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

Question 1 of 4

$8%$ of an amount is

$$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.

$\text(Known value)=$40$

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

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

$\text(Total value)=?$

$\text(Proportion Method)$

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 $x$

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

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

Hence,

$$40$ is

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

$$500$

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

First, find the

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

$8%$	$=$	$$40$

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

Hence,

$1%$ of the original amount is

$$5$ .

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

$1%$ value, which is

$5$ , by

$100$ .

$100%$	$=$	$5times100$
	$=$	$500$

Hence,

$$40$ is

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

$$500$

Question 2 of 4

$5%$ of an amount is

$$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.

$\text(Known value)=$135$

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

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

$\text(Total value)=?$

$\text(Proportion Method)$

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 $x$

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

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

Hence,

$$135$ is

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

$$2700$

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

First, find the

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

$5%$	$=$	$$135$

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

Hence,

$1%$ of the original amount is

$$27$ .

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

$1%$ value, which is

$27$ , by

$100$ .

$100%$	$=$	$27times100$
	$=$	$2700$

Hence,

$$135$ is

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

$$2700$

Question 3 of 4

$3%$ of an amount is

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

(6000) $\text(kg)$

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

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

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

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

$\text(Total value)=?$

$\text(Proportion Method)$

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 $x$

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

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

Hence,

$180\text(kg)$ is

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

$6000 \text(kg)$

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

First, find the

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

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

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

Hence,

$1%$ of the original amount is

$60 \text(kg)$ .

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

$1%$ value, which is

$60$ , by

$100$ .

$100%$	$=$	$60times100$
	$=$	$6000$

Hence,

$180\text(kg)$ is

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

$6000 \text(kg)$

Question 4 of 4

A school has

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

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

(900) $\text(students)$

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

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

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

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

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

$\text(Proportion Method)$

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 $x$

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

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

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

$900 \text(students)$

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

First, find the

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

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

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

Hence,

$1%$ of the original amount is

$9 \text(students)$ .

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

$1%$ value, which is

$9$ , by

$100$ .

$100%$	$=$	$9times100$
	$=$	$900$

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

$900 \text(students)$

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

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