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Basic 4 · Mathematics · Number Operations

Mental Strategies for Multiplication

In this topic you will use quick mental strategies to multiply.

By the end of these notes you should be able to:

  • Multiply by 10 and 100
  • Use doubling and halving
  • Use the split (distributive) strategy

What you already know

  • Multiplication facts

Copy everything that has a blue line on its left into your notebook. The other parts are for reading.

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Number
Sub-strand
Number Operations
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B4.1.2.2.2 – Apply mental mathematics strategies for multiplication

Introduction

A trader sells 25 bags of rice at GH₵4 each. She works out 25 × 4 = 100 in her head in a second. How? She knows clever strategies.

1. Multiplying by 10 and 100

× 10: add one zero. 34 × 10 = 340.

× 100: add two zeros. 34 × 100 = 3,400.

2. Mental Strategies

Mental multiplication strategies
StrategyExampleHow
doubling16 × 4double 16 = 32, double again = 64
doubling and halving25 × 450 × 2 = 100
× 546 × 546 × 10 = 460, half = 230
split (distributive)7 × 147 × 10 + 7 × 4 = 70 + 28 = 98
× 99 × 2310 × 23 − 23 = 230 − 23 = 207
A rectangle split into 7 × 10 and 7 × 4 parts
Figure 1: The split strategy Draw a split rectangle for 6 × 13.Illustration: Sirbus

Example

8 × 15 in your head.

  1. Halve 8 = 4, double 15 = 30.
  2. 4 × 30 = 120

Answer: 8 × 15 = 120

Tip: Choose the strategy that makes the numbers easiest.

New words

mental
Done in your head.
strategy
A clever method.
double
To multiply by 2.
halve
To divide by 2.
split
To break a number into parts.
distributive
Multiplying each part and adding.

Summary

  • To multiply by 10 or 100, add zeros.
  • Doubling and halving keeps the product the same.
  • Split a number into tens and ones to multiply.
  • × 9 = × 10 then subtract one group.

Class activity: Strategy Match

  1. Your partner says a multiplication like 5 × 48.
  2. Solve it in your head.
  3. Explain the strategy you used.

You need: Bottle tops, Bundles of sticks, Exercise books

Exercises

Answer in your exercise book first, then check your answers.

  1. 1. 56 × 10 = ?

    • A. 560
    • B. 5,600
    • C. 56
    • D. 66
    Show answer
    Answer: 560Add one zero.

  2. 2. 25 × 8 = ?

    • A. 200
    • B. 160
    • C. 250
    • D. 225
    Show answer
    Answer: 20025 × 4 = 100, doubled = 200.

  3. 3. Which shows the split strategy for 6 × 17?

    • A. 6 × 10 + 6 × 7
    • B. 6 + 17
    • C. 60 × 17
    • D. 6 × 17 × 10
    Show answer
    Answer: 6 × 10 + 6 × 7Split 17 into 10 and 7.

  4. 4. 43 × 100 = 4,300

    • A. True
    • B. False
    Show answer
    Answer: TrueAdd two zeros.

  5. 5. 9 × 15 = 150 − 15 = 125

    • A. True
    • B. False
    Show answer
    Answer: False150 − 15 = 135.

  6. 6. 12 × 5 = half of 12 × 10 = ______

    Show answer
    Answer: 60120 ÷ 2 = 60.

  7. 7. Use doubling and halving to find 14 × 5.

    Show answer
    Answer: 7 × 10 = 70Halve 14, double 5.

  8. 8. A box has 24 pencils. Find the number in 9 boxes using the × 9 strategy.

    Show answer
    Answer: 24 × 10 = 240; 240 − 24 = 216 pencils× 10 then subtract one group.

Homework

  1. Work out the cost of 5 items at a shop price in your head. Check on paper.