Percentages and Ratios
Primary 6 · Mathematics
Percentages and Ratios
Lesson 1 of 6
15 min
Let's begin
Keza brings her report home. She scored 45 out of 50 in Mathematics and 17 out of 20 in English. Her father asks, "Which subject did you do better in?" Keza is stuck: 45 is bigger than 17, but the tests were out of different totals.
Percentages solve Keza's problem. They turn every score into a score "out of 100", so you can compare them fairly. By the end of this lesson you will be able to answer her father.
The word percent means "for each 100" or "out of 100". Its sign is %. So 37% means 37 out of every 100.
Picture a square cut into 100 small equal squares. If 37 of them are coloured, then 37% of the big square is coloured. If all 100 are coloured, that is 100%: the whole thing. Half of it is 50%.
Write the percentage over 100, then simplify.
Worked example
Write 35% as a fraction.
Step 1: 35% = 35100.
Step 2: 35 and 100 can both be divided by 5. 35 ÷ 5 = 7 and 100 ÷ 5 = 20.
Answer: 35% = 720.
Worked example
Write 8% as a fraction. 8% = 8100. Divide both by 4: 8100 = 225.
Divide by 100. Dividing by 100 moves the decimal point two places to the left.
45% = 45 ÷ 100 = 0.45
7% = 7 ÷ 100 = 0.07 (you need a 0 to fill the empty place)
12.5% = 12.5 ÷ 100 = 0.125
Do the opposite: multiply by 100, which moves the decimal point two places to the right, then write the % sign.
0.6 = 0.6 × 100 = 60%
0.125 = 0.125 × 100 = 12.5%
1.5 = 1.5 × 100 = 150% (more than one whole)
Way 1: make the denominator 100. 34: multiply the top and bottom by 25 to get 75100, which is 75%. For 720, multiply the top and bottom by 5 to get 35100 = 35%.
Way 2: multiply by 100. This works for every fraction. 38 × 100 = 300 ÷ 8 = 37.5, so 38 = 37.5%.
| Fraction | Decimal | Percentage |
|---|---|---|
| 12 | 0.5 | 50% |
| 14 | 0.25 | 25% |
| 34 | 0.75 | 75% |
| 15 | 0.2 | 20% |
| 110 | 0.1 | 10% |
| 1100 | 0.01 | 1% |
Mathematics: 4550. Multiply the top and bottom by 2 to get 90100 = 90%.
English: 1720. Multiply the top and bottom by 5 to get 85100 = 85%.
90% is more than 85%, so Keza did better in Mathematics.
Tip
Per cent = per hundred. Going into a percentage, the decimal point jumps two places to the right (× 100). Coming out of a percentage, it jumps two places back to the left (÷ 100).
Answers
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Quick check
Write 40% as a fraction in its simplest form.
