This sub-topic teaches you how to find the starting amount of something when you only know a part of it and what percentage that part represents. This is useful for problems involving discounts, increases, or changes over time, where you need to work backwards to find the initial value.
❓ Before you read — have a guess: If a shirt is on sale for 20% off, what percentage of its original price are you paying?
80%
⚡ Key points — the 5 things to remember
The original quantity always represents 100%.
A percentage increase means the new amount is more than 100% of the original.
A percentage decrease (discount) means the new amount is less than 100% of the original.
To find the original quantity, divide the known part by its corresponding percentage (as a decimal or fraction).
Always ensure you are using the correct percentage that corresponds to the given part.
What you must be able to do
Find the starting amount when you know a part of it and its percentage.
Solve word problems about finding the whole amount when you are given a part and its percentage.
The Original Quantity is Always 100%
The original amount (or whole) is the starting value before any changes like increases or decreases. It always represents 100%. A part is a portion of this original amount, expressed as a percentage.
If an amount increases by 10%, the new amount is 100% + 10% = 110% of the original.
If an amount decreases by 20%, the new amount is 100% - 20% = 80% of the original.
You must always know what percentage the given 'part' represents.
The sale price of $80 is 80% of the unknown original price.
When you are asked to find the original quantity, you are looking for the value that represents 100%. The problem will give you a 'part' of this original quantity and tell you what percentage that 'part' is. For example, if a shirt is sold at a 20% discount, the price you pay is 80% of the original price. The price you pay is the 'part', and 80% is its corresponding percentage.
⚠️ Common Mistake
If a discounted price is $80 after a 20% discount, I should add 20% of $80 to find the original price. — Correct: The discounted price of $80 is 80% of the original price. You cannot add 20% of the new price to find the original. The 20% discount was taken from the original price.
💡 Exam Tip
Always identify what percentage the given number represents. If it's a discounted price, it's (100% - discount percentage). If it's an increased amount, it's (100% + increase percentage).
💡 Exam Tip
Draw a simple model to visualise the relationship between the part and the whole. This helps you see what 100% means.
📍 Singapore Focus
In retail and shopping scenarios, understanding that the sale price is a 'part' and the original price is the 'whole' (100%) is key. For example, when a shop gives a discount, the price you pay is a smaller percentage of the original.
Calculate Original Quantity: Part ÷ Percentage
To find the original amount (the whole), you divide the given part by the percentage it represents. This percentage must be written as a decimal or a fraction.
Convert percentages to decimals (e.g., 80% = 0.8) or fractions (e.g., 80% = 80/100) before dividing.
The formula helps you reverse a percentage change to find the starting value.
P / (X / 100)
Original Amount
The starting quantity (the whole)
$
P
The part or new amount given
$
X
The percentage that P represents
%
Worked example🧰 Before-after concept
After a 15% increase, the number of students in a club became 92. What was the original number of students?
Find the percentage of the original amount that 92 students represent.
Why this step?We need to know what percentage the new number (92) is of the original amount.
Convert this percentage to a decimal.
Why this step?Percentages must be converted to decimals or fractions for calculations.
Divide the new number of students by the decimal percentage to find the original number.
Why this step?Dividing the part by its percentage (as a decimal) gives us the whole (original amount).
80 students
✏️ Now you try
A shop sold a toy for $42 after a 30% discount. What was the original price of the toy?
What percentage of the original price does $42 represent?100% - 30% = 70%
Convert this percentage to a decimal.70% = 0.7
Calculate the original price.$42 / 0.7 = $60
Reveal the answer$60
92 students represent 115% of the original number.
This method is crucial for problems where you know the result of a percentage change and need to find the starting point. Think of it as reversing the operation. If something increased, you divide by (1 + increase percentage). If it decreased, you divide by (1 - decrease percentage).
⚠️ Common Mistake
To find the original amount, I should divide by '20' if the percentage is 20%. — Correct: You must divide by the decimal or fractional form of the percentage. 20% is 0.20 or 20/100, not just 20.
