Explain how the distributive law applies to division expressions with a common divisor | Maths

Starter quiz

For the following equation, which operation should we undertake first? 5 + 8 − 1 ÷ 2 =

Addition

Subtraction

Division ✓
For the following equation, which operation should we undertake first? (5 + 7) ÷ 2 =

Addition ✓

Subtraction

Division
12 + 12 ÷ 3 = ______

'16' ✓
Match the equations to the correct solutions.

5 + 8 ÷ 2 =

⇔

9 ✓

(12 + 8) ÷ 4 =

⇔

5 ✓

14 + 10 ÷ 2 =

⇔

19 ✓

(30 + 20) ÷ 5 =

⇔

10 ✓
Match the equations to the correct solutions.

30 − 10 ÷ 2 =

⇔

25 ✓

(16 − 4) ÷ 4 =

⇔

3 ✓

14 − 8 ÷ 2 =

⇔

10 ✓

(20 − 10) ÷ 5 =

⇔

2 ✓
Tick the equation which has the lowest value.

30 + 20 ÷ 5 =

(30 + 20) ÷ 5 =

30 − 20 ÷ 5 =

(30 − 20) ÷ 5 = ✓

Exit quiz

Which expression has the same value as this expression? 24 ÷ 4 + 40 ÷ 4

(24 + 40) ÷ 4 ✓

(24 + 4) ÷ 4

(24 + 4) ÷ 40
How many coins are there in total? Which of the following correctly shows how to use the distributive law to solve this problem?

(30 + 8) ÷ 2

(30 + 18) ÷ 2 ✓

(18 + 18) ÷ 2
35 ÷ 5 + 15 ÷ 5 = ______

'10' ✓
There are four tables in a classroom. Sam shares out 32 workbooks equally and Jun shares out 12 textbooks equally. How many books are there on each table? ______ books.

'11' ✓
Which expression matches this problem? The new version of Battle Robots game uses teams of 4 Jun has 20 robots and Sam has 32 robots. Who can make the most teams, and by how many?

(20 − 32) ÷ 4

(32 − 20) ÷ 4 ✓

(32 − 4) ÷ 20
Jun has 35 p in 5-pence coins and Sam has 25 p in 5-pence coins. How many more coins does Jun have than Sam? Jun has ______ more coins.

'2' ✓

Worksheet

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Lesson Details

Key learning points

5 divided by ___ minus 3 divided by ___ is equal to 2 divided by ___
Where there is a common divisor, the dividends can be subtracted and the difference divided by the divisor.
The distributive law can be very useful for solving problems where there is a common divisor.
You can use brackets in an equation to show that you have used the distributive law.

Common misconception

When writing the subtraction expression within the equation, children may write the parts to be divided in the order they appear in the problem, rather than putting the greatest one first.

Explore where the parts to be divided need to be written in a different order to how they appear in the problem. Compare this with addition and explore commutativity so that children can see how addition is commutative but subtraction is not.

Keywords

Distributive law - The distributive law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.
Divisor - The divisor is what we are dividing by.
Dividend - The dividend is the amount we are dividing.