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
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- 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
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- 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.
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- The sum of the first 10 integers is ______. (Do not use a calculator.)
- '55' ✓
Exit quiz
- The __________ says that multiplying a sum is the same as multiplying each addend and summing the result.
- commutative law
- associative law
- distributive law ✓
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- Match each law with an example of the law.
- Commutative⇔✓
- Associative⇔✓
- Distributive⇔✓
- Without using a calculator, use the distributive law to work out: = ______
- '13' ✓
- Without using a calculator, use the distributive law to work out: = ______
- '4950' ✓
- Work out the missing number: ______
- '0.7' ✓
- Work out the missing number: ______
- '0.8' ✓
Worksheet
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Presentation
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Video
Lesson Details
Key learning points
- 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.
Common misconception
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
Keywords
Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.
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