💡 Exam Tip
Always write the percentage as a decimal (e.g., 115% = 1.15) or a fraction (e.g., 115/100) before dividing.
💡 Exam Tip
Check your answer: If you found an original amount after a discount, the original amount should be higher than the discounted price. If it was an increase, the original amount should be lower than the new amount.
📍 Singapore Focus
This calculation is used in business and financial scenarios to find the cost price when you know the selling price and profit percentage, or to determine the original population before a recorded change.
🪤 Watch for these traps
The wrong answers examiners plant to catch you — and how to dodge them.
Tempting answer$80 + (20% of $80) = $96 (for a 20% discount problem).
Looks right because Students mistakenly think the 20% discount applies to the new, smaller amount.
But actually The 20% discount was applied to the original price, not the discounted price. The $80 is 80% of the original.
✓ How to avoid it Always identify the base for the percentage. The discount is of the original.
Tempting answer$500 (if $100 is 20% of the original, student calculates $100 / 20).
Looks right because Student sees 'divide by percentage' and uses the number directly.
But actually Percentages must be converted to decimals or fractions (e.g., 20% = 0.2) before division.
✓ How to avoid it Remember that 'percent' means 'per hundred'. Always divide by (percentage / 100).
🔍 Question Decoder
What exam phrasings are really asking for.
When the question says…
It is testing…
Your move
What was the original price?
Finding the whole given a part and its percentage.
Identify the given part and its corresponding percentage (100% ± change), then divide.
Find the amount before the increase/decrease.
Finding the original quantity.
Determine if the given amount is (100% + increase) or (100% - decrease) of the original.
🧭 Understand → Plan → Work → Check
How to answer: Word problems involving finding the original quantity.
1Understand: Read the problem carefully. What is given? What do you need to find?
1 mark
2Plan: Decide which percentage the given value represents. Choose the correct formula or method (e.g., model drawing, division).
1 mark
3Work: Show all your calculations clearly, step-by-step, with units.
1-2 marks
4Check: Does your answer make sense? Is it reasonable? (e.g., if it was a discount, original should be higher).
Example: A bicycle was sold for $270 after a 10% discount. What was its original price?
✅ Earns the mark
“1. Understand: Given: Sale price = $270, Discount = 10%. Find: Original price.
2. Plan: The sale price ($270) is 100% - 10% = 90% of the original price. To find the original price (100%), I will divide $270 by 90%.
3. Work:
90% = $270
1% = $270 ÷ 90 = $3
100% = $3 × 100 = $300
Original price = $270 / 0.9 = $300
4. Check: $300 - (10% of $300) = $300 - $30 = $270. The answer is reasonable.
The original price was $300.”
This answer clearly shows understanding of the problem, a logical plan, correct calculations with units, and a final check, earning full marks.
This answer incorrectly applies the 10% discount to the sale price instead of the original price, showing a misunderstanding of the base for percentage calculations. It would lose marks for incorrect method.
🗝️ Words that earn marks
100% represents the original amountsetting up the problem to find the whole.
Part / Corresponding Percentageexplaining the calculation step to find the original.
Convert percentage to decimal/fractionperforming the division calculation.
🎯
Test Yourself
Generate practice questions on Finding the Original Quantity
2
Calculating Percentage Increase and Decrease
This section teaches you how to calculate how much a quantity has grown or shrunk, expressed as a percentage. You will learn to find the percentage increase when something gets bigger, and the percentage decrease when something gets smaller. Understanding these calculations is important for solving real-world problems involving changes in amounts over time.
❓ Before you read — have a guess: When calculating percentage change, which amount should always be used as the base (the number you divide by)?
The original amount.
⚡ Key points — the 6 things to remember
Percentage increase shows how much a quantity has grown relative to its original size.
Percentage decrease shows how much a quantity has shrunk relative to its original size.
Always use the original amount as the base (denominator) when calculating percentage increase or decrease.
