Question

The calculation needed to find the cost of the factory tour was $5(29 students). Melissa used the expression $5(20 + 9). Mrs. Garcia used the expression $5(14 + 15). Explain why Mrs. Garcia’s method may be more difficult to do mentally.

Answer 1

Actually, I find Mrs. Garcia's method easier to do mentally. It depends on how well you know your multiples of 5. (5*15 = 75 is one I use fairly frequently)

Melissa's method has you calculate 5*20 = 100 and 5*9 = 45, then add the 3-digit number 100 to the 2-digit number 45, with the result 145. Adding 45 to 00 is easy and there are no "carry" operations involved, so the math is relatively straightfoward and easy.

Mrs. Garcia's method has you calculate 5*14 = 70 and 5*15 = 75, then add those 2-digit numbers together. Most folks don't have ready access to the product 5*15=75, so forming that product adds difficulty. The sum 70+75 involves a carry operation, so the math is a bit more complicated. The result is 145.

(The reason I find Mrs. Garcia's method easier is that I can do the final sum by doubling 7 tens, then adding 5. The only 3-digit number I have to carry in my head is the final result.)

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Subtraction adds a bit of complexity, but you could do the product as $5(30 -1) = $150 - 5 = $145.
Or, you can do it as $5(28 +1) = $140 +5 = $145.

Multiplying 5 by an even number is as easy as dividing that number in half, then appending a zero.
  5*14 = 10*7 = 70
  5*28 = 10*14 = 140.

Answer 2

Answer:

Mrs. Garcia’s method expands 29, using numbers that are not as easy to mentally multiply. The number 29 should be expanded using place value like Melissa did to make the multiplication simpler.

Step-by-step explanation: