Adding and subtracting fractions with the same denominator

Step 6 · Long division and equivalent fractions topics

Add and subtract fractions with the same denominator, move between mixed numbers and fractions greater than 1, and solve word problems with them.

Adding and subtracting parts

When the denominators match, the parts are the same size, so you just count them. $\frac{2}{8}$ + $\frac{3}{8}$ is 2 eighths and 3 eighths: 5 eighths, $\frac{5}{8}$ .

2/8 + 3/8

2 eighths and 3 eighths make 5 eighths.

Subtraction works the same way: take away parts of the same size and count what is left.

Example: Subtracting

What is $\frac{7}{10}$ − $\frac{4}{10}$ ?

Both are tenths.
7 tenths take away 4 tenths is 3 tenths.

Answer $\frac{3}{10}$

Mixed numbers and fractions greater than 1

A fraction can be more than 1. $\frac{7}{4}$ is 7 fourths: 4 fourths make 1 whole, and 3 fourths are left. As a mixed number that is $1\frac{3}{4}$ .

3/4

7 fourths: one whole bar and 3 fourths of another, which is 1 3/4.

Example: Adding mixed numbers

What is $2\frac{3}{5}$ + $1\frac{4}{5}$ ?

Add the wholes: 2 + 1 = 3.
Add the fifths: $\frac{3}{5}$ + $\frac{4}{5}$ = $\frac{7}{5}$ = $1\frac{2}{5}$ .
3 + $1\frac{2}{5}$ = $4\frac{2}{5}$ .

Answer $4\frac{2}{5}$

Example: Taking away from a whole

What is 3 − $\frac{1}{4}$ ?

Trade 1 whole for $\frac{4}{4}$ : 3 = 2 + $\frac{4}{4}$ .
$\frac{4}{4}$ − $\frac{1}{4}$ = $\frac{3}{4}$ .

Answer $2\frac{3}{4}$

Word problems with fractions

Example: A recipe

A recipe uses $\frac{3}{4}$ cup of flour for the dough and $\frac{2}{4}$ cup for the topping. How much flour is that?

$\frac{3}{4}$ + $\frac{2}{4}$ = $\frac{5}{4}$ .
$\frac{5}{4}$ = $1\frac{1}{4}$ .

Answer $1\frac{1}{4}$ cups

Example: A ribbon

A ribbon is $5\frac{1}{3}$ feet long. Ali cuts off $2\frac{2}{3}$ feet. How much is left?

Write both in thirds: $5\frac{1}{3}$ = $\frac{16}{3}$ and $2\frac{2}{3}$ = $\frac{8}{3}$ .
$\frac{16}{3}$ − $\frac{8}{3}$ = $\frac{8}{3}$ .
$\frac{8}{3}$ = $2\frac{2}{3}$ .

Answer $2\frac{2}{3}$ feet

A fraction times a whole number is repeated adding: 3 × $\frac{2}{5}$ = $\frac{2}{5}$ + $\frac{2}{5}$ + $\frac{2}{5}$ = $\frac{6}{5}$ .

Try it yourself

Work each one on paper first, then open the answer to check.

What is $\frac{3}{6}$ + $\frac{2}{6}$ ?
Show answer
$\frac{5}{6}$
What is $\frac{9}{10}$ − $\frac{6}{10}$ ?
Show answer
$\frac{3}{10}$
Write $\frac{11}{4}$ as a mixed number.
Show answer
$2\frac{3}{4}$
What is $1\frac{2}{3}$ + $2\frac{2}{3}$ ?
Show answer
$4\frac{1}{3}$ . 3 wholes, and $\frac{4}{3}$ = $1\frac{1}{3}$ .
A jug has $\frac{7}{8}$ liter of juice and $\frac{3}{8}$ liter is drunk. How much is left?
Show answer
$\frac{4}{8}$ liter, which is $\frac{1}{2}$ liter.