An increase of X% means the new amount is (100 + X)% of the original amount.
A decrease of X% means the new amount is (100 - X)% of the original amount.
The 'amount of increase' or 'amount of decrease' is the difference between the new and original quantities.
What you must be able to do
Calculate the percentage increase between two quantities.
Calculate the percentage decrease between two quantities.
Understanding Percentage Increase
A percentage increase tells you how much a quantity has grown, shown as a part of its original amount (the starting value). For example, if a price goes up, the percentage increase tells you how much more it is compared to its first price.
To find the percentage increase, first find the actual amount of increase.
The amount of increase is the difference between the new amount and the original amount.
The original amount is always considered 100% before any increase.
Percentage Increase = (Increase / Original Amount) × 100%
Increase
The actual amount by which the quantity has grown
units (e.g., $, kg, cm)
Original Amount
The starting quantity before any change
units (e.g., $, kg, cm)
Percentage Increase
The increase expressed as a percentage
%
Worked example🧰 Before-after concept
The population of Town A was 8000 people last year. This year, the population increased to 9600 people. What was the percentage increase in population?
Find the amount of increase in population.
Why this step?We find the difference to know how much the population actually grew.
Calculate the percentage increase.
Why this step?We divide the increase by the original population and multiply by 100% to express the growth as a percentage of the starting population.
20%
✏️ Now you try
A plant grew from 50 cm to 65 cm. What is the percentage increase in its height?
Step 1: Find the amount of increase in height.Amount of increase = 65 cm - 50 cm = 15 cm
Step 2: Calculate the percentage increase.Percentage increase = (15 cm / 50 cm) × 100% = 30%
Reveal the answer30%
⚠️ Common Mistake
A 20% increase means the new amount is 20% of the original amount. — Correct: A 20% increase means the new amount is 100% (original) + 20% (increase) = 120% of the original amount.
💡 Exam Tip
Always identify the 'original amount' first. This is the starting value before any change.
💡 Exam Tip
When calculating percentage increase, remember that the 'new amount' will always be larger than the 'original amount'.
💡 Exam Tip
If a question asks for the 'new amount' after an increase, you can find it by calculating Original Amount × (1 + Percentage Increase as decimal).
📍 Singapore Focus
Percentage increase is often used in real-life scenarios like tracking population changes (e.g., how much a town's population grew) or before-and-after scenarios involving growth (e.g., a plant's height increase, weight gain).
Understanding Percentage Decrease
A percentage decrease tells you how much a quantity has shrunk, shown as a part of its original amount (the starting value). For example, if a price goes down during a sale, the percentage decrease tells you how much less it is compared to its first price.
To find the percentage decrease, first find the actual amount of decrease.
The amount of decrease is the difference between the original amount and the new amount.
The original amount is always considered 100% before any decrease.
Percentage Decrease = (Decrease / Original Amount) × 100%
Decrease
The actual amount by which the quantity has shrunk
units (e.g., $, kg, cm)
Original Amount
The starting quantity before any change
units (e.g., $, kg, cm)
Percentage Decrease
The decrease expressed as a percentage
%
Worked example🧰 Before-after concept
A shop sold a toy for $80. During a sale, the price was reduced to $64. What was the percentage decrease in the price of the toy?
Find the amount of decrease in price.
Why this step?We find the difference to know how much the price actually dropped.
Calculate the percentage decrease.
Why this step?We divide the decrease by the original price and multiply by 100% to express the drop as a percentage of the starting price.
20%
✏️ Now you try
The number of students in a club decreased from 40 to 34. What was the percentage decrease in the number of students?
Step 1: Find the amount of decrease in students.Amount of decrease = 40 - 34 = 6 students
⚠️ Common Mistake
To find percentage decrease, you divide the decrease by the new (smaller) amount. — Correct: To find percentage decrease, you must always divide the decrease by the original (larger) amount.
💡 Exam Tip
Always identify the 'original amount' first. This is the starting value before any change.
