Increase and Decrease an Amount by a Percent

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Question 1 of 5

1. Question
Increase $$60$ by $80%$
- $$$ (108)
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ converts it into a fraction.

Increasing Amount by Percentage

$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$

First, solve for $80%$ of the original amount, $$60$ . Use fractions for easier computation.

$80%times$ $60$

$=$ $80/100times60/1$ Convert to fraction form

$=$ $\frac{4800}{100}$

$=$ $$48$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$ $=$ $\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$

$=$ $$60$ $+$ $$48$

$=$ $$108$

$$60$ increased by $80%$ is $$108$

$$108$
Question 2 of 5

2. Question
Increase $$400$ by $32%$
- $$$ (528)
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ converts it into a fraction.

Increasing Amount by Percentage

$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$

Method One

First, solve for $32%$ of the original amount, $$400$ . Use fractions for easier computation.

$32%times$ $400$

$=$ $32/100times400/1$ Convert to fraction form

$=$ $32/1times4/1$ Simplify

$=$ $\frac{128}{1}$

$=$ $$128$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$ $=$ $\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$

$=$ $$400$ $+$ $$128$

$=$ $$528$

$$400$ increased by $32%$ is $$528$

$$528$

Method Two

First, get the new total percentage by adding $32$ to the amount’s percentage, which is $100$ .

$\text(Percentage)$ $=$ $100+32$

$=$ $132%$

Finally, to get the percentage of an amount, simply solve for their product. Use fractions for easier computation.

$132%times400$

$=$ $132/100times400/1$ Convert to fraction form

$=$ $132/1times4/1$ Simplify

$=$ $\frac{528}{1}$

$=$ $528$

$$400$ increased by $32%$ is $$528$

$$528$
Question 3 of 5

3. Question
Increase $150 \text(km)$ by $9%$

Round your answer to one decimal place
- (163.5) $\text(km)$
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ converts it into a fraction.

Increasing Amount by Percentage

$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$

First, solve for $9%$ of the original value, $150 \text(km)$ . Use fractions for easier computation.

$9%times$ $150$

$=$ $9/100times150/1$ Convert to fraction form

$=$ $9/10times15/1$ Simplify

$=$ $\frac{135}{10}$

Since the value is being divided by $10$ , simply move the decimal point $1$ place to the left.

Hence, $9%$ of $150 \text(km)$ is $\underline{\color{#9a00c7}{13.5\;\text{km}}}$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$ $=$ $\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$

$=$ $150$ $+$ $13.5$

$=$ $163.5 \text(km)$

$150 \text(km)$ increased by $9%$ is $163.5 \text(km)$

$163.5 \text(km)$
Question 4 of 5

4. Question
Decrease $300 \text(g)$ by $40%$

Round your answer to one decimal place
- (180) $\text(g)$
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ converts it into a fraction.

Decreasing Amount by Percentage

$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$

First, solve for $40%$ of the original amount, $300 \text(g)$ . Use fractions for easier computation.

$40%times$ $300$

$=$ $40/100times300/1$ Convert to fraction form

$=$ $40/1times3/1$ Simplify

$=$ $\frac{120}{1}$

$=$ $120 \text(g)$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$ $=$ $\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$

$=$ $300$ $-$ $120$

$=$ $180$

$300 \text(g)$ decreased by $40%$ is $180 \text(g)$

$180 \text(g)$
Question 5 of 5

5. Question
Decrease $$450$ by $30%$
- $$$ (315)
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ converts it into a fraction.

Decreasing Amount by Percentage

$\mathsf{\color{#007DDC}{new\;amount}}=\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$

First, solve for $30%$ of the original amount, $$450$ . Use fractions for easier computation.

$30%times$ $450$

$=$ $30/100times450/1$ Convert to fraction form

$=$ $3/1times45/1$ Simplify

$=$ $\frac{135}{1}$

$=$ $$135$

Next, use the formula to get the new amount

$\mathsf{\color{#007DDC}{new\;amount}}$ $=$ $\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$

$=$ $450$ $-$ $135$

$=$ $315$

$$450$ decreased by $30%$ is $$315$

$$315$

Increase and Decrease an Amount by a Percent

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Quiz summary

Information

1. Question

Hint

Well Done!

Increasing Amount by Percentage

2. Question

Hint

Nice Job!

Increasing Amount by Percentage

3. Question

Hint

Excellent!

Increasing Amount by Percentage

4. Question

Hint

Fantastic!

Decreasing Amount by Percentage

5. Question

Hint

Keep Going!

Decreasing Amount by Percentage

Quizzes

	$80%times$ $60$

$=$	$80/100times60/1$	Convert to fraction form

$=$	$\frac{4800}{100}$

$=$	$$48$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$
	$=$	$$60$ $+$ $$48$
	$=$	$$108$

	$32%times$ $400$

$=$	$32/100times400/1$	Convert to fraction form

$=$	$32/1times4/1$	Simplify

$=$	$\frac{128}{1}$

$=$	$$128$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$
	$=$	$$400$ $+$ $$128$
	$=$	$$528$

	$132%times400$

$=$	$132/100times400/1$	Convert to fraction form

$=$	$132/1times4/1$	Simplify

$=$	$\frac{528}{1}$

$=$	$528$

	$9%times$ $150$

$=$	$9/100times150/1$	Convert to fraction form

$=$	$9/10times15/1$	Simplify

$=$	$\frac{135}{10}$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}+\mathsf{\color{#9a00c7}{increase}}$
	$=$	$150$ $+$ $13.5$
	$=$	$163.5 \text(km)$

	$40%times$ $300$

$=$	$40/100times300/1$	Convert to fraction form

$=$	$40/1times3/1$	Simplify

$=$	$\frac{120}{1}$

$=$	$120 \text(g)$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$300$ $-$ $120$
	$=$	$180$

	$30%times$ $450$

$=$	$30/100times450/1$	Convert to fraction form

$=$	$3/1times45/1$	Simplify

$=$	$\frac{135}{1}$

$=$	$$135$

$\text(Percentage)$	$=$	$100+32$
	$=$	$132%$

$\mathsf{\color{#007DDC}{new\;amount}}$	$=$	$\mathsf{\color{#00880A}{original}}-\mathsf{\color{#9a00c7}{decrease}}$
	$=$	$450$ $-$ $135$
	$=$	$315$