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Basic 5 · Mathematics · Number Operations

Multi-Step Word Problems

In this topic you will solve word problems that need two or more of the four operations.

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

  • Identify the steps needed in a word problem
  • Choose and order the correct operations
  • Check answers for reasonableness

What you already know

  • Multiplying by 2-digit numbers

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

Strand
Number
Sub-strand
Number Operations
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B5.1.2.5.1 – Solve multi-step word problems involving the four basic operations

Introduction

Mr Asante bought 15 bags of cement at GH₵95 each and paid a transport fee of GH₵120. He paid with GH₵1,600. How much change did he receive? This needs three steps.

1. A Problem-Solving Plan

  1. Understand: What is given? What must I find?
  2. Plan: Which operations, and in what order?
  3. Solve: Work out each step clearly.
  4. Check: Is the answer sensible? Estimate.

2. Worked Examples

Example 1

Mr Asante's change.

  1. Cost of cement: 15 × 95 = GH₵1,425
  2. Add transport: 1,425 + 120 = GH₵1,545
  3. Change: 1,600 − 1,545 = GH₵55

Answer: Mr Asante received GH₵55 change.

Example 2

A farmer harvested 1,248 oranges. He packed them equally into 24 baskets and sold each basket for GH₵35. How much did he earn?

  1. Oranges per basket: 1,248 ÷ 24 = 52
  2. He has 24 baskets to sell.
  3. Earnings: 24 × 35 = GH₵840

Answer: He earned GH₵840.

A builder buying cement bags and paying at a hardware shop
Figure 1: A shopping problem Draw a picture for a word problem you write.Illustration: Sirbus

3. Order of Operations

When a problem is written as one number sentence, do multiplication and division before addition and subtraction.

Example: 120 + 15 × 95 = 120 + 1,425 = 1,545.

Tip: Underline key words: "each", "altogether", "shared", "left", "change".

4. Key Words and Operations

Key words
OperationKey words
additionaltogether, total, sum, in all
subtractionleft, remain, difference, change
multiplicationeach, every, times, groups of
divisionshared, equally, each gets, how many groups

Key words are only hints. "Each" can appear in a multiplication problem ("15 bags at GH₵95 each") and in a division problem ("How many does each child get?"). Always read the whole problem and picture what is happening before you choose the operation. Then write each step as a number sentence with a label, so that anyone reading your work can follow it.

New words

multi-step
Needing more than one operation.
operation
Add, subtract, multiply or divide.
reasonable
Making sense.
order of operations
The rule for which operation to do first.
estimate
A close, rounded value.
key word
A word that hints at the operation.

Summary

  • Understand, plan, solve and check.
  • Choose and order the operations carefully.
  • Multiply and divide before adding and subtracting in one sentence.
  • Estimate to check your answer.

Class activity: Problem Writers

  1. Write a three-step word problem about a school event.
  2. Swap with another group and solve it.
  3. Present the solution with all steps.

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

Exercises

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

  1. 1. Which key word usually means divide?

    • A. Shared equally
    • B. Altogether
    • C. Left
    • D. More than
    Show answer
    Answer: Shared equallySharing means division.

  2. 2. 20 + 6 × 5 = ?

    • A. 50
    • B. 130
    • C. 31
    • D. 60
    Show answer
    Answer: 50Multiply first: 30 + 20.

  3. 3. Ama buys 3 books at GH₵45 each and pays with GH₵200. Her change is…

    • A. GH₵65
    • B. GH₵135
    • C. GH₵155
    • D. GH₵35
    Show answer
    Answer: GH₵653 × 45 = 135; 200 − 135.

  4. 4. Checking answers helps find mistakes.

    • A. True
    • B. False
    Show answer
    Answer: TrueEstimation checks reasonableness.

  5. 5. In 50 − 4 × 5, we subtract first.

    • A. True
    • B. False
    Show answer
    Answer: FalseMultiply first: 50 − 20 = 30.

  6. 6. Add, subtract, multiply and divide are the four ______.

    Show answer
    Answer: operationsThey are operations.

  7. 7. A class of 42 pupils contributes GH₵5 each. They spend GH₵150 on a party. How much is left?

    Show answer
    Answer: GH₵6042 × 5 = 210; 210 − 150 = 60.

  8. 8. A factory makes 1,350 sachets of water an hour. It works 8 hours a day for 6 days. How many sachets are made?

    Show answer
    Answer: 64,800 sachets1,350 × 8 = 10,800; × 6 = 64,800.

Homework

  1. Write and solve two multi-step word problems about prices at your local market.