💡 Exam Tip
When calculating percentage decrease, remember that the 'new amount' will always be smaller than the 'original amount'.
💡 Exam Tip
If a question asks for the 'new amount' after a decrease, you can find it by calculating Original Amount × (1 - Percentage Decrease as decimal).
📍 Singapore Focus
Percentage decrease is commonly seen in situations like retail and shopping scenarios (e.g., discounts, sales), population changes (e.g., a decrease in animal count), or before-and-after scenarios involving reduction (e.g., weight loss, amount of liquid used).
🪤 Watch for these traps
The wrong answers examiners plant to catch you — and how to dodge them.
Tempting answerIf a price increased by 25%, the new price is 25% of the original price.
Looks right because Students might confuse 'percentage increase' with the 'percentage of the new value'.
But actually A 25% increase means the new price is 100% (original) + 25% (increase) = 125% of the original price.
✓ How to avoid it Always add the percentage increase to 100% to find the new percentage of the original amount.
Tempting answerTo find the percentage decrease, divide the amount of decrease by the new (final) amount.
Looks right because The new amount is the quantity present after the change, so it might seem like the relevant base.
But actually Percentage change (increase or decrease) is always calculated based on the original amount. The original amount is the reference point for the change.
✓ How to avoid it Before calculating, clearly identify the 'original amount' and use it as the denominator in your fraction.
🔍 Question Decoder
What exam phrasings are really asking for.
When the question says…
It is testing…
Your move
What is the percentage increase?
Calculation of percentage increase.
Find the amount of increase, then divide by the original amount and multiply by 100%.
Find the percentage decrease.
Calculation of percentage decrease.
Find the amount of decrease, then divide by the original amount and multiply by 100%.
The number grew by X%. What is the new number?
Finding the new amount after a percentage increase.
Calculate Original Amount × (1 + X/100).
The value dropped by Y%. What is the new value?
Finding the new amount after a percentage decrease.
Calculate Original Amount × (1 - Y/100).
🧭 Understand → Plan → Work → Check
How to answer: Word problems involving percentage increase or decrease.
1Understand: Read the question carefully. What is given? What do you need to find?
1 mark
2Plan: Choose the correct formula or method (e.g., bar model). Identify the original amount.
1 mark
3Work: Show all your calculation steps clearly with units.
1-2 marks
4Check: Is your answer reasonable? Does it make sense in the context of the problem? Write down your final answer with units.
1 mark
Example: A plant grew from 50 cm to 65 cm. What is the percentage increase in its height?
✅ Earns the mark
“Understand:
Original height = 50 cm
New height = 65 cm
Find: Percentage increase in height.
Plan:
1. Find the amount of increase.
2. Use the formula: Percentage Increase = (Increase / Original Amount) × 100%.
Work:
Amount of increase = 65 cm - 50 cm = 15 cm
Percentage increase = (15 cm / 50 cm) × 100%
= (3/10) × 100%
= 30%
Check:
10% of 50 cm is 5 cm. 30% is 3 x 5 cm = 15 cm. 50 cm + 15 cm = 65 cm. The answer is reasonable.
Answer: The percentage increase in the plant's height is 30%.”
This answer clearly shows all four steps. It identifies the given information, plans the solution, shows detailed working with units, and includes a check for reasonableness. The final answer is stated clearly with units.
This answer loses marks because it uses the new amount (65 cm) as the base for calculating percentage increase instead of the original amount (50 cm). It also lacks clear steps, units, and a final statement.
🗝️ Words that earn marks
Original amountidentifying the starting value before any change, which is the base for percentage calculations.
Amount of increasecalculating the difference between the new, larger quantity and the original quantity.
Amount of decreasecalculating the difference between the original quantity and the new, smaller quantity.
Percentage increasestating the final answer for how much a quantity has grown relative to its original size.
Percentage decreasestating the final answer for how much a quantity has shrunk relative to its original size.
