Quickly multiply when the unit digits add up to 10

Introduction

This mathematics trick helps to quickly multiply a pair of numbers when:

• The sum of unit digits of the pair should be equal to 10.
• The remaining digits of both the numbers should be exactly the same.

• Examples of such pair of numbers:

  • 73 ✕ 77
  • 32 ✕ 38
  • 41 ✕ 49
  • 65 ✕ 65
  • 84 ✕ 86

Choose a pair of Multiplier & Multiplicand

The Trick is...

38 ✕ 32 = 1216

The Trick in detail

• Step 1: Ignoring the unit digit (or the ones digit) of either multiplicand or multiplier, take the remaining digits as a number.
• Step 2: Multiply the remaining digits as a number by its successor.
• Step 3: Multiply the unit digits of the multiplier and the multiplicand.
• Step 4: Place the products from Step 2 and Step 3 to get the required solution of the given multiplication problem.

Some pairs of bigger numbers

Let's use the same trick to quickly find the product of some pairs of bigger numbers whose sum of unit digits is equal to 10.

• Step 1: Ignoring the unit digit (or the ones digit) of either multiplicand or multiplier, take the remaining digits as a number.
• Step 2: Multiply the remaining digits as a number by its successor using the trick.†
• Step 3: Multiply the unit digits of the multiplier and the multiplicand.
• Step 4: Place the products from Step 2 and Step 3 to get the required solution of the given multiplication problem.