Fast Trick to Multiply Numbers Between 10 and 20

Fast Trick to Multiply Numbers Between 10 and 20

Fast Trick to Multiply Numbers Between 10 and 20

Multiplication is often seen as a daunting task, especially when dealing with numbers in the teens. But what if we told you there’s a simple mental math trick to multiply two numbers between 10 and 20 without using a calculator?

In this article, we’ll break down the fastest way to multiply numbers between 10 and 20 using an easy step-by-step method. Whether you’re preparing for an exam, improving your mental math, or just love number tricks, this technique will make multiplication a breeze!

Understanding the Trick

Let’s take an example: 14 × 17

Step-by-Step Approach

  1. Choose a base number
    • The simplest base to use is 10 because these numbers are slightly above it.
  2. Find the excess over 10
    • For 14, the excess over 10 is 4
    • For 17, the excess over 10 is 7
  3. Add the excess to the other number
    • Add 7 (from 17) to 14, which gives 21
    • Alternatively, add 4 (from 14) to 17, which also gives 21
  4. Multiply by 10
    • Multiply 21 by 10 → 210
  5. Multiply the excess values together
    • Multiply 4 × 7 → 28
  6. Add the two results together
    • 210 + 28 = 238

Thus, 14 × 17 = 238

Why Does This Trick Work?

This method is based on algebraic expansion:(x+a)×(x+b)=x2+x(a+b)+ab(x + a) \times (x + b) = x^2 + x(a + b) + ab(x+a)×(x+b)=x2+x(a+b)+ab

Where x = 10, a = 4, and b = 7, giving us:102+10(a+b)+(a×b)10^2 + 10(a + b) + (a \times b)102+10(a+b)+(a×b)

which simplifies to our calculated result.

More Examples

Example 1: 12 × 16

  1. Excess over 10 → (12 → 2, 16 → 6)
  2. Add excess to the other number → 12 + 6 = 18
  3. Multiply by 10 → 18 × 10 = 180
  4. Multiply excess values → 2 × 6 = 12
  5. Final sum → 180 + 12 = 192

Thus, 12 × 16 = 192

Example 2: 15 × 19

  1. Excess over 10 → (15 → 5, 19 → 9)
  2. Add excess to the other number → 15 + 9 = 24
  3. Multiply by 10 → 24 × 10 = 240
  4. Multiply excess values → 5 × 9 = 45
  5. Final sum → 240 + 45 = 285

Thus, 15 × 19 = 285

Practice Questions

Try using this trick to quickly solve these:

  1. 13 × 18 = ?
  2. 11 × 17 = ?
  3. 16 × 19 = ?
  4. 12 × 15 = ?

Comment your answers below!

Final Thoughts

Mastering this trick will not only make your mental math faster but also help you develop a deeper understanding of number relationships. With enough practice, you’ll be able to solve such problems in seconds.

Fast Trick to Multiply Numbers Between 10 and 20