Percent of an Amount 1

Years

Year 11

Percentages

Percent of an Amount

Percent of an Amount 1

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Question 1 of 5

1. Question
What is $4 %$ $4%$ of $$ 700$ $$700$ ?
- $$$ $$$ (28)
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ $100$ converts it into a fraction.

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

$4 % \times 700$ $4%times700$

$=$ $=$ $\frac{4}{100} \times \frac{700}{1}$ $4/100times700/1$ Convert to fraction form

$=$ $=$ $\frac{4}{1} \times \frac{7}{1}$ $4/1times7/1$ Simplify

$=$ $=$ $\frac{28}{1}$

$=$ $=$ $28$ $28$

Hence, $4 %$ $4%$ of $$ 700$ $$700$ is $\underline{$28}$

$$ 28$ $$28$

Question 2 of 5

What is

27 %

$27%$ of

600 grams

$600 \text(grams)$ ?

(162) $grams$ $\text(grams)$

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A percentage describes an amount’s relation to a whole. Dividing it by

100

$100$ converts it into a fraction.

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

	$27 % \times 600$ $27%times600$

$=$ $=$	$\frac{27}{100} \times \frac{600}{1}$ $27/100times600/1$	Convert to fraction form

$=$ $=$	$\frac{27}{1} \times \frac{6}{1}$ $27/1times6/1$	Simplify

$=$ $=$	$\frac{162}{1}$

$=$ $=$	$162$ $162$

Hence,

27 %

$27%$ of

600 grams

$600 \text(grams)$ is $\underline{162\;\text{grams}}$

162

$162$

grams

$\text(grams)$

Question 3 of 5

What is

35 %

$35%$ of

60 litres

$60 \text(litres)$ ?

(21) $litres$ $\text(litres)$

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A percentage describes an amount’s relation to a whole. Dividing it by

100

$100$ converts it into a fraction.

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

	$35 % \times 60$ $35%times60$

$=$ $=$	$\frac{35}{100} \times \frac{60}{1}$ $35/100times60/1$	Convert to fraction form

$=$ $=$	$\frac{35}{10} \times \frac{6}{1}$ $35/10times6/1$	Simplify

$=$ $=$	$\frac{210}{10}$

$=$ $=$	$\frac{21}{1}$	Simplify

$=$ $=$	$21$ $21$

Hence,

35 %

$35%$ of

60 litres

$60 \text(litres)$ is $\underline{21\;\text{litres}}$

21

$21$

litres

$\text(litres)$

Question 4 of 5

4. Question
What is $45 %$ $45%$ of $2$ $2$ metres?
- (0.9) $metres$ $\text(metres)$
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A percentage describes an amount’s relation to a whole. Dividing it by $100$ $100$ converts it into a fraction.

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

$45 % \times 2$ $45%times2$

$=$ $=$ $\frac{45}{100} \times \frac{2}{1}$ $45/100times2/1$ Convert to fraction form

$=$ $=$ $\frac{90}{100}$

Since the value is being divided by $100$ $100$ , simply move the decimal point $2$ $2$ places to the left.

Hence, $45 %$ $45%$ of $2$ $2$ metres is $\underline{0.9\;\text{metres}}$

$0.9$ $0.9$ $metres$ $\text(metres)$

Question 5 of 5

What is

33 \frac{1}{3} %

$33 1/3%$ of

$ 180

$$180$ ?

$$$ $$$ (60)

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Transforming a Fraction from Mixed to Improper

=

$=$

\frac{(c \times a) + b}{c}

$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{a})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$

A percentage describes an amount’s relation to a whole. Dividing it by

100

$100$ converts it into a fraction.

First, convert the percentage value into an improper fraction by multiplying the denominator by the whole number and then adding the numerator

$\color{#00880A}{33}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}$	$=$ $=$	$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{33})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}$

	$=$ $=$	$\frac{99+1}{3}$

	$=$ $=$	$\frac{100}{3}\%$

Next, convert the percentage into a fraction by dividing it by

100

$100$

Dividing fractions is the same as multiplying the dividend by the divisor’s reciprocal

$Fraction$ $\text(Fraction)$	$=$ $=$	$\frac{\frac{100}{3}}{\color{#CC0000}{100}}$

	$=$ $=$	$\frac{100}{3}\div{\color{#CC0000}{100}}$	Change from a fraction to division

	$=$ $=$	$\frac{100}{3}\times\frac{1}{100}$	Get the divisor’s reciprocal then multiply

	$=$ $=$	$\frac{1}{3}$	Simplify

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

	$\frac{1}{3} \times 180$ $1/3times180$

$=$ $=$	$\frac{1}{3} \times \frac{180}{1}$ $1/3times180/1$	Convert to fraction form

$=$ $=$	$\frac{180}{3}$

$=$ $=$	$60$ $60$

Hence,

33 \frac{1}{3} %

$33 1/3%$ of

$ 180

$$180$ is $\underline{$60}$

$ 60

$$60$

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Transforming a Fraction from Mixed to Improper

Quizzes

	$4 % \times 700$ $4%times700$

$=$ $=$	$\frac{4}{100} \times \frac{700}{1}$ $4/100times700/1$	Convert to fraction form

$=$ $=$	$\frac{4}{1} \times \frac{7}{1}$ $4/1times7/1$	Simplify

$=$ $=$	$\frac{28}{1}$

$=$ $=$	$28$ $28$

	$45 % \times 2$ $45%times2$

$=$ $=$	$\frac{45}{100} \times \frac{2}{1}$ $45/100times2/1$	Convert to fraction form

$=$ $=$	$\frac{90}{100}$