🎯
Test Yourself
Generate practice questions on Calculating Percentage Increase and Decrease
3
Solving Word Problems with Percentage Change
This sub-topic teaches you how to solve word problems where quantities increase or decrease by a certain percentage. You will learn to find new amounts after a change, or work backwards to find the original amount before a change, using clear steps and understanding what each percentage represents.
❓ Before you read — have a guess: If a price increases by 10%, what percentage of the original price is the new price?
110%
⚡ Key points — the 5 things to remember
The original amount always represents 100%.
A percentage increase means the new amount is more than 100% of the original.
A percentage decrease means the new amount is less than 100% of the original.
Always identify the 'original amount' (100%) before calculating percentage changes.
To find the original amount, determine what percentage the given 'part' represents.
What you must be able to do
Solve word problems involving percentage increase or decrease.
Calculating New Amount after Percentage Increase
Percentage increase happens when a quantity grows larger. The new amount is the original amount plus the amount of increase.
The original amount is always 100%.
If there is a percentage increase, the new amount will be (100% + percentage increase) of the original amount.
NA = OA × (1 + PI / 100)
NA
New Amount
$
OA
Original Amount
$
PI
Percentage Increase
%
Worked example🧰 Before-after concept
A shop bought a bicycle for $250. It wants to make a 20% profit. What is the selling price of the bicycle?
100% = $250 (Cost price)
Why this step?This identifies the original value (Cost price) as 100%.
Profit = 20%
Why this step?This states the percentage of profit the shop wants to make.
Selling price = 100% + 20% = 120%
Why this step?This calculates the total percentage of the selling price relative to the cost price.
120% = (120/100) × $250
Why this step?This sets up the calculation to find the value of 120% of the original amount.
120% = 1.2 × $250
Why this step?This converts the percentage to a decimal for easier multiplication.
Selling price = $300
Why this step?This gives the final selling price after the profit.
$300
✏️ Now you try
A farmer harvested 300 kg of corn last year. This year, his harvest increased by 15%. How much corn did he harvest this year?
What percentage represents the harvest this year?100% + 15% = 115%
Calculate the amount of corn harvested this year.(115/100) × 300 kg = 1.15 × 300 kg = 345 kg
Reveal the answer345 kg
The cost price is 100%. A 20% profit means the selling price is 120% of the cost price.
⚠️ Common Mistake
If a shop makes a 20% profit on a $250 bicycle, the selling price is $20. — Correct: 20% profit means the selling price is 20% more than the cost price. You need to calculate 20% of $250, then add it to $250, or find 120% of $250.
💡 Exam Tip
Students often calculate the profit amount (e.g., 20% of $250) and give that as the final answer. Remember, profit is added to the cost price to get the selling price.
📍 Singapore Focus
In business, profit is the money gained when the selling price is higher than the cost price. The percentage profit is always calculated based on the cost price.
Calculating New Amount after Percentage Decrease
Percentage decrease happens when a quantity becomes smaller. The new amount is the original amount minus the amount of decrease.
The original amount is always 100%.
If there is a percentage decrease, the new amount will be (100% - percentage decrease) of the original amount.
NA = OA × (1 - PD / 100)
NA
New Amount
$
OA
Original Amount
$
PD
Percentage Decrease
%
Worked example🧰 Draw a model
A jacket originally cost $120. During a sale, it was given a 30% discount. What was the sale price of the jacket?
100% = $120 (Original price)
Why this step?This identifies the original value as 100%.
Discount = 30%
Why this step?This states the percentage of discount applied.
Sale price = 100% - 30% = 70%
Why this step?This calculates the total percentage of the sale price relative to the original price.
70% = (70/100) × $120
Why this step?This sets up the calculation to find the value of 70% of the original amount.
70% = 0.7 × $120
Why this step?This converts the percentage to a decimal for easier multiplication.
Sale price = $84
Why this step?This gives the final sale price after the discount.
$84
✏️ Now you try
A school had 500 students last year. This year, the student population decreased by 8%. How many students are there this year?
