Question 1

What is the left-to-right method for addition?

Accepted Answer

Basic addition is taught by adding from right to left. For example, 456 + 789 would be solved by adding the rightmost column to get 5, carry one, and then work towards the leftmost column by carrying over digits. While this is an effective method when using paper, it is harder when calculating mentally because numbers read from left to right and it is also confusing to have to swap the digits mentally.

Question 2

What is the trick for multiplying by 11 or 111?

Accepted Answer

For any number n, n x 11 = n x (10 + 1) = 10n + n. This means multiplying a number by 11 is the same as adding that number with the same number but with an extra 0 added to it. For example, 34 x 11 = 340 + 34 = 374. A quicker method is to notice that 374 is just 34 with a 7 (because 3 + 4 = 7) sandwiched in between the two digits. For 3-digit numbers, the unit digit is the same, the tens digit is the unit plus the tens, the hundreds digit is the hundred plus the tens, and the thousands is the hundreds, keeping in mind any carrying. Similarly, multiplying by 111 means adding the number with one extra zero and two extra zeros.

Question 3

How do you square numbers quickly using neighboring squares?

Accepted Answer

Using the property (n+1) squared = n squared + 2n + 1 can be very helpful for quickly solving squares that are one unit more than easy squares. For example, 31 squared = (30 + 1) squared = 900 + 60 + 1 = 961. Similarly, (n-1) squared = n squared - 2n + 1 works for squares one unit less, e.g., 39 squared = (40 - 1) squared = 1600 - 80 + 1 = 1521. These methods take only a few seconds to do mentally.

Question 4

What is the quick way to square numbers ending in 5?

Accepted Answer

To square a number ending in 5, multiply the non-five part by itself plus 1, then add 25 at the end. For example, to find 35 squared, calculate 3 x (3 + 1) = 3 x 4 = 12 and add 25, to get 35 x 35 = 1225. More examples: 95 x 95 = 9 x 10 followed by 25 = 9025, and 125 x 125 = 12 x 13 followed by 25 = 15625.

Question 5

How can addition help check subtraction problems?

Accepted Answer

For subtraction problems, use addition to check your work. For example, 85 - 47 = 38. Check by adding: 38 + 47 = 85. This reverse calculation confirms accuracy.

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