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Find Base from Percent of an Amount (Unitary Method) 1Find Base from Percent of an Amount (Unitary Method) 1
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Question 1 of 4
1. Question
`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
2. Question
`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. Question
`3%` of an amount is `180 \text(kg)`. Find the original amount.- (6000) `\text(kg)`
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)=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
4. Question
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)`
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