Primary 5 Percentage Study Guide

Primary 5 percentage in five short steps: the hundred square, three spellings of one amount, a part as a percentage, a percentage of a quantity, then discount, GST and interest. Each step has something to tap and a question to try.

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What does percent mean?

Percent means out of a hundred, so any whole can be counted as 100%.

A percentage says how many parts there are in every hundred. On a hundred square the 100 small squares are the whole, so each square is 1%. Any other whole is read the same way: 3 of 5 equal parts is the same amount as 60 of 100 parts, which is 60%. So before any working, your child names the whole, because the whole is the 100%.

In this chapter, your child learns to:

read a shaded hundred square as a count out of 100;
write one amount as a fraction, a decimal and a percentage;
express a part of a whole as a percentage of that whole;
find a percentage of a quantity, such as 45% of 600 buns;
work out a discount, then GST, and a year of interest.

Step 1

Reading a percentage on a hundred square

Count the rows as tens, then the single squares. A hundred square has 10 rows of 10, so the whole is 100 small squares and each one is 1 hundredth, or 1%. Count the shaded squares a row at a time: 2 full rows and 4 more make 24. That count can be spelt three ways, 24/100, 0.24 and 24%, and every spelling is the same 24 squares. The squares left unshaded are 100 minus 24 = 76, so they are 76%.

Tap a button to shade more or fewer squares

fraction24/100

decimal0.24

percentage24%

2 full rows and 4 more squares are shaded: 24 out of 100. That is 24/100, 0.24 or 24%.

Try it

A cinema has exactly 100 seats. 31 of the seats are taken. What percentage of the seats is empty?

▶ Watch the lesson: Out of a hundred Practise 6 questions →

Step 2

Converting fractions, decimals and percentages

The fraction over 100 links the decimal and the percentage. To change a percentage into a decimal, write it over 100, then divide by 100: keep the decimal point fixed and move the digits two places to the right. A decimal with one place holds tenths, and 7 tenths are 70 hundredths, so 0.7 is 70%. A fraction becomes a percentage once its denominator is made 100, for example 11/25 = 44/100 = 44%.

Tap Next step

fraction?

decimal?

percentage48%

Given 48%. Percent means out of a hundred, so 48% is 48 parts out of 100. Tap Next step.

Try it

Express 0.06 as a percentage.

▶ Watch the lesson: Three spellings Practise 7 questions →

Step 3

Expressing a part as a percentage

Part over whole, then times 100%. First find the whole: it is the amount named after the words "percentage of", and it is 100%. Write the part over the whole and simplify the fraction. Then multiply by 100%. Multiplying by 100% leaves the amount as it was and only changes how it is written, so 3/5 of a book is 60% of the book.

Tap Next step

A book has 40 pages. Wei Jie has read 24 of them. What percentage of the book has he read?

The question asks for a percentage of the book, so all 40 pages are the whole, and the whole is 100%. Tap Next step.

Try it

A choir has 9 girls and 16 boys. What percentage of the choir are girls?

▶ Watch the lesson: Part as a percentage Practise 10 questions →

Step 4

Finding a percentage of a quantity

Percentage over 100, times the whole. The whole bar is 100%. To find 45% of 600 buns, write 45 over 100 and multiply by 600: 45/100 × 600. Cancel first, because 100 goes into 600 six times, which leaves 45 × 6 = 270 buns. That 6 is also 1% of the buns, so the same answer comes from finding 1% and multiplying by 45.

Tap a percentage, or drag the slider

A bakery baked 600 buns on Saturday.

Percentage

25% of 600 = 25/100 × 600

= 25 × 6 = 150

25% of 600 buns is 25/100 × 600. 100 goes into 600 six times, so this is 25 × 6 = 150 buns. The 6 is 1% of the buns.

Try it

A jar holds 250 beads. 36% of them are red. How many red beads are in the jar?

▶ Watch the lesson: A percentage of a quantity Practise 11 questions →

Step 5

Discount, GST and annual interest

Find the price that is 100% before you calculate. In a sale the original price is 100%, so a 20% discount leaves 100% minus 20% = 80% to pay. GST is charged on the discounted price, so that price is the new 100%, and 9% GST makes it 109%. When only the sale price is known, it is a percentage of the original: find 1%, then 100%. Annual interest is a percentage of the money saved, added once a year.

Tap Next step

A sofa has an original price of $1000. It has a 20% discount, then 9% GST is added. How much does the customer pay?

Start with the original price. The whole $1000 is 100%. Tap Next step.

Try it

A pair of shoes costs $80 before GST. 9% GST is added. How much does the customer pay?

▶ Watch the lesson: Discount, then GST Practise 11 questions →

Primary 5 percentage questions, worked line by lineTry each one on paper before opening anything, then ask for a hint or one working line at a time.

Three spellingsBasic

Express 17/25 as a percentage and as a decimal.

Make the denominator 100 first. 25 times what number is 100?

17/25 = (17 × 4)/(25 × 4) = 68/100
68/100 = 68%
68/100 = 0.68

Answer: 68% and 0.68

Part as a percentageBasic

Ravi scored 42 marks out of 50 in a spelling test. Express his score as a percentage of the full marks.

The full 50 marks are the whole. Put the part over the whole.

whole = 50 marks, part = 42 marks
42/50 = 21/25 = 84/100
84/100 = 84%

Answer: 84%

A percentage of a quantityIntermediate

A bottle holds 2 litres of syrup. 35% of the syrup is used. How many millilitres of syrup are left?

Change litres to millilitres first. Then find the percentage that is left.

2 litres = 2 × 1000 = 2000 ml
left = 100% − 35% = 65%
65/100 × 2000 = 65 × 20 = 1300 ml

Answer: 1300 ml

Discount, then GSTIntermediate

A bicycle has an original price of $250. It is sold at a 40% discount, and then 9% GST is added to the discounted price. How much does the customer pay?

The original price is 100% for the discount. The discounted price is 100% for the GST.

100% − 40% = 60%
60/100 × $250 = $150
100% + 9% = 109%
109/100 × $150 = $163.50

Answer: $163.50

Annual interestChallenge

Mr Lee put some money in a bank that pays 3% annual interest. After one year he had $4120 in the bank. How much money did he put in?

The money he put in is 100%. After a year of interest, he has more than 100% of it.

100% + 3% = 103%
103% = $4120, so 1% = $4120 ÷ 103 = $40
100% = 100 × $40 = $4000

Answer: $4000

Step 6

Check yourself

One question from each step. Nothing is saved, and every reply names the practice set that fits.

23% of a hundred square is shaded. How many of its small squares are shaded?

Express 0.9 as a percentage.

There are 25 pupils in a class. 6 of them wear glasses. What percentage of the class wear glasses?

What is 35% of 80 kg?

A bag has an original price of $60. It is sold at a 10% discount. How much does the customer pay?

0/5

Answer all five to see where to practise next.

For parents

Using the guide together. Before each step, ask your child to point at the whole and say aloud that it is 100%. Then tap through and let the readout confirm it. Each step takes a few minutes, and the question underneath shows whether the idea has landed.

When a word problem mentions money, ask which price stands for 100% at that moment: the original price, the price after the discount, or the amount in the bank. Writing that one line first, such as "$800 is the new 100%", keeps every later line to a single multiplication or division that your child can check.

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Lessons and practice

P5 Percentage lessons and practice

5 lesson videos and 45 questions across five subtopics, from Basic to Challenge, each with a worked solution.

Watch and practise →