Sec 1 · G1 (N(T))

Percentage

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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\%

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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\%

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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\%

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4. Money: discount

Name	Formula	Example
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 $15\%$
selling price after a $15\%$ discount	$85\%$ of the marked price	$\dfrac{85}{100} \times 80$ , so $68

📖 Worked example

The marked price of a rice cooker is $80. During a sale it is sold for $68. Find the percentage discount.

Step 1 of 2

Discount = marked price − selling price (in dollars)

\text{Discount} = 80 - 68

\phantom{\text{Discount}} = 12

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Sec 1 · G1 (N(T))

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\%

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\%

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\%

Practise this →

4. Money: discount

Name	Formula	Example
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 $15\%$
selling price after a $15\%$ discount	$85\%$ of the marked price	$\dfrac{85}{100} \times 80$ , so $68

📖 Worked example

The marked price of a rice cooker is $80. During a sale it is sold for $68. Find the percentage discount.

Step 1 of 2

Discount = marked price − selling price (in dollars)

\text{Discount} = 80 - 68

\phantom{\text{Discount}} = 12

Practise this →

Practise percentage with step-by-step help

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