Find Base from Percent of an Amount (Unitary Method) 2

Question 1 of 4

2 %

$2%$ of an amount is

$ 70

$$70$ . Find the original amount.

$$$ $$$ (3500)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Known value = $ 70

$\text(Known value)=$70$

Percentage of known value = 2 %

$\text(Percentage of known value)=2%$

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 $x$ $x$

$\frac{\color{#007DDC}{2}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{70}}{\color{#9a00c7}{x}}$

$2 \times x$ $2timesx$	$=$ $=$	$70 \times 100$ $70times100$	Cross multiply
$2 x$ $2x$	$=$ $=$	$7000$
$2 x$ $2x$ $\div 2$ $divide2$	$=$ $=$	$7000\color{#CC0000}{\div2}$	Divide both sides by $2$ $2$
$x$ $x$	$=$ $=$	$3500$ $3500$

Hence,

$ 70

$$70$ is

2 %

$2%$ of $\underline{\color{#9a00c7}{$3500}}$

$ 3500

$$3500$

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 $2$ $2$ .

$2 %$ $2%$	$=$ $=$	$$ 70$ $$70$

$2$ $2$ $\div 2$ $divide2$	$=$ $=$	$70$ $70$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$1$ $1$	$=$ $=$	$35$ $35$

Hence,

1 %

$1%$ of the original amount is

$ 35

$$35$ .

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

1 %

$1%$ value, which is

35

$35$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$35 \times 100$ $35times100$
	$=$ $=$	$3500$ $3500$

Hence,

$ 70

$$70$ is

2 %

$2%$ of $\underline{\color{#9a00c7}{$3500}}$

$ 3500

$$3500$

Question 2 of 4

8 %

$8%$ of an amount is

$ 72

$$72$ . Find the original amount.

$$$ $$$ (900)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Known value = $ 72

$\text(Known value)=$72$

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 $x$ $x$

$\frac{\color{#007DDC}{8}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{72}}{\color{#9a00c7}{x}}$

$8 \times x$ $8timesx$	$=$ $=$	$72 \times 100$ $72times100$	Cross multiply
$8 x$ $8x$	$=$ $=$	$7200$
$8 x$ $8x$ $\div 8$ $divide8$	$=$ $=$	$7200\color{#CC0000}{\div8}$	Divide both sides by $8$ $8$
$x$ $x$	$=$ $=$	$900$ $900$

Hence,

$ 72

$$72$ is

8 %

$8%$ of $\underline{\color{#9a00c7}{$900}}$

$ 900

$$900$

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 $8$ $8$ .

$8 %$ $8%$	$=$ $=$	$$ 72$ $$72$

$8$ $8$ $\div 8$ $divide8$	$=$ $=$	$72$ $72$ $\div 8$ $divide8$	Divide both sides by $8$ $8$
$1$ $1$	$=$ $=$	$9$ $9$

Hence,

1 %

$1%$ of the original amount is

$ 9

$$9$ .

To find the total value, 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,

$ 72

$$72$ is

8 %

$8%$ of $\underline{\color{#9a00c7}{$900}}$

$ 900

$$900$

Question 3 of 4

42 %

$42%$ of an amount is

77 cm

$77 \text(cm)$ . Find the original amount.

Round your answer to one decimal place

(183.3) $cm$ $\text(cm)$

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

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

Known value = 77 cm

$\text(Known value)=77 \text(cm)$

Percentage of known value = 42 %

$\text(Percentage of known value)=42%$

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 $x$ $x$

$\frac{\color{#007DDC}{42}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{77}}{\color{#9a00c7}{x}}$

$42 \times x$ $42timesx$	$=$ $=$	$77 \times 100$ $77times100$	Cross multiply
$42 x$ $42x$	$=$ $=$	$7700$
$42 x$ $42x$ $\div 42$ $divide42$	$=$ $=$	$7700\color{#CC0000}{\div42}$	Divide both sides by $42$ $42$
$x$ $x$	$=$ $=$	$183.3$ $183.3$	Rounded to one decimal place

Hence,

77 cm

$77 \text(cm)$ is

42 %

$42%$ of $\underline{\color{#9a00c7}{183.3\;\text{cm}}}$

183.3 cm

$183.3 \text(cm)$

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 $42$ $42$ .

$42 %$ $42%$	$=$ $=$	$77 cm$ $77 \text(cm)$

$42$ $42$ $\div 42$ $divide42$	$=$ $=$	$77$ $77$ $\div 42$ $divide42$	Divide both sides by $42$ $42$
$1$ $1$	$=$ $=$	$1.833 \dots$ $1.833…$

Hence,

1 %

$1%$ of the original amount is

1.833 \dots cm

$1.833… \text(cm)$ .

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

1 %

$1%$ value, which is

1.833 \dots

$1.833…$ , by

100

$100$ .

$100 %$ $100%$	$=$ $=$	$1.833 \dots \times 100$ $1.833…times100$
	$=$ $=$	$183.3$ $183.3$	Rounded to one decimal place

Hence,

77 cm

$77 \text(cm)$ is

42 %

$42%$ of $\underline{\color{#9a00c7}{183.3\;\text{cm}}}$

183.3 cm

$183.3 \text(cm)$

Question 4 of 4

Andrew earned

$ 481

$$481$ as a commission for selling office furniture. If his commission rate is

9 \frac{1}{4} %

$9 1/4%$ how much was made in sales?

$$$ $$$ (5200)

Incorrect

Need Text

Play

Remaining Time -0:00

Stream TypeLIVE

Loaded: 0%

Progress: 0%

0:00

Fullscreen

00:00

Mute

A commission is expressed as a percentage of the value of goods sold.

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

Commission earned = $ 481

$\text(Commission earned)=$481$

Commission rate = 9 \frac{1}{4} %

$\text(Commission rate)=9 1/4%$

Percentage of total sales = 100 %

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

Total sales = ?

$\text(Total sales)=?$

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 $x$ $x$

$\frac{\color{#007DDC}{9\;\frac{1}{4}}}{\color{#e85e00}{100}}$	$=$ $=$	$\frac{\color{#00880A}{481}}{\color{#9a00c7}{x}}$

$9 \frac{1}{4} \times x$ $9 1/4timesx$	$=$ $=$	$481 \times 100$ $481times100$	Cross multiply

$9 \frac{1}{4} x$ $9 1/4x$	$=$ $=$	$48{,}100$
$9 \frac{1}{4} x$ $9 1/4x$ $\div 9 \frac{1}{4}$ $divide9 1/4$	$=$ $=$	$48{,}100\color{#CC0000}{\div9\;\frac{1}{4}}$	Divide both sides by $9 \frac{1}{4}$ $9 1/4$
$x$ $x$	$=$ $=$	$5200$ $5200$

Hence, Andrew’s total sales were $\underline{\color{#9a00c7}{$5200}}$

$ 5200

$$5200$

Find Base from Percent of an Amount (Unitary Method) 2

Try VividMath Premium to unlock full access

Quiz summary

Information

1. Question

Hint

Fantastic!

2. Question

Hint

Fantastic!

3. Question

Hint

Nice Job!

4. Question

Hint

Keep Going!

Quizzes