Mental Math Shortcut on Multiplying by 5

Mental math shortcut is one of the topics that we will be discussing in this blog. After discussing multiplication by 11 and squaring numbers ending in 5, let us discuss about the shortcut of multiplying by 5.

The Mental Math Calculation

Example 1: How do you multiply 28 × 5?

Instead of multiplying 28 by 5,

(1) Multiply 28 by 10: 28 × 10 = 280 

(2) Divide the product in (1) by 2: 280  ÷ 2 = 140

Example 2: 65 × 5

(1) Multiply 28 by 10: 65× 10 = 650

(2) Divide the product in (1) by 2: 650 ÷ 2 = 325

multiplying by 5

Notice that in dividing 650 by 2, you can split 650 into 600 and 50 and get half of each. Half of 600 is 300 and half of 50 is 25, so the quotient is 325.

Example: 360 × 5

(1) Multiply 360 by 10: 360× 10 = 3600

(2) Divide the product in (1) by 2: 3600 ÷ 2 = 1800

The method above will work for larger number of digits. It is easy to master it so you can experiment with different numbers and explore how the shortcut works.

The Secret Behind the Math Shortcut

The secret behind the mental math shortcut is easy that even elementary school students can detect them. Multiplying a number by 5 is the same as multiplying by 10 and dividing by 2. If we let n be the number, then multiplying by 10 (Step 1) gives a product of 10n. Now, if we divide 10n by 2 (Step 2), the result is 5n which is n multiplied by 5.

 

Leave a Reply

Your email address will not be published. Required fields are marked *