PSLE Mathematics · Primary 5 and 6
Percentage
A percentage is a fraction out of 100. In upper primary you find a percentage of a quantity, express one quantity as a percentage of another, work with discount, GST and annual interest, find the whole when you know a part, and calculate percentage increase and decrease. Percentage questions reuse the same thinking as fractions and ratio, and they appear often in real-life money problems. This guide explains each type with clean examples, then walks through a full discount problem before three practice questions.
What the syllabus expects
- Express a fraction or decimal as a percentage, and a percentage as a fraction or decimal
- Express one quantity as a percentage of another
- Find a percentage part of a whole
- Solve problems involving discount, GST and annual interest
- Find the whole given a part and the percentage it represents
- Find percentage increase and percentage decrease
What a percentage means
35% means 35 out of 100, so 35% = 35/100 = 7/20 = 0.35. To change a fraction into a percentage, multiply it by 100%: 3/8 × 100% = 37.5%. To find a percentage of a quantity, change the percentage into a fraction or a decimal and multiply: 15% of $80 = 15/100 × 80 = $12. To express one quantity as a percentage of another, first write it as a fraction of the whole: 18 out of 24 pupils is 18/24 × 100% = 75%. Both quantities must be in the same unit, so 45 cm as a percentage of 2 m is 45/200 × 100% = 22.5%. Remember that 100% always stands for the whole, and deciding what that whole is comes first in every harder question.
Discount, GST and annual interest
A discount is an amount taken off the usual price. A 20% discount on a $45 bag is 20% × $45 = $9, so the sale price is $45 − $9 = $36. You can also say the customer pays 80% of $45, which is $36. GST is a tax added on top of a price. If the question says GST is 9%, a $200 bill becomes 109% of $200 = $218. When there is a discount as well, GST is charged on the price after the discount. Annual interest is money a bank pays each year on savings. At 2% interest per year, $5000 earns 2% × $5000 = $100 in one year. In each case, decide what 100% stands for: the usual price, the price before GST, or the amount saved in the bank.
Finding the whole from a part
When you know the amount that matches a percentage, use the unitary method. If 30% of the pupils in a hall is 84 pupils, then 10% is 84 ÷ 3 = 28 pupils, and 100% is 28 × 10 = 280 pupils. The same method finds a usual price from a sale price. After a 25% discount a shirt costs $27. The $27 is the part the customer pays, which is 100% − 25% = 75% of the usual price. So 75% = $27, 25% = $9 and 100% = $36. Matching the amount to the right percentage, 75% here and not 25%, is the step that decides the answer. Always check by working forwards: 25% of $36 is $9, and $36 − $9 = $27.
Percentage increase and decrease
Percentage change always compares the change with the original value. Percentage change = change ÷ original value × 100%. If the number of members in a club rises from 40 to 50, the increase is 10, and 10/40 × 100% = 25%. If the number then falls from 50 back to 40, the decrease is 10/50 × 100% = 20%, because the original value for this change is 50. This is why a 10% increase followed by a 10% decrease does not bring you back to the start. $100 increased by 10% is $110, and $110 decreased by 10% is $99. Work out each new amount in turn, and always ask which value you are comparing with.
Worked example
A shop sells a television at a 15% discount. Ms Wong pays $1020 for it after the discount. (a) What was the usual price of the television? (b) How much did she save?
- The usual price is the whole, so usual price = 100%.
- Ms Wong pays the part left after the discount: 100% − 15% = 85% of the usual price, so 85% = $1020.
- 1% = $1020 ÷ 85 = $12.
- Usual price = 100% = 100 × $12 = $1200.
- Amount saved = $1200 − $1020 = $180, which is also 15% × $1200 = $180.
- Check: 85% of $1200 = 0.85 × 1200 = $1020, which matches the question.
Answer: (a) $1200 (b) $180
Common mistakes
- Using the new value as the base for a percentage change. A rise from 40 to 50 is 10/40 = 25%, not 10/50 = 20%. Divide by the original value.
- Matching the sale price to the discount percentage. After a 20% discount, the price paid is 80% of the usual price, so set 80% equal to the sale price.
- Assuming a percentage increase and then the same percentage decrease cancel out. The second percentage is taken of a different amount, so work each step separately.
- Comparing quantities in different units, such as writing 45 cm out of 2 m as 45/2. Change to 45 cm out of 200 cm first.
- Adding GST before taking off the discount when the question says GST is charged on the discounted price. Take off the discount first, then add GST.
- Giving 0.25 when the question asks for a percentage. Multiply by 100% and write 25%.
Exam tips
- Begin each problem by writing '100% = ?' so you know which quantity is the whole before you calculate.
- When finding the whole, step through easy percentages such as 1%, 5% or 10% before scaling up to 100%.
- In multi-step money problems, set out each stage on its own line (usual price, discount, sale price, GST, total) so that each percentage is taken of the right amount.
Practice questions
1. Easy: 42 of the 120 pupils in a hall wear spectacles. What percentage of the pupils wear spectacles?
Show answer
35%. Working: 42/120 × 100% = 0.35 × 100% = 35%.
2. Medium: The price of a pen increased from $2.40 to $3.00. Find the percentage increase.
Show answer
25%. Working: the increase is $3.00 − $2.40 = $0.60, and 0.60/2.40 × 100% = 25%.
3. Harder: A dinner set usually costs $480. It is sold at a 25% discount, and then 9% GST is charged on the discounted price. How much does a customer pay altogether?
Show answer
$392.40. Working: discounted price = 75% of $480 = $360. GST = 9% of $360 = $32.40. Total = $360 + $32.40 = $392.40.
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