Using Percentages with Proportions

Question 1 of 5

What percentage

(%)

$(%)$ of

247

$247$ is

83

$83$ ?

Round your answer to one decimal place

(33.6) $%$ $%$

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To understand the problem better, draw a line diagram and list down the values as shown below.

Known value = 83

$\text(Known value)=83$

Total value = 247

$\text(Total value)=247$

Percentage of total value = 100 %

$\text(Percentage of total value)=100%$

Percentage of known value = ?

$\text(Percentage of known value)=?$

Proportion Method

$\text(Proportion Method)$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the percentage of the amount be $r$ $r$ .

$\frac{\color{#00880A}{83}}{\color{#9a00c7}{247}}$	$=$ $=$	$\frac{\color{#007DDC}{r}}{\color{#e85e00}{100}}$

$247 \times r$ $247timesr$	$=$ $=$	$83 \times 100$ $83times100$	Cross multiply
$247 r$ $247r$	$=$ $=$	$8300$
$247 r$ $247r$ $\div 247$ $divide247$	$=$ $=$	$8300\color{#CC0000}{\div247}$	Divide both sides by $247$ $247$

$r$ $r$	$=$ $=$	$33.6$ $33.6$	Rounded to one decimal place

Hence,

83

$83$ is $\underline{\color{#007DDC}{33.6\%}}$ of

247

$247$ .

33.6 %

$33.6%$

Fraction Method

$\text(Fraction Method)$

To find the missing value, simply multiply the fraction of the known values by

100

$100$ .

The fraction can be written as the known value

(

$($ $83$ $83$

)

$)$ over the total value

(

$($ $247$ $247$

)

$)$ .

	$\frac{\color{#00880A}{83}}{\color{#9a00c7}{247}}\times100$

$=$ $=$	$\frac{83}{247} \times \frac{100}{1}$ $83/247times100/1$	Convert values to fraction form
$=$ $=$	$\frac{8300}{247}$

$=$ $=$	$33.6$ $33.6$	Rounded to one decimal place

Hence,

83

$83$ is $\underline{\color{#007DDC}{33.6\%}}$ of

247

$247$ .

33.6 %

$33.6%$

Question 2 of 5

What percentage

(%)

$(%)$ of

600 kg

$600 \text(kg)$ is

18 kg

$18 \text(kg)$ ?

(3) $%$ $%$

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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.

Known value = 18 kg

$\text(Known value)=18 \text(kg)$

Total value = 600 kg

$\text(Total value)=600 \text(kg)$

Percentage of total value = 100 %

$\text(Percentage of total value)=100%$

Percentage of known value = ?

$\text(Percentage of known value)=?$

Proportion Method

$\text(Proportion Method)$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the percentage on the amount be $r$ $r$

$\frac{\color{#007DDC}{r}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{18}}{\color{#9a00c7}{600}}$

$600 \times r$ $600timesr$	$=$ $=$	$18 \times 100$ $18times100$	Cross multiply
$600 r$ $600r$	$=$ $=$	$1800$
$600 r$ $600r$ $\div 600$ $divide600$	$=$ $=$	$1800\color{#CC0000}{\div600}$	Divide both sides by $600$ $600$

$r$ $r$	$=$ $=$	$\frac{1800}{600}$	Simplify

$r$ $r$	$=$ $=$	$3$ $3$

Hence,

18 kg

$18 \text(kg)$ is $\underline{\color{#007DDC}{3\%}}$ of

600 kg

$600 \text(kg)$ .

3 %

$3%$

1 % Method

$1% \text(Method)$

First, find the

1 %

$1%$ of the total value

(

$($ $600$ $600$

)

$)$ by dividing the total amount by

100

$100$ .

$1 %$ $1%$	$=$ $=$	$600$ $600$ $\div 100$ $divide100$
	$=$ $=$	$6$ $6$

Hence,

1 %

$1%$ of the original amount is

6 kg

$6 \text(kg)$ .

To find the percentage of the given amount, multiply the

1 %

$1%$ value, which is

6

$6$ , by a value to get it to $18$ $18$ .

Multiplying

6

$6$ by

3

$3$ will make it $18$ $18$

$1 %$ $1%$	$=$ $=$	$6$ $6$
$1 %$ $1%$ $\times 3$ $times3$	$=$ $=$	$6$ $6$ $\times 3$ $times3$	Multiply both sides by $3$ $3$
$3 %$ $3%$	$=$ $=$	$18$ $18$

Hence,

18 kg

$18 \text(kg)$ is $\underline{\color{#007DDC}{3\%}}$ of

600 kg

$600 \text(kg)$ .

3 %

$3%$

Question 3 of 5

What is

5 kg

$5 \text(kg)$ of fish as a percentage

(%)

$(%)$ of

250 kg

$250 \text(kg)$ of fish?

