Percentage

A sale sticker, a test score and a bank statement can all use the same small symbol: $\%$. It means “out of 100”. Once you identify the whole, a percentage question becomes a clear fraction calculation.

Parents: let your child predict before opening each explanation, then ask them to point to the whole before calculating.

By the end you will be able to use the $\%$ symbol, find a percentage of an amount, convert between forms, and solve forward discount, stated-rate GST and one-year simple-interest questions.

Percent means out of 100

A percentage tells you how many parts there are in every 100 equal parts. The symbol $\%$ is read as “percent”. For example, $25\%$ means $\frac{25}{100}$.

The bottom of the fraction is the whole. If 25 of 100 squares are shaded, the shaded part is $25\%$ of the grid. The lab lets you vary the stated whole and percentage so you can see the part change.

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Percentage parts out of 100

🤔 Predict first: What is 25% of 200?

255075

Find a percentage of a quantity

To find a percentage of an amount, change the percentage to a fraction over 100 and multiply by the amount. Here the stated rate is $15\%$ and the whole is $80.

Show the worked solution

Find the percentage part

$$15\%\text{ of }\$80=\frac{15}{100}\times80$$

$$=\$12$$

Another mental route is to find $10\%$ first by dividing by 10, then combine it with another $5\%$. Both routes must give the same part of the same whole.

Write one quantity as a percentage of another

When a question gives a part and a whole, put the part on top and the whole underneath. Then multiply by 100. If 18 of 24 answers are correct, the whole is 24, so the fraction is $\frac{18}{24}$.

Show the worked solution

Part over whole

$$\frac{18}{24}=\frac{3}{4}$$

$$\frac{3}{4}\times100=75\%$$

Convert between percentage, fraction and decimal

The three forms describe the same value. For a percentage to fraction, write it over 100 and simplify. For a percentage to decimal, divide by 100. For a decimal to percentage, multiply by 100.

$40\%$ is $\frac{40}{100}=\frac{2}{5}$ and is also 0.4. In the other direction, 0.35 is $35\%$ because 0.35 multiplied by 100 is 35.

Find a discount from the original price

A discount is a reduction from the original price. First find the discount amount using the stated discount rate. Then subtract that amount from the original price to find the sale price. This is a forward percentage calculation: the original price is already given.

The original price of a bag is $80. The stated discount rate is $20\%$.

Show the worked solution

Discount then sale price

$$20\%\text{ of }\$80=\frac{20}{100}\times80=\$16$$

$$\text{Sale price}=\$80-\$16=\$64$$

Find GST using the stated rate

For a GST question, use the rate written in that question. Do not assume that a rate from a receipt, website or current law belongs in the calculation. The item costs $50 before GST, and the stated GST rate for this question is $9\%$.

Show the worked solution

GST at the stated rate

$$9\%\text{ of }\$50=\frac{9}{100}\times50=\$4.50$$

$$\text{Total}=\$50+\$4.50=\$54.50$$

Find one-year simple annual interest

Interest is the extra money paid on savings for a stated time. This P5 method uses simple annual interest for one year: multiply the stated yearly rate by the starting amount. The account pays $2\%$ per year on $600 for 1 year.

Show the worked solution

One-year simple interest

$$\text{Interest}=\frac{2}{100}\times\$600\times1=\$12$$

$$\text{Amount after 1 year}=\$600+\$12=\$612$$

Practise with three worked steps

Try each problem before opening its solution. The givens stay visible so you can choose the method before seeing the answer.

Practice 1 — percentage part. Find $35\%$ of 60.

Reveal solution: Practice 1

Percentage part

$$35\%\text{ of }60=\frac{35}{100}\times60$$

$$=21$$

The answer is 21.

Practice 2 — original-price discount. A game costs $120 before a stated discount of $15\%$. Find the discount and the sale price.

Reveal solution: Practice 2

Discount from the original price

$$15\%\text{ of }\$120=\frac{15}{100}\times120=\$18$$

$$\text{Sale price}=\$120-\$18=\$102$$

The discount is $18 and the sale price is $102.

Practice 3 — one-year simple interest. An account pays $3\%$ simple annual interest on $400 for 1 year. Find the interest and the amount after 1 year.

Reveal solution: Practice 3

Interest for one year

$$\text{Interest}=\frac{3}{100}\times\$400\times1=\$12$$

$$\text{Amount}=\$400+\$12=\$412$$

The interest is $12 and the amount after 1 year is $412.

Watch out — these are easily mixed up

Quick recap

🎯 Mastery check

Answer all 8 — your progress is saved on this device.

1. What is 15% of 80?

   121516

2. A pupil gets 27 out of 30 marks. What percentage is this?

   75%90%92%

3. What is 0.35 written as a percentage?

   3.5%0.35%35%

4. The original price of a bag is $80. The stated discount rate is 20%. What is the discount amount?

   $16$20$64

5. An item costs $50 before GST. The stated GST rate is 9%. What is the total price?

   $59$54.50$45.50

6. An account pays 2% simple annual interest on $600 for 1 year. How much interest is paid?

   $120$2$12

7. Which statement is correct?

   25% means 25 out of 1025% means 25 out of 10025% means 100 out of 25

8. The original price is $80 and the stated discount rate is 20%. What is the sale price?

   $16$64$100

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