SOLUTION: Below are the multiplication problems. 1). 17 x 23 ( I was informed to subtract 9 from 400). 2. 23 x 37 ( I was informed to subtract 49 from 900). 3). 18 x 30 ( I was inf

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Question 1206526: Below are the multiplication problems.
1). 17 x 23 ( I was informed to subtract 9 from 400).
2. 23 x 37 ( I was informed to subtract 49 from 900).
3). 18 x 30 ( I was informed to subtract 36 from 576).
What type of math strategy is this?
Found 3 solutions by math_tutor2020, greenestamps, josgarithmetic:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I'll focus on problem 1 only.

Note how 20 is the midpoint of 17 and 23.
midpoint = (a+b)/2

17 x 23 = (20 - 3) x (20 + 3)
17 x 23 = 20^2 - 3^2
17 x 23 = 400 - 9
17 x 23 = 391
I used the difference of squares rule.
The other two problems will use a similar approach.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


These are all examples of a strategy for mental calculations based on the pattern (A+B)(A-B)=A^2-B^2

17*23 = (20-3)(20+3) = 20^2-3^2 = 400-9

23*37 = (30-7)(30+7) = 30^2-7^2 = 900-49

18*30 = (24-6)(24+6) = 576-36 = 540

While that strategy can of course be used on the last example, it is not a good place to use it, since 18*30 is much more easily calculated as 18*3*10.
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
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3).
18 x 30 ( I was informed to subtract 36 from 576).
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?
Why use THOSE?






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