terms?

2/5 + 1/4 = 13/20 filled; 7/20 remains

Example 37

hard

Compute

\frac{3}{8}+\frac{5}{12}+\frac{1}{6}

and simplify.

Example 38

hard

A pizza is cut into 8 slices; a second pizza is cut into 6 slices. Tom eats

\frac{3}{8}

of the first and

\frac{1}{6}

of the second. What total fraction of one pizza did he eat?

Example 39

challenge

Find positive integers

a

and

b

with

a<b

such that

\frac{1}{a}+\frac{1}{b}=\frac{1}{2}

. List all solutions.

Example 40

challenge

Telescoping: compute

\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}+\cdots+\frac{1}{9\cdot 10}

← Back to Adding Fractions with Unlike Denominators Formula Explained Practice Mode

Related Concepts

Adding Fractions with Like Denominators Equivalent Fractions Least Common Multiple Subtracting Fractions with Unlike Denominators Mixed-Improper Conversion

Background Knowledge

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

adding fractions like denominatorsequivalent fractionsleast common multiple