Answer:
- (10 -2)(45)
- 8(40 +5)
- (8)(5)(10 -1)
Explanation:
There are various mental math strategies that can be used for this problem. Here, we are specifically asked for one involving addition or subtraction, as the distributive property applies to the product of a value and a sum.
Option 1
We can write 8 = 10 -2, as both 10 and 2 are easy to multiply by:
8 × 45 = (10 -2)(45) = 450 -90 = 360
Option 2
We can write 45 = 40 +5, which is how you would do this multiplication in the conventional "long multiplication" way.
8 × 45 = 8(40 +5) = 320 +40 = 360
Option 3
If you recognize that 45 = 9×5, you can rewrite 45 as either of ...
- 45 = (10 -1)(5)
- 45 = (10 -1)(5) = 50 -5
Then the distributive property application could be either of ...
8 × 45 = (8)(5)(10 -1) = 400 -40 = 360
8 × 45 = (8)(50 -5) = 400 -40 = 360
__
Additional comment
Multiplication methods can also be used to compute this mentally:
8 × 45 = 4×2 × 45 = 4 × (2×45) = 4 × 90
8 × 45 = 8 × 5 × 9 = 40 × 9
8 × 45 = 2×2×2 × 45 = 2(2(2×45))