Primary 6 Percentage Study Guide
Primary 6 percentage in six short steps, from a hundred square to word problems where the 100% moves. Each step names the 100% first and works one line at a time, then the worked examples and a short check close the guide.
Start here
What is a percentage?
Percent means out of 100, and the whole is 100%.
A percentage compares a part with a whole that is counted as 100. 37% means 37 out of every 100, so it can also be written 37/100 or 0.37. Before any working, your child asks which amount is the 100%. In a sale it is the original price; for GST it is the price after the discount.
In this chapter, your child learns to:
- read a percentage on a hundred square and write it as a fraction or a decimal;
- find a percentage of a quantity, and express a part as a percentage of the whole;
- find the whole from a part and its percentage, through 1%;
- find a percentage increase or decrease, measured against the original;
- work a discount, then GST, and a second change on the new amount;
- use the quantity that stays the same when the total changes.
Step 1
Percentages, fractions and decimals
Write it over 100 first. A hundred square is 100 equal small squares, so 37 shaded squares are 37 out of 100. That one count has three spellings: 37/100, 0.37 and 37%. To change one spelling into another, write it as a fraction over 100 first. The decimal and the percentage are both in that line, so 0.4 = 40/100 = 40% and 7/20 = 35/100 = 35%.
Drag the slider, or tap a number
A hundred square has 100 equal squares. 28 of them are shaded. What percentage of the square is not shaded?
Step 2
Percentage of a quantity
Name the whole first. The whole is the amount after the words "percentage of", and it is 100%. To find a percentage of the whole, write the percentage over 100 and multiply by the whole. To turn a part into a percentage, write the part over the whole and multiply by 100%.
Tap Next step
A stall sold 400 chicken rice sets in one month.
A wall is 60 m long. 18 m of it has been painted. What percentage of the wall has not been painted?
Step 3
Finding the whole from a percentage
Go down to 1%, then up to 100%. A number that comes with a percentage is a part, not the whole. If 40% of the pupils is 240 pupils, divide by 40 to get 1%, then multiply by 100 to get 100%. Write one line each, joined by equals signs. The whole comes out bigger than the part, which checks the answer.
Tap Next step
40% of the pupils in a school walk to school. That is 240 pupils.
80% of the seats in a hall were filled for a concert. 480 seats were filled. How many seats are in the hall?
Step 4
Percentage increase and decrease
Measure the change against the original. The amount at the start is the original, and the original is the 100%. Find the change first. Then write the change over the original and multiply by 100%. An increase goes past the 100% line; a decrease takes some off it. The amount at the end is never the one you divide by.
Tap Next step
A jacket costs $200. In a sale, the price is 30% less. What is the sale price?
Step 5
Discount, GST and a percentage of a percentage
Each change has its own 100%. A discount is worked on the original price. GST is worked on the price after the discount, so that price becomes the new 100%. A second change works the same way: it is a percentage of the amount after the first change. That is why going up 20% and then down 20% does not bring a price back.
Tap Next step
A TV's original price is $500. It has a 20% discount, then 9% GST is added.
A camera's original price is $600. It has a 20% discount, then 9% GST is added. How much does the customer pay?
Step 6
Percentage questions with an unchanged quantity
Keep the unchanged part the same number of units. When only one kind is added, the other kind does not change; only its share of the total changes. Write each percentage share as a ratio and simplify it. Then use an equivalent ratio so the unchanged part is the same number of units before and after. The extra units are the amount that was added.
Tap Next step
Football cards were 40% of an album. 60 basketball cards were added, and football cards became 25%.
A box holds only pens and pencils. Pens are 20% of them. After 30 more pencils are put in, pens are 10%. How many pens are in the box?
Primary 6 percentage questions, worked step by stepWork each percentage question on paper first, then open the hint or reveal the working line by line.
There are 40 pupils in a class. 18 of them wear spectacles. What percentage of the class do not wear spectacles?
- not wearing spectacles = 40 − 18 = 22
- 22/40 = 11/20 = 55/100
- 55/100 = 55%
A study lamp has an original price of $80. It is sold at a 15% discount. How much does the customer pay?
- 100% − 15% = 85%
- 85/100 × $80 = $68
A baker sold 35% of his muffins in the morning and 25% in the afternoon. He had 120 muffins left. How many muffins did he bake?
- sold = 35% + 25% = 60%
- left = 100% − 60% = 40%
- 40% = 120, so 1% = 120 ÷ 40 = 3
- 100% = 100 × 3 = 300
A library lent out 500 books in March. In April, the number fell by 20%. In May, it rose by 30% of the number lent out in April. How many books did the library lend out in May?
- April = 80/100 × 500 = 400
- April's 400 books are the new 100%
- May = 130/100 × 400 = 520
A shop had only silver and gold balloons. Silver balloons were 75% of them. After the shop bought 90 more gold balloons, silver balloons were 60% of them. How many silver balloons did the shop have?
- before: silver : gold = 75 : 25 = 3 : 1
- after: silver : gold = 60 : 40 = 3 : 2
- silver is 3 units in both, so gold added = 2 units − 1 unit = 1 unit
- 1 unit = 90
- silver = 3 × 90 = 270
Step 7
Check yourself
Five quick percentage questions. Nothing is recorded, and each reply names the question type to revisit.
1. Express 0.08 as a percentage.
2. What is 15% of $60?
3. 30% of a ribbon is 45 cm long. How long is the whole ribbon?
4. A stall sold 80 bowls of laksa on Monday and 100 on Tuesday. Find the percentage increase.
5. A bag costs $200. Its price goes up by 10%, then the new price goes down by 10%. What does the bag cost now?
How to use this guide. At every step, ask your child one question before tapping anything: which amount is the 100% here? Let the bars confirm the answer, then try the question under them. Each step takes a few minutes.
In a problem with two changes, cover the working and ask your child to say the 100% for each stage in words, such as "the price after the discount", before writing a number. Each line is then one division or one multiplication, so a chain such as 40% = 240, 1% = 6, 100% = 600 can be checked line by line.
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P6 Percentage lessons and practice
9 lesson videos and 68 questions across nine subtopics, from Basic to Challenge, each with a worked solution.
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