Let's Learn Mathematics

Halving & Doubling

Introduction

Mental math strategies are techniques that allow us to perform calculations quickly and efficiently in our heads, without the need for paper, calculators, or other tools. These strategies leverage number properties and mathematical relationships to simplify complex problems.

In this lesson, we'll focus specifically on the halving and doubling strategy, which is particularly useful for multiplication problems. This technique takes advantage of the fact that sometimes it's easier to work with numbers that are half or double the original numbers in a calculation.

Halving and Doubling Strategy

The Basic Idea

The halving and doubling technique involves adjusting two numbers being multiplied, that is:

Half one of the numbers, and

Double the other number.

If $a$ and $b$ are two numbers, we can express their product in a different way:

\(a \times b\)

$\Rightarrow \left(\dfrac{a}{2} \times 2b\right)$

It can also be written as:

$\Rightarrow \left(2a \times \dfrac{b}{2}\right) $

When one number is halved and the other is doubled, the product remains the same. We can use this to simplify multiplication problems by converting them into easier calculations.

Step-by-Step Process

  1. Identify if one of the numbers can be easily halved (even numbers work best)
  2. Halve one number while doubling the other
  3. Repeat the process if it makes the calculation simpler
  4. Multiply the resulting numbers

When to Use

This strategy is particularly useful when:

  • One number is even and can be easily halved
  • One number ends with 5 or 0
  • You're multiplying by numbers like 4, 8, 16, etc. (powers of 2)

Examples

Question 1

Use the halving and doubling strategy to calculate 18 × 15.

$18 \times 15$

$\Rightarrow \left(\dfrac{18}{2}\right) \times \left( 15 \times 2 \right)$

$\Rightarrow 9 \times 30 $

$\Rightarrow 270$

Question 2

Calculate 24 × 50 using the halving and doubling method.

$24 \times 50$

$\Rightarrow \left(\dfrac{24}{2}\right) \times (50 \times 2)$

$\Rightarrow 12 \times 100$

$\Rightarrow 1,200$

Question 3

Find the product of 45 × 8 using mental math strategies.

$45 \times 8$

(Since 8 is a power of 2, you can double 45 and halve 8:)

$\Rightarrow (45 \times 2) \times (8 \div 2)$

$\Rightarrow 90 \times 4$

$\Rightarrow 360$

Question 4

Use halving and doubling to calculate 125 × 16.

$125 \times 16$

$\Rightarrow (125 \times 2) \times \left(\dfrac{16}{2}\right) $

$\Rightarrow 250 \times 8$

$\Rightarrow 2,000$

Question 5

Calculate 35 × 12 using mental math strategies.

$35 \times 12$

(Double the odd number 35 and halve 12:)

$\Rightarrow (35 \times 2) \times (12 \div 2)$

$\Rightarrow 70 \times 6$

$\Rightarrow 420$

Practice Exercise

Question 1

Use the halving and doubling strategy to calculate \( 36 \times 25 \).

900

Question 2

Calculate \( 48 \times 50 \) using the halving and doubling method.

2,400

Question 3

Find the product of \( 32 \times 15 \) using mental math strategies.

480

Question 4

Use halving and doubling to calculate \( 125 \times 24 \).

3,000

Question 5

Calculate \( 56 \times 25 \) using the halving and doubling strategy.

1,400

Ready for more challenges?

Full Practice Set


Quick Test

You have 60 minutes to complete the test. Try to work on your speed as you prepare towards the final exam.

Good luck and remember to check your answers with the solutions provided. If you have any questions, feel free to ask your teacher or refer to the video lessons for more help.

Multiple Choice Questions

This section contains 40 multiple choice questions. You have 60 minutes to complete it.

Each question has four options labeled A to D. Select the correct answer for each question.

60:00
Question 1 of 140