Find Base from Percent of an Amount (Unitary Method) 1

Question 1 of 4

8 %

$8%$ of an amount is

$ 40

$$40$ . Find the original amount.

$$$ $$$ (500)

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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 = $ 40

$\text(Known value)=$40$

Percentage of known value = 8 %

$\text(Percentage of known value)=8%$

Percentage of total value = 100 %

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

Total value = ?

$\text(Total value)=?$

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 original amount be $x$ $x$

$\frac{\color{#007DDC}{8}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{40}}{\color{#9a00c7}{x}}$
$\frac{8}{100}$ $8/100$	$=$ $=$	$\frac{40}{x}$ $40/x$

$8 \times x$ $8timesx$	$=$ $=$	$40 \times 100$ $40times100$	Cross multiply
$8 x$ $8x$	$=$ $=$	$4000$
$8 x$ $8x$ $\div 8$ $divide8$	$=$ $=$	$4000\color{#CC0000}{\div8}$	Divide both sides by $8$ $8$
$x$ $x$	$=$ $=$	$500$ $500$

Hence,

$ 40

$$40$ is

8 %

$8%$ of $\underline{\color{#9a00c7}{$500}}$

$ 500

$$500$

1 % Method - Unitary Method

$1% \text(Method) -\text(Unitary Method)$

First, find the

1 %

$1%$ of the total value by dividing both known values by $8$ $8$ .

$8 %$ $8%$	$=$ $=$	$$ 40$ $$40$

$8$ $8$ $\div 8$ $divide8$	$=$ $=$	$40$ $40$ $\div 8$ $divide8$	Divide both sides by $8$ $8$
$1$ $1$	$=$ $=$	$5$ $5$

Hence,

1 %

$1%$ of the original amount is

$ 5

$$5$ .

To find the total value, which is $100 %$ $100%$ of the value, multiply the

1 %

$1%$ value, which is

5

$5$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$5 \times 100$ $5times100$
	$=$ $=$	$500$ $500$

Hence,

$ 40

$$40$ is

8 %

$8%$ of $\underline{\color{#9a00c7}{$500}}$

$ 500

$$500$

Question 2 of 4

5 %

$5%$ of an amount is

$ 135

$$135$ . Find the original amount.

$$$ $$$ (2700)

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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 = $ 135

$\text(Known value)=$135$

Percentage of known value = 5 %

$\text(Percentage of known value)=5%$

Percentage of total value = 100 %

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

Total value = ?

$\text(Total value)=?$

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 original amount be $x$ $x$

$\frac{\color{#007DDC}{5}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{135}}{\color{#9a00c7}{x}}$

$5 \times x$ $5timesx$	$=$ $=$	$135 \times 100$ $135times100$	Cross multiply
$5 x$ $5x$	$=$ $=$	$13{,}500$
$5 x$ $5x$ $\div 5$ $divide5$	$=$ $=$	$13{,}500\color{#CC0000}{\div5}$	Divide both sides by $5$ $5$
$x$ $x$	$=$ $=$	$2700$ $2700$

Hence,

$ 135

$$135$ is

5 %

$5%$ of $\underline{\color{#9a00c7}{$2700}}$

$ 2700

$$2700$

1 % Method - Unitary Method

$1% \text(Method) -\text(Unitary Method)$

First, find the

1 %

$1%$ of the total value by dividing both known values by $5$ $5$ .

$5 %$ $5%$	$=$ $=$	$$ 135$ $$135$

$5$ $5$ $\div 5$ $divide5$	$=$ $=$	$135$ $135$ $\div 5$ $divide5$	Divide both sides by $5$ $5$
$1$ $1$	$=$ $=$	$27$ $27$

Hence,

1 %

$1%$ of the original amount is

$ 27

$$27$ .

To find the total value, which is $100 %$ $100%$ of the value, multiply the

1 %

$1%$ value, which is

27

$27$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$27 \times 100$ $27times100$
	$=$ $=$	$2700$ $2700$

Hence,

$ 135

$$135$ is

5 %

$5%$ of $\underline{\color{#9a00c7}{$2700}}$

$ 2700

$$2700$

Question 3 of 4

3 %

$3%$ of an amount is

180 kg

$180 \text(kg)$ . Find the original amount.

