In the previous post, we have learned an interesting math shortcut on squaring numbers from 50 to 70. Before we explain why the shortcut works, we first continue this series by learning a shortcut on squaring numbers from 30 to 50. Notice that the steps are almost similar.
Example 1: 472
Step 1: First, consider how far is 47 from 50 (the base). This means that we want 50 – 47 = 3.
Step 2: Subtract 3 from 25. This gives us 23. This gives us 2 as the thousands and 3 as the hundreds digit of the product. That is, 472 = 23xx where xx are the tens and ones digits.
Note: The number 25 comes from squaring the tens digit of 50 (the base).
Step 3: To get xx, we square 3, the number we subtracted in Step 2. This gives us 9. Since xx represents a 2-digit number, we add 0 to make it 09.
The last post about multiplying by 11only works for two-digit numbers. There’s also a simple trick for multiplying by 11 for larger numbers, and it’s very easy! Let’s have an example of 236 × 11.
First, we write the problem like this:
0236 × 11
We write a zero in front of the number we are multiplying. You’ll see why in a moment. To find the product when multiplied by 11, we simply add each digit to the digit on its right, starting with the units digit.
The units digit is 6, but there is no digit to the right of 6, so we add 0: