Sec 1 · G2 (N(A))

Percentage

Practise percentage with step-by-step help. Free account.

1. Percentages, fractions and decimals

Percentage	Fraction	Decimal
$45\%$	$\dfrac{9}{20}$	$0.45$
$12.5\%$	$\dfrac{1}{8}$	$0.125$
$150\%$	$\dfrac{3}{2}$	$1.5$

One quantity as a percentage of another: 18 out of 40

\displaystyle \dfrac{18}{40} \times 100\%

e.g.

\displaystyle \dfrac{18}{40} \times 100

\displaystyle = 45

$45\%$

A percentage of a quantity: 35% of $240

\displaystyle \dfrac{35}{100} \times 240

e.g.

\displaystyle \dfrac{35}{100} \times 240

\displaystyle = 84

📖 Worked example

Express $75$ as a percentage of $120$ .

Step 1 of 1

Write the first quantity as a fraction of the second, then multiply by 100%

\dfrac{75}{120} \times 100\%

= 62.5\%

📖 Worked example

Write $37\dfrac{1}{2}\%$ as a fraction in its simplest form.

Step 1 of 2

Write the mixed number as an improper fraction first

37\dfrac{1}{2}

= \dfrac{75}{2}

Practise this →

2. Percentage change

Name	Formula	Example: $80 to $100
percentage increase	$\dfrac{\text{increase}}{\text{original}} \times 100\%$	$\dfrac{20}{80} \times 100\%$ , so $25\%$
percentage decrease	$\dfrac{\text{decrease}}{\text{original}} \times 100\%$	$100 to $80: $\dfrac{20}{100} \times 100\%$ , so $20\%$
new value	$\text{original} \times \dfrac{100 \pm r}{100}$	$80 \times \dfrac{125}{100}$ , so $100$

📖 Worked example

The price of a cup of kopi rose from $1.60 to $1.84. Find the percentage increase in the price.

Step 1 of 2

Find the increase

\text{Increase} = 1.84 - 1.60

\phantom{\text{Increase}} = 0.24

📖 Worked example

Siti invests $4,000. The value of her investment grows by 20% in the first year and by 25% in the second year. Find its value after two years.

Step 1 of 2

Write each change as a percentage of the value before it

\text{1st change: } 100\% + 20\% = 120\%

\text{2nd change: } 100\% + 25\% = 125\%

📖 Worked example

The number of visitors to a museum in 2023 was 3,800. This was 5% fewer than in 2022. In 2024, the number was 4,180. Find the percentage increase in the number of visitors to a museum from 2022 to 2024.

Step 1 of 4

Work backwards to 2022: the 2023 number is what percentage of it?

100\% - 5\% = 95\% \rightarrow 3800

Practise this →

3. Reverse percentage

After a 20% discount the price is $96: the original is 80%

\displaystyle 80\% \to 96

e.g.

\displaystyle \dfrac{96}{80} \times 100

\displaystyle = 120

the original price is $120

📖 Worked example

The monthly rent of a shop went up by 10% to $1,980. Find the rent before the increase.

Step 1 of 3

Write the new value as a percentage of the original

100\% + 10\% = 110\%

📖 Worked example

Of the durians at a stall, 45% are sold in the morning. 40% of the rest are sold in the afternoon, and the remaining 66 are left unsold. Find the total number of durians at the stall.

Step 1 of 3

The rest, after the first group: (100% − the first percentage) of the total

100\% - 45\% = 55\%

Practise this →

4. Money: profit, loss and discount

Name	Formula	Example
profit	selling price $-$ cost price	$50 $-$ $40, so $10
percentage profit	$\dfrac{\text{profit}}{\text{cost price}} \times 100\%$	$\dfrac{10}{40} \times 100\%$ , so $25\%$
percentage loss	$\dfrac{\text{loss}}{\text{cost price}} \times 100\%$	$40 to $30: $\dfrac{10}{40} \times 100\%$ , so $25\%$
discount	marked price $-$ selling price	$80 $-$ $68, so $12
percentage discount	$\dfrac{\text{discount}}{\text{marked price}} \times 100\%$	$\dfrac{12}{80} \times 100\%$ , so $15\%$
GST ( $9\%$ )	price $\times 1.09$	$200 $\times 1.09$ , so $218

📖 Worked example

A trader bought a table lamp for $60 and sold it for $52.50. Find the percentage loss.

Step 1 of 2

Loss = cost price − selling price (in dollars)

\text{Loss} = 60 - 52.50

\phantom{\text{Loss}} = 7.50

📖 Worked example

The marked price of a laptop is $150. A shop sells it at a discount of 10% and still makes a profit of 35% on the cost price. Find the cost price of the laptop.

Step 1 of 2

The selling price: (100% − the discount) of the MARKED price

\text{Selling price} = \dfrac{90}{100} \times 150

\phantom{\text{Selling price}} = 135

Practise this →

5. Simple interest

Symbol	Meaning	Example
$P$	principal: the amount deposited or borrowed	$ $2000$
$R$	rate, in % per year (per annum)	$3$
$T$	time, in years	$4$
$I$	interest	$ $240$

Simple interest

\displaystyle I = \dfrac{PRT}{100}

e.g.

\displaystyle I = \dfrac{2000 \times 3 \times 4}{100}

\displaystyle I = 240

Total amount: principal + interest

\displaystyle A = P + I

e.g.

\displaystyle A = 2000 + 240

\displaystyle A = 2240

Time in months: change to years first

\displaystyle T = \dfrac{\text{months}}{12}

e.g.

\displaystyle T = \dfrac{18}{12}

\displaystyle T = 1.5

📖 Worked example

Chen Wei puts $1,000 in a fixed deposit account that pays 1.5% per annum simple interest. Find the total amount in the account after 4 years.

Step 1 of 2

Substitute P, R and T into the formula

I = \dfrac{PRT}{100}

I = \dfrac{1000 \times 1.5 \times 4}{100}

= 60

📖 Worked example

Mei Ling deposits some money in a bank that pays simple interest of 2% per annum. After 5 years, the interest earned is $100. Find the amount of money Mei Ling deposited.

Step 1 of 2

Put the numbers you know into the formula

I = \dfrac{PRT}{100}

100 = \dfrac{P \times 2 \times 5}{100}

Practise this →

6. GST, service charge and discounts

A $50.00 restaurant bill: a 10% service charge of $5.00 makes $55.00, then 9% GST on $55.00 is $4.95, making $59.95.

Charge	Multiply by	Example
$10\%$ service charge	$1.10$	$50 \times 1.10$ , so $ $55$
$9\%$ GST	$1.09$	$55 \times 1.09$ , so $ $59.95$
$15\%$ discount	$0.85$	$80 \times 0.85$ , so $ $68$

Restaurant bill: service charge first, then GST on that total

\displaystyle 50 \times 1.10 \times 1.09

e.g.

\displaystyle 50 \times 1.10 \times 1.09

\displaystyle = 59.95

Discount first, then GST

\displaystyle 80 \times 0.85 \times 1.09

e.g.

\displaystyle 80 \times 0.85 \times 1.09

\displaystyle = 74.12

Price before GST: the price with GST is 109%

\displaystyle 109\% \to 218

e.g.

\displaystyle \dfrac{218}{109} \times 100

\displaystyle = 200

the price before GST is $200

📖 Worked example

The table shows the food a family ordered at a restaurant. A 10% service charge is added to the bill, and then 9% GST is charged on the total. Find the amount the family pays, correct to the nearest cent.

Item	Price
Fried rice	$8.50
Iced lemon tea	$3.20
Chilli crab	$48.00

Step 1 of 3

Add up the bill (in dollars)

8.50 + 3.20 + 48.00 = 59.70

📖 Worked example

The price of an air-conditioner, including 9% GST, is $446.90. Find its price before GST.

Step 1 of 3

The price with GST is what percentage of the price before GST? (in dollars)

100\% + 9\% = 109\%

109\% \rightarrow 446.90

📖 Worked example

The table shows the food a family ordered at a restaurant. Members get a 15% discount on the food, then a 10% service charge is added, and then 9% GST is charged on the total. The family are members. Find the amount they pay, correct to the nearest cent.

Item	Price
Chicken rice	$7.60
Tom yum soup	$11.80
Roti prata set	$6.60

Step 1 of 4

Add up the food (in dollars)

7.60 + 11.80 + 6.60 = 26

Practise this →

7. Instalments and hire purchase

Term	Meaning	Example
cash price	the price paid all at once	$ $1200$
deposit	paid at the start	$25\%$ of $1200$ : $ $300$
loan (balance)	cash price $-$ deposit	$ $900$
instalments	equal monthly payments	$30 \times 36$ : $ $1080$
hire-purchase price	deposit $+$ all the instalments	$ $1380$

Extra paid on hire purchase

\displaystyle \text{HP price} - \text{cash price}

e.g.

\displaystyle 1380 - 1200

\displaystyle = 180

Monthly instalment: interest on the loan for the whole time, then share it out

\displaystyle \dfrac{\text{loan} + \text{interest}}{\text{number of months}}

e.g.

\displaystyle \dfrac{900 + 180}{30}

\displaystyle = 36

$8\%$ per annum for $30$ months ( $2.5$ years): $\dfrac{900 \times 8 \times 2.5}{100}$ , so $180 interest

Interest as a percentage of the loan

\displaystyle \dfrac{\text{interest}}{\text{loan}} \times 100\%

e.g.

\displaystyle \dfrac{180}{900} \times 100

\displaystyle = 20

$20\%$ of the loan

📖 Worked example

The table shows the terms for buying a home theatre system on hire purchase. Find how much more the home theatre system costs on hire purchase than for cash.

Hire purchase	Home theatre system
Cash price	$1,200
Deposit	25% of the cash price
Monthly instalments	30 instalments of $36

Step 1 of 4

Deposit (in dollars)

\text{Deposit} = \dfrac{25}{100} \times 1200

\phantom{\text{Deposit}} = 300

📖 Worked example

Hui Min buys a sofa set on the hire-purchase terms in the table. The balance after the deposit is charged simple interest for the 18 months, and the balance plus the interest is paid back in 18 equal monthly instalments. Find each monthly instalment.

Hire purchase	Sofa set
Cash price	$960
Deposit	10% of the cash price
Interest on the balance	5% per annum, simple interest
Repayment	18 equal monthly instalments

Step 1 of 5

Deposit (in dollars)

\text{Deposit} = \dfrac{10}{100} \times 960

\phantom{\text{Deposit}} = 96

📖 Worked example

Jun Jie buys a piano on the hire-purchase terms in the table. The amount still owed after the deposit is the loan, and the interest is simple interest on the loan for the 36 months. Find the rate of simple interest per annum.

Hire purchase	Piano
Cash price	$960
Deposit	25% of the cash price
Monthly instalments	36 instalments of $23.60

Step 1 of 5

Deposit (in dollars)

\text{Deposit} = \dfrac{25}{100} \times 960

\phantom{\text{Deposit}} = 240

📖 Worked example

Siti buys an air-conditioner on the hire-purchase terms in the table. The balance after the deposit is charged simple interest for the 30 months, and the balance plus the interest is paid back in the instalments shown. Find the cash price of the air-conditioner.

Hire purchase	Air-conditioner
Deposit	20% of the cash price
Interest on the balance	8% per annum, simple interest
Monthly instalments	30 instalments of $38.40

Step 1 of 3

All the instalments repay the loan plus its interest

30 \times 38.40 = 1152

📖 Worked example

Jun Jie buys a car on the terms in the table. Find the monthly instalment.

Buying the car
List price	$120,000
Dealer's discount	5% of the list price
Registration and other fees	$1,850 (paid in cash)
Down payment	40% of the price after the discount
Car loan	the rest of the price, at 3% per annum simple interest for 6 years, paid back in equal monthly instalments

Step 1 of 4

The price after the discount (in dollars)

\dfrac{95}{100} \times 120000 = 114000

Practise this →

Practise percentage with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

Start free

Sec 1 · G2 (N(A))

Percentage

Practise percentage with step-by-step help. Free account.

Start free

1. Percentages, fractions and decimals

Percentage	Fraction	Decimal
$45\%$	$\dfrac{9}{20}$	$0.45$
$12.5\%$	$\dfrac{1}{8}$	$0.125$
$150\%$	$\dfrac{3}{2}$	$1.5$

One quantity as a percentage of another: 18 out of 40

\displaystyle \dfrac{18}{40} \times 100\%

e.g.

\displaystyle \dfrac{18}{40} \times 100

\displaystyle = 45

$45\%$

A percentage of a quantity: 35% of $240

\displaystyle \dfrac{35}{100} \times 240

e.g.

\displaystyle \dfrac{35}{100} \times 240

\displaystyle = 84

📖 Worked example

Express $75$ as a percentage of $120$ .

Step 1 of 1

Write the first quantity as a fraction of the second, then multiply by 100%

\dfrac{75}{120} \times 100\%

= 62.5\%

📖 Worked example

Write $37\dfrac{1}{2}\%$ as a fraction in its simplest form.

Step 1 of 2

Write the mixed number as an improper fraction first

37\dfrac{1}{2}

= \dfrac{75}{2}

Practise this →

2. Percentage change

Name	Formula	Example: $80 to $100
percentage increase	$\dfrac{\text{increase}}{\text{original}} \times 100\%$	$\dfrac{20}{80} \times 100\%$ , so $25\%$
percentage decrease	$\dfrac{\text{decrease}}{\text{original}} \times 100\%$	$100 to $80: $\dfrac{20}{100} \times 100\%$ , so $20\%$
new value	$\text{original} \times \dfrac{100 \pm r}{100}$	$80 \times \dfrac{125}{100}$ , so $100$

📖 Worked example

The price of a cup of kopi rose from $1.60 to $1.84. Find the percentage increase in the price.