(2) $%$ $%$

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First, summarise the data for easier understanding of the problem.

Given weight = 5 kg

$\text(Given weight)=5 \text(kg)$

Total weight = 250 kg

$\text(Total weight)=250 \text(kg)$

Percentage of total value = 100 %

$\text(Percentage of total value)=100%$

Percentage of given weight = ?

$\text(Percentage of given weight)=?$

To find the missing value, simply multiply the fraction of the known values by

100

$100$ .

The fraction can be written as the given weight

(

$($ $5$ $5$

)

$)$ over the total value

(

$($ $250$ $250$

)

$)$ .

	$\frac{\color{#00880A}{5}}{\color{#9a00c7}{250}}\times100$

$=$ $=$	$\frac{5}{250} \times \frac{100}{1}$ $5/250times100/1$	Convert values to fraction form
$=$ $=$	$\frac{500}{250}$

$=$ $=$	$2$ $2$

Hence,

5 kg

$5 \text(kg)$ is $\underline{\color{#007DDC}{2\%}}$ of

250 kg

$250 \text(kg)$ .

2 %

$2%$

Question 4 of 5

What percentage

(%)

$(%)$ of

$ 150

$$150$ is

$ 12

$$12$ ?

(8) $%$ $%$

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First, summarise the data and draw a diagram for easier understanding of the problem

Given amount = $ 12

$\text(Given amount)=$12$

Total amount = $ 150

$\text(Total amount)=$150$

Percentage of total value = 100 %

$\text(Percentage of total value)=100%$

Percentage of given amount = ?

$\text(Percentage of given amount)=?$

Proportion Method

$\text(Proportion Method)$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the percentage of the amount be $r$ $r$

$\frac{\color{#00880A}{12}}{\color{#9a00c7}{150}}$	$=$ $=$	$\frac{\color{#007DDC}{r}}{\color{#e85e00}{100}}$

$150 \times r$ $150timesr$	$=$ $=$	$12 \times 100$ $12times100$	Cross multiply
$150 r$ $150r$	$=$ $=$	$1200$
$150 r$ $150r$ $\div 150$ $divide150$	$=$ $=$	$1200\color{#CC0000}{\div150}$	Divide both sides by $150$ $150$

$r$ $r$	$=$ $=$	$\frac{120}{15}$	Simplify

$r$ $r$	$=$ $=$	$8$ $8$

Hence,

$ 12

$$12$ is $\underline{\color{#007DDC}{8\%}}$ of

$ 150

$$150$ .

8 %

$8%$

Fraction Method

$\text(Fraction Method)$

To find the missing value, simply multiply the fraction of the known values by

100

$100$ .

The fraction can be written as the known value

(

$($ $12$ $12$

)

$)$ over the total value

(

$($ $150$ $150$

)

$)$ .

	$\frac{\color{#00880A}{12}}{\color{#9a00c7}{150}}\times100$

$=$ $=$	$\frac{12}{150} \times \frac{100}{1}$ $12/150times100/1$	Convert values to fraction form
$=$ $=$	$\frac{1200}{150}$

$=$ $=$	$\frac{120}{15}$	Simplify

$=$ $=$	$8$ $8$

Hence,

$ 12

$$12$ is $\underline{\color{#007DDC}{8\%}}$ of

$ 150

$$150$ .

8 %

$8%$

Question 5 of 5

If you spend

20 %

$20%$ of your savings to buy a

$ 1200

$$1200$ laptop, how much is your total savings?

$$$ $$$ (6000)

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First, use a rectangle and list down the values: percentages on the left side and amounts on the right side.

Known value = 1200

$\text(Known value)=1200$

Percentage of known value = 20 %

$\text(Percentage of known value)=20%$

Percentage of total value = 100 %

$\text(Percentage of total value)=100%$

Total value = ?

$\text(Total value)=?$

To find the missing value, cross-multiply the fraction of the percentages by the fraction of the given and total value.

Let the original amount be $x$ $x$

$\frac{\color{#007DDC}{20}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{1200}}{\color{#9a00c7}{x}}$

$20 \times x$ $20timesx$	$=$ $=$	$1200 \times 100$ $1200times100$	Cross multiply
$20 x$ $20x$	$=$ $=$	$120{,}000$
$20 x$ $20x$ $\div 20$ $divide20$	$=$ $=$	$120{,}000\color{#CC0000}{\div20}$	Divide both sides by $20$ $20$

$x$ $x$	$=$ $=$	$\frac{12{,}000}{2}$	Simplify

$x$ $x$	$=$ $=$	$6000$ $6000$

Hence, the total savings is $\underline{\color{#9a00c7}{$6000}}$

$ 6000

$$6000$

Using Percentages with Proportions

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