What percentage represents the student population this year?100% - 8% = 92%
Calculate the number of students this year.(92/100) × 500 = 0.92 × 500 = 460 students
Reveal the answer460 students
The original price is 100%. A 30% discount means the sale price is 70% of the original price.
⚠️ Common Mistake
If a jacket has a 30% discount from $120, the sale price is $30. — Correct: 30% discount means the sale price is 30% less than the original price. You need to calculate 30% of $120, then subtract it from $120, or find 70% of $120.
💡 Exam Tip
A common mistake is to calculate the discount amount (e.g., 30% of $120) and forget to subtract it from the original price. The question asks for the sale price, which is the price after the discount.
📍 Singapore Focus
In retail, a discount is an amount taken off the original price. The price after the discount is called the sale price.
Finding the Original Amount
Sometimes you are given the new amount after a percentage change and need to find the original amount before the change. This requires you to work backwards.
The original amount is always 100%.
The given 'new amount' represents a certain percentage of the original amount (either 100% + increase or 100% - decrease).
To find the original amount, first find the value of 1% of the original, then multiply by 100.
OA = Part / (Percentage of Original / 100)
OA
Original Amount
$
Part
Given Amount (New Amount)
$
Percentage of Original
Percentage the given amount represents (e.g., 120% or 80%)
%
Worked example🧰 Work backwards
After a 25% discount, a pair of shoes was sold for $90. What was its original price?
Sale price ($90) represents 100% - 25% = 75% of the original price.
Why this step?This identifies what percentage of the original price the given sale price represents.
75% = $90
Why this step?This links the calculated percentage to the given value.
1% = $90 / 75
Why this step?This finds the value of one percentage unit.
1% = $1.20
Why this step?This calculates the exact value of 1%.
Original price (100%) = $1.20 × 100
Why this step?This uses the value of 1% to find the full original amount (100%).
Original price = $120
Why this step?This gives the final original price.
$120
✏️ Now you try
A shop sold a watch for $165, making a 10% profit. What was the cost price of the watch?
What percentage of the cost price does the selling price ($165) represent?100% + 10% = 110%
If 110% = $165, find the value of 1%.1% = $165 / 110 = $1.50
The sale price of $90 represents 75% of the original price. We need to find the value of 100%.
⚠️ Common Mistake
If a dress is sold for $120 after a 20% discount, its original price is $120 + 20% of $120. — Correct: The 20% discount is based on the original price. So, $120 represents (100% - 20%) = 80% of the original price. You need to find 100%.
💡 Exam Tip
When finding the original amount, students often try to 'reverse' the percentage by adding or subtracting the percentage of the new amount. Always remember that the original amount is 100%, and the given 'part' (new amount) represents a different percentage of that 100%.
📍 Singapore Focus
When a shop sells an item for less than its cost price, it makes a loss. The percentage loss is always calculated based on the cost price.
🪤 Watch for these traps
The wrong answers examiners plant to catch you — and how to dodge them.
Tempting answerGiving only the amount of increase or decrease, not the new total.
Looks right because You correctly calculated the percentage part, like the discount amount or profit amount.
But actually The question usually asks for the new amount (e.g., sale price, selling price, new quantity), which means you must add or subtract the change from the original.
✓ How to avoid it Always re-read the question carefully to identify whether it asks for the 'change' or the 'new amount'.
Tempting answerWhen finding the original amount after a decrease, adding the percentage of the new amount back.
Looks right because It seems logical to reverse the operation by adding a percentage.
But actually Percentage changes are always based on the original amount (100%). If an item is sold at a 20% discount, the sale price is 80% of the original, not 80% of the sale price itself.
✓ How to avoid it Identify what percentage the given amount represents (e.g., if 20% discount, the sale price is 80% of the original). Then find 100%.
Tempting answerConfusing the base for percentage change (e.g., calculating profit percentage based on selling price instead of cost price).
