Q. When your doing a multiplication problem, for example 84 times 37 = 3,108, how do you check the answer without a calculator?
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A. I'm kinda confused on how to check the answer, do i do 84 times 400??
here is a very old trick:
add up the digits of each factor
87---> 8+4 = 12 , do it again --- 1+2 = 3
37 ----> 3+7 = 10 ---> 1+0=1
multiply them : 3*1 = 3
take the answer and add up the digits
3108 ---> 3+1+0+8 = 12 -- 1+2 = 3
same result!, extremely high probability that our answer is correct
This is called "casting out nines"
To check the answer to a multiplication problem like 84 times 37 = 3,108, you can use a technique called estimation. Here's how you can check it without a calculator:
1. Round the numbers: Round 84 to the nearest multiple of 10, which is 80. Round 37 to the nearest multiple of 10, which is 40.
2. Multiply: Now, multiply the rounded numbers - 80 times 40. The product is 3,200.
3. Compare: Compare the estimated product (3,200) with the actual product (3,108). The numbers are close, which means the original answer is likely correct.
By using estimation, we can quickly check our answer without having to calculate the exact product again.