Step 1 of 2

Find the increase

\text{Increase} = 1.84 - 1.60

\phantom{\text{Increase}} = 0.24

📖 Worked example

Siti invests $4,000. The value of her investment grows by 20% in the first year and by 25% in the second year. Find its value after two years.

Step 1 of 2

Write each change as a percentage of the value before it

\text{1st change: } 100\% + 20\% = 120\%

\text{2nd change: } 100\% + 25\% = 125\%

📖 Worked example

Step 1 of 4

Work backwards to 2022: the 2023 number is what percentage of it?

100\% - 5\% = 95\% \rightarrow 3800

Practise this →

3. Reverse percentage

After a 20% discount the price is $96: the original is 80%

\displaystyle 80\% \to 96

e.g.

\displaystyle \dfrac{96}{80} \times 100

\displaystyle = 120

the original price is $120

📖 Worked example

The monthly rent of a shop went up by 10% to $1,980. Find the rent before the increase.

Step 1 of 3

Write the new value as a percentage of the original

100\% + 10\% = 110\%

📖 Worked example

Of the durians at a stall, 45% are sold in the morning. 40% of the rest are sold in the afternoon, and the remaining 66 are left unsold. Find the total number of durians at the stall.

Step 1 of 3

The rest, after the first group: (100% − the first percentage) of the total

100\% - 45\% = 55\%

Practise this →

4. Money: profit, loss and discount

Name	Formula	Example
profit	selling price $-$ cost price	$50 $-$ $40, so $10
percentage profit	$\dfrac{\text{profit}}{\text{cost price}} \times 100\%$	$\dfrac{10}{40} \times 100\%$ , so $25\%$
percentage loss	$\dfrac{\text{loss}}{\text{cost price}} \times 100\%$	$40 to $30: $\dfrac{10}{40} \times 100\%$ , so $25\%$
discount	marked price $-$ selling price	$80 $-$ $68, so $12
percentage discount	$\dfrac{\text{discount}}{\text{marked price}} \times 100\%$	$\dfrac{12}{80} \times 100\%$ , so $15\%$
GST ( $9\%$ )	price $\times 1.09$	$200 $\times 1.09$ , so $218

📖 Worked example

A trader bought a table lamp for $60 and sold it for $52.50. Find the percentage loss.

Step 1 of 2

Loss = cost price − selling price (in dollars)

\text{Loss} = 60 - 52.50

\phantom{\text{Loss}} = 7.50

📖 Worked example

The marked price of a laptop is $150. A shop sells it at a discount of 10% and still makes a profit of 35% on the cost price. Find the cost price of the laptop.

Step 1 of 2

The selling price: (100% − the discount) of the MARKED price

\text{Selling price} = \dfrac{90}{100} \times 150

\phantom{\text{Selling price}} = 135

Practise this →

5. Simple interest

Symbol	Meaning	Example
$P$	principal: the amount deposited or borrowed	$ $2000$
$R$	rate, in % per year (per annum)	$3$
$T$	time, in years	$4$
$I$	interest	$ $240$

Simple interest

\displaystyle I = \dfrac{PRT}{100}

e.g.

\displaystyle I = \dfrac{2000 \times 3 \times 4}{100}

\displaystyle I = 240

Total amount: principal + interest

\displaystyle A = P + I

e.g.

\displaystyle A = 2000 + 240

\displaystyle A = 2240

Time in months: change to years first

\displaystyle T = \dfrac{\text{months}}{12}

e.g.

\displaystyle T = \dfrac{18}{12}

\displaystyle T = 1.5

📖 Worked example

Chen Wei puts $1,000 in a fixed deposit account that pays 1.5% per annum simple interest. Find the total amount in the account after 4 years.

Step 1 of 2

Substitute P, R and T into the formula

I = \dfrac{PRT}{100}

I = \dfrac{1000 \times 1.5 \times 4}{100}

= 60

📖 Worked example

Mei Ling deposits some money in a bank that pays simple interest of 2% per annum. After 5 years, the interest earned is $100. Find the amount of money Mei Ling deposited.

Step 1 of 2

Put the numbers you know into the formula

I = \dfrac{PRT}{100}

100 = \dfrac{P \times 2 \times 5}{100}

Practise this →

6. GST, service charge and discounts

Charge	Multiply by	Example
$10\%$ service charge	$1.10$	$50 \times 1.10$ , so $ $55$
$9\%$ GST	$1.09$	$55 \times 1.09$ , so $ $59.95$
$15\%$ discount	$0.85$	$80 \times 0.85$ , so $ $68$

Restaurant bill: service charge first, then GST on that total

\displaystyle 50 \times 1.10 \times 1.09

e.g.

