Checking and securing understanding of the distributive law | Maths

Starter quiz

An operation is __________ if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.
- commutative
- associative ✓
- irregular
- unneeccary
Select all the examples of the associative law.
- 31 + 4 = 4 + 31
- (17 + 3) + 3 = 17 + (3 + 3) ✓
- 2 × 8 × 5 = 2 × (8 × 5) ✓
- 15 – 10 = 10 – 15
Use the commutative law you can rewrite 10 + 4 as ______.
- '4 + 10' ✓
Match each calculation to an equivalent commutative calculation.
- 3 + 12 + 4
  
  ⇔
  
  12 + 3 + 4 ✓
- 3 × 12 × 4
  
  ⇔
  
  4 × 3 × 12 ✓
- A + 3 + B
  
  ⇔
  
  B + A + 3 ✓
Andeep says, "Division is commutative because 12 ÷ 4 ÷ 3 = 1 and is the same as 12 ÷ 3 ÷ 4 = 1." Select the correct statement.
- He is correct as both answers do equal 1.
- He is incorrect as the commutative law would also give 4 ÷ 3 ÷ 12 which isn't 1 ✓
- He is correct as he has repositioned all the numbers.
The sum of the first 10 integers is ______. (Do not use a calculator.)
- '55' ✓

The __________ says that multiplying a sum is the same as multiplying each addend and summing the result.
- commutative law
- associative law
- distributive law ✓
Match each law with an example of the law.
- Commutative
  
  ⇔
  
  $9 + 10 + 11 = 9 + 11 + 10$ ✓
- Associative
  
  ⇔
  
  $(5 × 4) × 2 = 5 × (4 × 2)$ ✓
- Distributive
  
  ⇔
  
  $12 × (4 + 3) = 48 + 36$ ✓
Without using a calculator, use the distributive law to work out: $1.3\times7.2 + 1.3\times2.8$ = ______
- '13' ✓
Without using a calculator, use the distributive law to work out: $50\times99$ = ______
- '4950' ✓
Work out the missing number: $22 \times 0.3 + 22 \times$ ______ $= 22$
- '0.7' ✓
Work out the missing number: $4.8 \times 0.6 + 4.8 \times 1.2 − 4.8 \times$ ______ $= 4.8$
- '0.8' ✓

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The distributive law can be used when two (or more) values have a common factor.
By using the distributive law, calculations can be made easier.
Any common factor can be used but the highest is often the most efficient.

The distributive law only uses addition eg 24 x 99 = 24 x (90 + 9) = 24 x 90 + 24 x 9

Subtraction is important as it can simplify the calculation 24 x 99 = 24 x (100 - 1) = 24 x 100 - 24 x 1

Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.