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Using Percentages with Proportions>
Using Percentages with ProportionsUsing Percentages with Proportions
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Question 1 of 5
1. Question
What percentage `(%)` of `247` is `83`?Round your answer to one decimal place- (33.6) `%`
Hint
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To understand the problem better, draw a line diagram and list down the values as shown below.`\text(Known value)=83``\text(Total value)=247``\text(Percentage of total value)=100%``\text(Percentage of known 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 percentage of the amount be `r`.$$\frac{\color{#00880A}{83}}{\color{#9a00c7}{247}}$$ `=` $$\frac{\color{#007DDC}{r}}{\color{#e85e00}{100}}$$ `247timesr` `=` `83times100` Cross multiply `247r` `=` $$8300$$ `247r``divide247` `=` $$8300\color{#CC0000}{\div247}$$ Divide both sides by `247` `r` `=` `33.6` Rounded to one decimal place Hence, `83` is $$\underline{\color{#007DDC}{33.6\%}}$$ of `247`.`33.6%``\text(Fraction Method)`To find the missing value, simply multiply the fraction of the known values by `100`.The fraction can be written as the known value `(``83``)` over the total value `(``247``)`.$$\frac{\color{#00880A}{83}}{\color{#9a00c7}{247}}\times100$$ `=` `83/247times100/1` Convert values to fraction form `=` $$\frac{8300}{247}$$ `=` `33.6` Rounded to one decimal place Hence, `83` is $$\underline{\color{#007DDC}{33.6\%}}$$ of `247`.`33.6%` -
Question 2 of 5
2. Question
What percentage `(%)` of `600 \text(kg)` is `18 \text(kg)`?- (3) `%`
Hint
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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)=18 \text(kg)``\text(Total value)=600 \text(kg)``\text(Percentage of total value)=100%``\text(Percentage of known 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 percentage on the amount be `r`$$\frac{\color{#007DDC}{r}}{\color{#e85e00}{100}}$$ `=` $$\frac{\color{#00880A}{18}}{\color{#9a00c7}{600}}$$ `600timesr` `=` `18times100` Cross multiply `600r` `=` $$1800$$ `600r``divide600` `=` $$1800\color{#CC0000}{\div600}$$ Divide both sides by `600` `r` `=` $$\frac{1800}{600}$$ Simplify `r` `=` `3` Hence, `18 \text(kg)` is $$\underline{\color{#007DDC}{3\%}}$$ of `600 \text(kg)`.`3%``1% \text(Method)`First, find the `1%` of the total value `(``600``)` by dividing the total amount by `100`.`1%` `=` `600``divide100` `=` `6` Hence, `1%` of the original amount is `6 \text(kg)`.To find the percentage of the given amount, multiply the `1%` value, which is `6`, by a value to get it to `18`.Multiplying `6` by `3` will make it `18``1%` `=` `6` `1%``times3` `=` `6``times3` Multiply both sides by `3` `3%` `=` `18` Hence, `18 \text(kg)` is $$\underline{\color{#007DDC}{3\%}}$$ of `600 \text(kg)`.`3%` -
Question 3 of 5
3. Question
What is `5 \text(kg)` of fish as a percentage `(%)` of `250 \text(kg)` of fish?- (2) `%`
Hint
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First, summarise the data for easier understanding of the problem.`\text(Given weight)=5 \text(kg)``\text(Total weight)=250 \text(kg)``\text(Percentage of total value)=100%``\text(Percentage of given weight)=?`
To find the missing value, simply multiply the fraction of the known values by `100`.The fraction can be written as the given weight `(``5``)` over the total value`(``250``)`.$$\frac{\color{#00880A}{5}}{\color{#9a00c7}{250}}\times100$$ `=` `5/250times100/1` Convert values to fraction form `=` $$\frac{500}{250}$$ `=` `2` Hence, `5 \text(kg)` is $$\underline{\color{#007DDC}{2\%}}$$ of `250 \text(kg)`.`2%` -
Question 4 of 5
4. Question
What percentage `(%)` of `$150` is `$12`?- (8) `%`
Hint
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Fantastic!
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First, summarise the data and draw a diagram for easier understanding of the problem`\text(Given amount)=$12``\text(Total amount)=$150``\text(Percentage of total value)=100%``\text(Percentage of given amount)=?`
`\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`$$\frac{\color{#00880A}{12}}{\color{#9a00c7}{150}}$$ `=` $$\frac{\color{#007DDC}{r}}{\color{#e85e00}{100}}$$ `150timesr` `=` `12times100` Cross multiply `150r` `=` $$1200$$ `150r``divide150` `=` $$1200\color{#CC0000}{\div150}$$ Divide both sides by `150` `r` `=` $$\frac{120}{15}$$ Simplify `r` `=` `8` Hence, `$12` is $$\underline{\color{#007DDC}{8\%}}$$ of `$150`.`8%``\text(Fraction Method)`To find the missing value, simply multiply the fraction of the known values by `100`.The fraction can be written as the known value `(``12``)` over the total value `(``150``)`.$$\frac{\color{#00880A}{12}}{\color{#9a00c7}{150}}\times100$$ `=` `12/150times100/1` Convert values to fraction form `=` $$\frac{1200}{150}$$ `=` $$\frac{120}{15}$$ Simplify `=` `8` Hence, `$12` is $$\underline{\color{#007DDC}{8\%}}$$ of `$150`.`8%` -
Question 5 of 5
5. Question
If you spend `20%` of your savings to buy a `$1200` laptop, how much is your total savings?- `$` (6000)
Hint
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Keep Going!
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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)=1200``\text(Percentage of known value)=20%``\text(Percentage of total value)=100%``\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`$$\frac{\color{#007DDC}{20}}{\color{#e85e00}{100}}$$ `=` $$\frac{\color{#00880A}{1200}}{\color{#9a00c7}{x}}$$ `20timesx` `=` `1200times100` Cross multiply `20x` `=` $$120{,}000$$ `20x``divide20` `=` $$120{,}000\color{#CC0000}{\div20}$$ Divide both sides by `20` `x` `=` $$\frac{12{,}000}{2}$$ Simplify `x` `=` `6000` Hence, the total savings is $$\underline{\color{#9a00c7}{$6000}}$$`$6000`
Quizzes
- Ratios 1
- Ratios 2
- Ratios 3
- Ratios 4
- Proportions 1
- Proportions 2
- Dividing Quantities
- Rates 1
- Rates 2
- Rates 3
- Rates 4
- Scales 1
- Scales 2
- Scales 3
- Find Base from Percent of an Amount (Unitary Method) 1
- Find Base from Percent of an Amount (Unitary Method) 2
- Using Percentages with Proportions
- Find Original Amount Before Percent Change (Unitary Method)