Divide a proper fraction by a whole number

What you will learn

• Divide a proper fraction by a whole number

Models used: number sentences, stories, tables.

Before you start

• Multiply mixed numbers by whole numbers

Share the shaded part

We have three quarters of a cake to share between 2 children.

1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   We have three quarters of a cake to share between 2 children.

   Half a cake shared among 3 gives one sixth each: the half is cut into three.

2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Split each shaded quarter in half. Now there are 6 shaded eighths.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

3. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Each child gets 3 of those eighths. Together they still receive the original amount.

   3/4 ÷ 2 = 3/8

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   3/8 = 3/8: the same length, so the same amount.

Worked example: A new example, together

Calculate 2/3 ÷ 3.

1. Compare equal-sized fractional units. Read each value with the heading above its column.

   Picture cutting the shaded part into the required number of equal pieces.

   Dividing amounts expressed in the same fractional units compares their counts.

   Compare equal-sized fractional units

   Amount	One group size
   2/3	3

2. Compare equal-sized fractional units. Read each value with the heading above its column.

   Think: how many groups of size 3 fit into 2/3?

   Compare equal-sized fractional units

   Amount	One group size
   2/3	3

   Calculate 2/3 ÷ 3.

   2/9

3. Compare equal-sized fractional units. Read each value with the heading above its column.

   Think: how many groups of size 3 fit into 2/3?

   Compare equal-sized fractional units

   Amount	One group size
   2/3	3

4. Compare equal-sized fractional units. Read each value with the heading above its column.

   Rename into the same units: 2 parts shared into groups of 9 parts.

   Compare equal-sized fractional units

   Amount	One group size
   2/3	3

5. Compare equal-sized fractional units. Read each value with the heading above its column.

   2 ÷ 9 = 2/9.

   Compare equal-sized fractional units

   Amount	One group size
   2/3	3

6. Compare equal-sized fractional units. Read each value with the heading above its column.

   Check the result against the question we started with.

   2/9 × 3 = 2/3.

   We found 2/9. Dividing amounts expressed in the same fractional units compares their counts.

   Compare equal-sized fractional units

   Amount	One group size
   2/3	3

Common mistakes to discuss

• Dividing both numbers. Sharing a fraction makes the pieces smaller. 1/2 ÷ 3 = 1/6, because each half is split into three.

Check your understanding

• Divide a proper fraction by a whole number
• share a fraction into smaller equal parts
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.