Basic 6 · Mathematics · Fractions
Comparing Fractions, Decimals and Percentages
In this topic you will compare and order a mixture of common fractions, decimals (up to thousandths) and percentages.
By the end of these notes you should be able to:
- Convert between fractions, decimals and percentages
- Compare and order a mixture of them
- Solve real-life comparison problems
What you already know
- Fractions and decimals (Basic 5)
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
- B6.1.3.1.1 – Compare and order a mixture of fractions: common percent and decimal fractions (up to thousandths)
Introduction
Ama scored ¾ in a test, Kofi scored 0.72 and Esi scored 78%. Who did best? To compare, we must write all three in the same form.
1. Three Forms of the Same Value
| Fraction | Decimal | Percentage |
|---|---|---|
| ½ | 0.5 | 50% |
| ¼ | 0.25 | 25% |
| ¾ | 0.75 | 75% |
| ⅕ | 0.2 | 20% |
| 1/10 | 0.1 | 10% |
| ⅛ | 0.125 | 12.5% |
| 1/1000 | 0.001 | 0.1% |
2. Converting
- Fraction → decimal: divide the numerator by the denominator (3 ÷ 8 = 0.375).
- Decimal → percentage: multiply by 100 (0.375 × 100 = 37.5%).
- Percentage → decimal: divide by 100 (64% = 0.64).
- Percentage → fraction: write over 100 and simplify (64% = 64/100 = 16/25).
3. Comparing and Ordering
Example 1
Who did best: Ama ¾, Kofi 0.72, Esi 78%?
- Ama: ¾ = 0.75
- Kofi: 0.72
- Esi: 78% = 0.78
Answer: 0.78 > 0.75 > 0.72, so Esi did best, then Ama, then Kofi.
Example 2
Order from smallest: 0.405, ⅖, 41%, 0.4
- ⅖ = 0.400; 41% = 0.410; write 0.4 as 0.400 and 0.405 as 0.405
- Compare thousandths: 0.400, 0.400, 0.405, 0.410
Answer: ⅖ = 0.4 < 0.405 < 41%
Tip: Add zeros to decimals so they all have the same number of places before comparing.
Common mistake: 0.5 is not smaller than 0.45. Write 0.50 and 0.45, then compare: 0.50 > 0.45.
Percentages are used in many places: shops advertise "20% off", banks pay interest in percentages, and test scores are often given as percentages. Being able to switch between fractions, decimals and percentages helps you decide which offer is better or which score is higher. For example, a 30% discount is better than a ¼ discount because ¼ = 25%.
New words
- decimal
- A number with a decimal point, e.g. 0.75.
- percentage
- A number out of 100 (%).
- thousandths
- The third place after the decimal point.
- equivalent
- Equal in value.
- convert
- To change from one form to another.
- order
- To arrange by size.
Summary
- Fractions, decimals and percentages can show the same value.
- Convert all to decimals (or percentages) before comparing.
- Add zeros to decimals to compare place by place.
- Order from smallest to largest or largest to smallest.
Class activity: Value Line-Up
- Each pupil gets a card with a fraction, decimal or percentage.
- Convert your card to a decimal.
- Line up in order from smallest to largest.
You need: Fraction strips cut from old cartons, Bottle tops, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. ¼ as a percentage is…
- A. 25%
- B. 4%
- C. 40%
- D. 14%
Show answer
Answer: 25%0.25 × 100.2. Which is largest?
- A. 0.8
- B. 3/4
- C. 78%
- D. 0.708
Show answer
Answer: 0.80.800 is biggest.3. 0.375 as a fraction is…
- A. 3/8
- B. 3/5
- C. 37/5
- D. 3/75
Show answer
Answer: 3/8375/1000 = 3/8.4. 50% = ½
- A. True
- B. False
Show answer
Answer: TrueHalf of 100.5. 0.09 > 0.1
- A. True
- B. False
Show answer
Answer: False0.09 < 0.10.6. 0.6 = ______%
Show answer
Answer: 60× 100.7. Order from largest: 0.65, ⅗, 62%.
Show answer
Answer: 0.65, 62%, ⅗0.65 > 0.62 > 0.60.8. Convert 7/20 to a decimal and a percentage.
Show answer
Answer: 0.35 and 35%7 ÷ 20 = 0.35.
Homework
- Find three prices with discounts in percentages and write each as a fraction and a decimal.