Division of Whole Numbers as Fractions

Discover the amazing connection between division and fractions!

1. A Division Can Be Written as a Fraction

The Big Idea

When you divide something equally, you create fractions!

number shared ÷ people sharing = $\dfrac{\text{number shared}}{\text{people sharing}}$

Example: Sharing 1 Pizza Among 3 Children

1 pizza cut into 3 equal parts

Situation: 1 pizza is shared equally among 3 children.

Division: 1 ÷ 3 = ?

Each child gets: $\frac{1}{3}$ of the pizza

Key Insight: The number being shared (1) becomes the numerator. The number of people sharing (3) becomes the denominator.

More Examples: Sharing 1 Item

1 ÷ 2 = $\frac{1}{2}$

one half

1 ÷ 4 = $\frac{1}{4}$

one quarter

1 ÷ 5 = $\frac{1}{5}$

one fifth

1 ÷ 8 = $\frac{1}{8}$

one eighth

2. Dividing Multiple Items Equally

The Pattern

When you share several items equally, the number of items goes on top and the number of people goes below.

number of items ÷ number of people = $\dfrac{\text{number of items}}{\text{number of people}}$

Example: Sharing 2 Pizzas Among 3 Children

Situation: 2 pizzas are shared equally among 3 children.

Division: 2 ÷ 3 = ?

Method: Cut each pizza into 3 equal pieces. Each child gets 2 pieces (one from each pizza), shaded in the picture for one child.

Each child gets: $\frac{2}{3}$ of a pizza

More Examples

3 ÷ 4 = $\frac{3}{4}$

4 ÷ 5 = $\frac{4}{5}$

4 ÷ 7 = $\frac{4}{7}$

3 ÷ 8 = $\frac{3}{8}$

6 ÷ 7 = $\frac{6}{7}$

5 ÷ 9 = $\frac{5}{9}$

Don't Forget to Simplify!

Some fractions can be simplified. Always give the fraction in its simplest form.

4 ÷ 6 = $\frac{4}{6}$ = $\frac{2}{3}$

Divide the numerator and the denominator by 2

6 ÷ 8 = $\frac{6}{8}$ = $\frac{3}{4}$

Divide the numerator and the denominator by 2

3. When There Are More Items Than People

Improper Fractions and Mixed Numbers

When the number of items is more than the number of people, each person gets more than 1 whole!

Example: Sharing 5 Cakes Among 4 Children

Situation: 5 cakes are shared equally among 4 children.

Step 1: 5 ÷ 4 = $\frac{5}{4}$ (improper fraction)

Step 2: Convert to mixed number: 5 ÷ 4 = 1 remainder 1. Each child gets 1 whole cake, and the last cake is cut into 4 equal quarters, one for each child.

Answer: $\frac{5}{4}$ = $1\frac{1}{4}$

Each child gets 1 whole cake and $\frac{1}{4}$ of another cake.

Converting Improper Fractions to Mixed Numbers

Method: Divide the numerator by the denominator.

The quotient becomes the whole number
The remainder becomes the new numerator
The denominator stays the same

7 ÷ 3 = $\frac{7}{3}$

7 = 3 × 2 + 1

= $2\frac{1}{3}$

9 ÷ 4 = $\frac{9}{4}$

9 = 4 × 2 + 1

= $2\frac{1}{4}$

11 ÷ 5 = $\frac{11}{5}$

11 = 5 × 2 + 1

= $2\frac{1}{5}$

17 ÷ 3 = $\frac{17}{3}$

17 = 3 × 5 + 2

= $5\frac{2}{3}$

4. Solving Word Problems

Problem-Solving Steps

Identify what is being shared and among how many
Write the division as a fraction
Simplify if possible
Convert to mixed number if needed
Include units in your answer

Practice 1: The Pizza Problem

4 pizzas are shared equally among 7 children. What fraction of a pizza does each child get?

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Solution:
4 ÷ 7 = $\frac{4}{7}$

Each child gets $\frac{4}{7}$ of a pizza.

Practice 2: The String Problem

Liz has 7 metres of string. She cuts it into 4 equal pieces. What is the length of each piece?

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Solution:
7 ÷ 4 = $\frac{7}{4}$
$\frac{7}{4}$ = $1\frac{3}{4}$

Each piece is $1\frac{3}{4}$ metres (or $\frac{7}{4}$ m) long.

Practice 3: The Water Problem

6 litres of water is poured equally into 8 flasks. How much water is in each flask?

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Solution:
6 ÷ 8 = $\frac{6}{8}$
$\frac{6}{8}$ = $\frac{3}{4}$ (divide the numerator and the denominator by 2)

Each flask has $\frac{3}{4}$ litre of water.

Practice 4: The Chocolate Problem

13 chocolate bars are shared equally among 5 children. How many chocolate bars does each child get?

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Solution:
13 ÷ 5 = $\frac{13}{5}$
13 = 5 × 2 + 3
$\frac{13}{5}$ = $2\frac{3}{5}$

Each child gets $2\frac{3}{5}$ chocolate bars.

Key Takeaways

1.A division can be written as a fraction: 3 ÷ 4 = $\frac{3}{4}$
2.The numerator is what's being shared; the denominator is how many are sharing
3.When numerator > denominator, you get an improper fraction (more than 1 whole)
4.Convert improper fractions to mixed numbers by dividing
5.Always simplify your fractions and include units in word problems