Simplify the following using the distributive property: 79(67 − 34).
Answer: 79 × 67 − 79 × 34 = 23 − 712 = 112.
Step-by-step solution
Idea: Distributive property: p(q − r) = pq − pr. Multiplying 79 into the bracket first lets the 7s cancel neatly.
- 79(67 − 34) = 79 × 67 − 79 × 34.½ mark
- 79 × 67 = 69 = 23 (the 7s cancel). 79 × 34 = 2136 = 712.½ mark
- 23 − 712 = 812 − 712.½ mark
- = 112.½ mark
7/9 (6/7 − 3/4) = 1/12
Check: Bracket first: 67 − 34 = 2428 − 2128 = 328, and 79 × 328 = 21252 = 112 ✓.
Answer to write in the exam
79(67 − 34) = 79 × 67 − 79 × 34
= 23 − 712
= 812 − 712
∴ = 112
Common mistakes that cost marks
- Multiplying 79 by the first term only: 79 × 67 − 34.
- Changing the minus to plus when opening the bracket.
- Writing 79 × 34 = 2113 by adding the denominators.
How this can come in the exam
MCQ (1 mark)
Using the distributive property, 58 × 17 − 58 × 9 =
- 5
- 58
- 8
- 858
Show answer
(A) 5
58(17 − 9) = 58 × 8 = 5.
Short answer (2 marks)
Simplify 45(158 + 512) using the distributive property.
Show answer
45 × 158 + 45 × 512 = 32 + 13 (1 mark) = 96 + 26 = 116 (1 mark).Try one yourself
Simplify 35(109 − 56) using the distributive property.
Show answer
23 − 12 = 16.
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- Find the rational number x such that: 56(x + 35) = 56x + 12.
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