(6000) $kg$ $\text(kg)$

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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 = 180 kg

$\text(Known value)=180 \text(kg)$

Percentage of known value = 3 %

$\text(Percentage of known value)=3%$

Percentage of total value = 100 %

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

Total value = ?

$\text(Total value)=?$

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 original amount be $x$ $x$

$\frac{\color{#007DDC}{3}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{180}}{\color{#9a00c7}{x}}$

$3 \times x$ $3timesx$	$=$ $=$	$180 \times 100$ $180times100$	Cross multiply
$3 x$ $3x$	$=$ $=$	$18{,}000$
$3 x$ $3x$ $\div 3$ $divide3$	$=$ $=$	$18{,}000\color{#CC0000}{\div3}$	Divide both sides by $3$ $3$
$x$ $x$	$=$ $=$	$6000$ $6000$

Hence,

180 kg

$180\text(kg)$ is

3 %

$3%$ of $\underline{\color{#9a00c7}{6000\;\text{kg}}}$

6000 kg

$6000 \text(kg)$

1 % Method - Unitary Method

$1% \text(Method) -\text(Unitary Method)$

First, find the

1 %

$1%$ of the total value by dividing both known values by $3$ $3$ .

$3 %$ $3%$	$=$ $=$	$180 kg$ $180 \text(kg)$

$3$ $3$ $\div 3$ $divide3$	$=$ $=$	$180$ $180$ $\div 3$ $divide3$	Divide both sides by $3$ $3$
$1$ $1$	$=$ $=$	$60$ $60$

Hence,

1 %

$1%$ of the original amount is

60 kg

$60 \text(kg)$ .

To find the total value, which is $100 %$ $100%$ of the value, multiply the

1 %

$1%$ value, which is

60

$60$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$60 \times 100$ $60times100$
	$=$ $=$	$6000$ $6000$

Hence,

180 kg

$180\text(kg)$ is

3 %

$3%$ of $\underline{\color{#9a00c7}{6000\;\text{kg}}}$

6000 kg

$6000 \text(kg)$

Question 4 of 4

A school has

657

$657$ students who travel to school by bus. If this represents

73 %

$73%$ of the students, how many students does the school have?

(900) $students$ $\text(students)$

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

Number of students taking the bus = 657

$\text(Number of students taking the bus)=657$

Percentage of students taking the bus = 73 %

$\text(Percentage of students taking the bus)=73%$

Percentage of total number of students = 100 %

$\text(Percentage of total number of students)=100%$

Total number of students = ?

$\text(Total number of students)=?$

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 original amount be $x$ $x$

$\frac{\color{#007DDC}{73}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{657}}{\color{#9a00c7}{x}}$

$73 \times x$ $73timesx$	$=$ $=$	$657 \times 100$ $657times100$	Cross multiply
$73 x$ $73x$	$=$ $=$	$65{,}700$
$73 x$ $73x$ $\div 73$ $divide73$	$=$ $=$	$65{,}700\color{#CC0000}{\div73}$	Divide both sides by $73$ $73$
$x$ $x$	$=$ $=$	$900$ $900$

Hence, the total number of students is $\underline{\color{#9a00c7}{900}}$

900 students

$900 \text(students)$

1 % Method - Unitary Method

$1% \text(Method) -\text(Unitary Method)$

First, find the

1 %

$1%$ of the total number of students by dividing both known values by $73$ $73$ .

$73 %$ $73%$	$=$ $=$	$657 students$ $657 \text(students)$

$73$ $73$ $\div 73$ $divide73$	$=$ $=$	$657$ $657$ $\div 73$ $divide73$	Divide both sides by $73$ $73$
$1$ $1$	$=$ $=$	$9$ $9$

Hence,

1 %

$1%$ of the original amount is

9 students

$9 \text(students)$ .

To find the total number of students, which is $100 %$ $100%$ of the value, multiply the

1 %

$1%$ value, which is

9

$9$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$9 \times 100$ $9times100$
	$=$ $=$	$900$ $900$

Hence, the total number of students is $\underline{\color{#9a00c7}{900}}$

900 students

$900 \text(students)$

Find Base from Percent of an Amount (Unitary Method) 1

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