Topic 3 of 9

Dividing whole numbers and unit fractions

Step 7 · Fraction and decimal arithmetic topics

See a fraction as a division, find how many unit fractions fit into a whole number, and share a unit fraction among several people.

A fraction is a division

$\frac{3}{4}$ is also 3 ÷ 4. Share 3 pizzas equally among 4 people and each gets $\frac{3}{4}$ of a pizza.

Pizza 1

Pizza 2

Pizza 3

3 pizzas, each cut into 4: every person takes one fourth of each pizza, 3/4 in all.

Example: A division as a fraction

7 meters of rope is cut into 2 equal pieces. How long is each piece?

7 ÷ 2 = $\frac{7}{2}$ .
$\frac{7}{2}$ = $3\frac{1}{2}$ .

Answer $3\frac{1}{2}$ meters

Whole number ÷ unit fraction

A unit fraction has 1 on top, like $\frac{1}{3}$ . 4 ÷ $\frac{1}{3}$ asks: how many thirds fit into 4? Each whole holds 3 thirds, so 4 wholes hold 4 × 3 = 12.

0 to 4 marked in thirds: 12 jumps of 1/3 reach 4.

Example: A whole number by a unit fraction

What is 5 ÷ $\frac{1}{4}$ ?

Each whole holds 4 fourths.
5 wholes hold 5 × 4 = 20 fourths.

Answer20

Unit fraction ÷ whole number

$\frac{1}{2}$ ÷ 3 asks: share half a cake among 3 people. Each gets a third of a half, which is $\frac{1}{6}$ of the cake.

A cake1/61/61/6

Half a cake shared by 3: each share is 1/6 of the whole cake.

Example: A unit fraction by a whole number

What is $\frac{1}{3}$ ÷ 4?

Share $\frac{1}{3}$ into 4 equal parts.
Each part is $\frac{1}{12}$ of the whole, because 3 × 4 = 12.

Answer $\frac{1}{12}$

Check by multiplying back: $\frac{1}{12}$ × 4 = $\frac{4}{12}$ = $\frac{1}{3}$ .

Try it yourself

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

Write 5 ÷ 8 as a fraction.
Show answer
$\frac{5}{8}$
What is 3 ÷ $\frac{1}{2}$ ?
Show answer
6. Each whole holds 2 halves.
What is 6 ÷ $\frac{1}{5}$ ?
Show answer
30.
What is $\frac{1}{4}$ ÷ 2?
Show answer
$\frac{1}{8}$
4 friends share $\frac{1}{2}$ pound of nuts equally. How much does each get?
Show answer
$\frac{1}{8}$ pound.