Looks right because You are using numbers from the problem.
But actually For profit/loss, the percentage is always based on the cost price (the original investment). For discounts, it's based on the original price.
✓ How to avoid it Clearly identify the 'original amount' or 'base amount' (which is 100%) before starting any percentage calculation.
🔍 Question Decoder
What exam phrasings are really asking for.
When the question says…
It is testing…
Your move
increased by 15%
Finding the new amount after an increase
New amount = Original amount × (100% + 15%)
decreased by 20%
Finding the new amount after a decrease
New amount = Original amount × (100% - 20%)
sold at 10% discount for $X
Finding the original price given the discounted price
$X represents (100% - 10%) of the original price. Find 100%.
made 25% profit, selling price $Y
Finding the cost price given the selling price and profit percentage
$Y represents (100% + 25%) of the cost price. Find 100%.
🧭 Understand → Plan → Work → Check
How to answer: Word problems involving percentage change, especially finding the original amount.
1Understand: Read the problem carefully. What is given? What do you need to find? Underline key numbers and units.
1 mark
2Plan: Decide which percentage represents the given amount. Draw a bar model if it helps. Choose the correct operations (e.g., find 1%, then 100%).
1 mark
3Work: Show all your steps clearly. Write down the percentage and its corresponding value. Carry units through your calculations.
2 marks
4Check: Is your answer reasonable? Does it make sense in the context of the problem? (e.g., original price should be higher after a discount).
1 mark
Example: A bag was sold for $180 after a 20% discount. What was the original price of the bag?
✅ Earns the mark
“Understand:
Given: Sale price = $180, Discount = 20%
Find: Original price
Plan:
If there was a 20% discount, the sale price ($180) represents (100% - 20%) = 80% of the original price. I need to find 100%.
Work:
80% = $180
1% = $180 ÷ 80 = $2.25
100% = $2.25 × 100 = $225
Check:
If original price was $225, 20% discount = 0.20 × $225 = $45. Sale price = $225 - $45 = $180. The answer is reasonable.
Answer: The original price of the bag was $225.”
This answer clearly shows all four steps. It correctly identifies the percentage for the given amount, calculates 1%, and then finds 100%. The 'Check' step confirms the answer's reasonableness. Units are consistently used.
❌ Loses the mark
“20% of $180 = $36
$180 + $36 = $216
Original price = $216”
This answer incorrectly assumes the 20% discount is based on the sale price ($180) instead of the original price. It misses the crucial step of identifying what percentage $180 represents. The working is not clearly linked to the concept of finding the original 100%.
🗝️ Words that earn marks
100% represents the original amountStarting any percentage problem to establish the base value.
1 unit represents XUsing the 'unitary method' to find the value of 1% or 1 unit before scaling up.
Total percentage is 100%Referring to the whole or original quantity.
Percentage increase/decrease is based on the originalExplaining why you use the 'before' value as the denominator for percentage change.
🎯
Test Yourself
Generate practice questions on Solving Word Problems with Percentage Change
Glossary
Key terms across this topic, in alphabetical order.
Cost price — The price at which a shop or seller buys an item.
Decrease — The amount by which a quantity has shrunk or become smaller.
Discount — An amount taken off the original price of an item.
Increase — The amount by which a quantity has grown or become larger.
Loss — The money lost when the selling price of an item is less than its cost price.
New amount — The quantity or value after a percentage increase or decrease.
Original amount — The starting quantity or value before any change (increase or decrease) occurs.
Part — A portion of the whole, represented by a specific percentage.
Percentage — A way to show a part of a whole, where the whole is divided into 100 equal parts.
Profit — The money gained when the selling price of an item is more than its cost price.
Sale price — The price of an item after a discount has been applied.
Selling price — The price at which a shop or seller sells an item to a customer.
Whole — The total amount or the entire quantity, which represents 100%.
Test yourself on Percentage
Turn reading into marks — practise real PSLE Maths questions on this exact topic, with every answer explained.