\displaystyle 50 \times 1.10 \times 1.09

\displaystyle = 59.95

Discount first, then GST

\displaystyle 80 \times 0.85 \times 1.09

e.g.

\displaystyle 80 \times 0.85 \times 1.09

\displaystyle = 74.12

Price before GST: the price with GST is 109%

\displaystyle 109\% \to 218

e.g.

\displaystyle \dfrac{218}{109} \times 100

\displaystyle = 200

the price before GST is $200

📖 Worked example

Item	Price
Fried rice	$8.50
Iced lemon tea	$3.20
Chilli crab	$48.00

Step 1 of 3

Add up the bill (in dollars)

8.50 + 3.20 + 48.00 = 59.70

📖 Worked example

The price of an air-conditioner, including 9% GST, is $446.90. Find its price before GST.

Step 1 of 3

The price with GST is what percentage of the price before GST? (in dollars)

100\% + 9\% = 109\%

109\% \rightarrow 446.90

📖 Worked example

Item	Price
Chicken rice	$7.60
Tom yum soup	$11.80
Roti prata set	$6.60

Step 1 of 4

Add up the food (in dollars)

7.60 + 11.80 + 6.60 = 26

Practise this →

7. Instalments and hire purchase

Term	Meaning	Example
cash price	the price paid all at once	$ $1200$
deposit	paid at the start	$25\%$ of $1200$ : $ $300$
loan (balance)	cash price $-$ deposit	$ $900$
instalments	equal monthly payments	$30 \times 36$ : $ $1080$
hire-purchase price	deposit $+$ all the instalments	$ $1380$

Extra paid on hire purchase

\displaystyle \text{HP price} - \text{cash price}

e.g.

\displaystyle 1380 - 1200

\displaystyle = 180

Monthly instalment: interest on the loan for the whole time, then share it out

\displaystyle \dfrac{\text{loan} + \text{interest}}{\text{number of months}}

e.g.

\displaystyle \dfrac{900 + 180}{30}

\displaystyle = 36

$8\%$ per annum for $30$ months ( $2.5$ years): $\dfrac{900 \times 8 \times 2.5}{100}$ , so $180 interest

Interest as a percentage of the loan

\displaystyle \dfrac{\text{interest}}{\text{loan}} \times 100\%

e.g.

\displaystyle \dfrac{180}{900} \times 100

\displaystyle = 20

$20\%$ of the loan

📖 Worked example

The table shows the terms for buying a home theatre system on hire purchase. Find how much more the home theatre system costs on hire purchase than for cash.

Hire purchase	Home theatre system
Cash price	$1,200
Deposit	25% of the cash price
Monthly instalments	30 instalments of $36

Step 1 of 4

Deposit (in dollars)

\text{Deposit} = \dfrac{25}{100} \times 1200

\phantom{\text{Deposit}} = 300

📖 Worked example

Hire purchase	Sofa set
Cash price	$960
Deposit	10% of the cash price
Interest on the balance	5% per annum, simple interest
Repayment	18 equal monthly instalments

Step 1 of 5

Deposit (in dollars)

\text{Deposit} = \dfrac{10}{100} \times 960

\phantom{\text{Deposit}} = 96

📖 Worked example

Hire purchase	Piano
Cash price	$960
Deposit	25% of the cash price
Monthly instalments	36 instalments of $23.60

Step 1 of 5

Deposit (in dollars)

\text{Deposit} = \dfrac{25}{100} \times 960

\phantom{\text{Deposit}} = 240

📖 Worked example

Hire purchase	Air-conditioner
Deposit	20% of the cash price
Interest on the balance	8% per annum, simple interest
Monthly instalments	30 instalments of $38.40

Step 1 of 3

All the instalments repay the loan plus its interest

30 \times 38.40 = 1152

📖 Worked example

Jun Jie buys a car on the terms in the table. Find the monthly instalment.

Buying the car
List price	$120,000
Dealer's discount	5% of the list price
Registration and other fees	$1,850 (paid in cash)
Down payment	40% of the price after the discount
Car loan	the rest of the price, at 3% per annum simple interest for 6 years, paid back in equal monthly instalments

Step 1 of 4

The price after the discount (in dollars)

\dfrac{95}{100} \times 120000 = 114000

Practise this →

Practise percentage with step-by-step help

Endless questions from basic to exam level. Get one wrong and see where it went wrong. Free account.

Start free