Basic 5 · Mathematics · Fractions
Word Problems with Fractions
In this topic you will solve real-life word problems involving fractions of quantities and multiplication with fractions.
By the end of these notes you should be able to:
- Find fractions of money, mass and length
- Solve multi-step fraction problems
- Check answers with models
What you already know
- Multiplying fractions and whole numbers
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
- Strand
- Number
- Sub-strand
- Fractions
- Indicator
- B5.1.3.1.6 – Use models to solve problems involving multiplication of a whole number by a fraction and a fraction by a whole number
Introduction
In everyday life we often use fractions: "I spent ¾ of my money", "⅓ of the class are boys". Today we solve such problems.
1. Fractions of Quantities
| Problem | Working | Answer |
|---|---|---|
| ¾ of GH₵120 | 120 ÷ 4 × 3 | GH₵90 |
| ⅖ of 35 kg | 35 ÷ 5 × 2 | 14 kg |
| ⅚ of 3 m (300 cm) | 300 ÷ 6 × 5 | 250 cm |
2. Multi-Step Problems
Example 1
Abena had GH₵240. She spent ⅜ on books and ¼ on shoes. How much was left?
- Books: ⅜ of 240 = 240 ÷ 8 × 3 = GH₵90
- Shoes: ¼ of 240 = GH₵60
- Spent: 90 + 60 = GH₵150
- Left: 240 − 150 = GH₵90
Answer: Abena had GH₵90 left.
Example 2
A school has 840 pupils. ⅝ are girls. How many boys are there?
- Girls: 840 ÷ 8 × 5 = 525
- Boys: 840 − 525 = 315
Answer: 315 boys
3. Using Bar Models
A bar model helps you see the parts. Draw a bar for the whole, divide it into equal parts by the denominator, and shade the parts asked for.
Tip: Always find the unit fraction (one part) first.
Read each problem carefully to see what it asks for. Some questions ask for the part (how many girls), while others ask for the rest (how many boys) or the amount left after spending. If a question asks for "the rest", you can find the part and subtract it from the whole. You can also find the fraction left directly: if ⅝ are girls, then ⅜ are boys, and ⅜ of 840 = 315. Both methods give the same answer, which is a good way to check your work.
New words
- quantity
- An amount that can be measured.
- bar model
- A drawing using a bar to show parts of a whole.
- unit fraction
- One equal part, e.g. ⅛.
- remainder
- What is left.
- mass
- How heavy something is.
- length
- How long something is.
Summary
- To find a fraction of a quantity, divide by the denominator and multiply by the numerator.
- Multi-step problems may need adding and subtracting after finding fractions.
- Bar models make the parts clear.
- Always find one part first.
Class activity: Market Fractions
- Each group receives a pretend budget (e.g. GH₵360).
- Spend fractions of it on items and calculate the amounts.
- Draw a bar model of your spending.
You need: Fraction strips cut from old cartons, Bottle tops, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. ½ of GH₵50 = ?
- A. GH₵25
- B. GH₵50
- C. GH₵100
- D. GH₵20
Show answer
Answer: GH₵2550 ÷ 2.2. ⅔ of 90 kg = ?
- A. 60 kg
- B. 30 kg
- C. 45 kg
- D. 135 kg
Show answer
Answer: 60 kg90 ÷ 3 × 2.3. A class of 36 has ¼ absent. How many are present?
- A. 27
- B. 9
- C. 12
- D. 24
Show answer
Answer: 2736 − 9 = 27.4. ¾ of 100 = 75
- A. True
- B. False
Show answer
Answer: True100 ÷ 4 × 3.5. ⅗ of 40 = 30
- A. True
- B. False
Show answer
Answer: False⅗ of 40 = 24.6. ⅛ of 64 = ______
Show answer
Answer: 864 ÷ 8.7. Kwame walked ⅚ of a 12 km journey. How far did he walk?
Show answer
Answer: 10 km12 ÷ 6 × 5.8. Mr Owusu earns GH₵1,800. He spends ⅓ on rent, ¼ on food and saves the rest. How much does he save?
Show answer
Answer: GH₵750Rent 600 + food 450 = 1,050; 1,800 − 1,050 = 750.
Homework
- Ask an adult about a monthly budget (real or pretend) and work out fractions spent on three items.