// Numbas version: exam_results_page_options {"name": "Percentages: Percentage of an amount ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false}, "question_groups": [{"questions": [{"tags": [], "functions": {}, "statement": "

Write the following question down on paper and evaluate it without using a calculator.

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If you are unsure of how to do a question, click on Show steps to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again.

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Percentage of an amount

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Writing a percentage as a fraction or a decimal can be useful in the following type of questions:

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$\\var{percent2}\\%$ of $\\var{amount2}$ is [[0]]

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Write the percentage as a fraction or decimal and replace the word 'of' with '$\\times$'.

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This question requires you know how to multiply fractions (multiply the tops and multiply the bottoms) and divide by $100$ (move the decimal place twice to make the number smaller).

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In particular, \\begin{align}\\var{percent2}\\% \\text{ of } \\var{amount2} &= \\frac{\\var{percent2}}{100}\\times \\var{amount2} \\\\&=\\frac{\\var{percent2}}{100}\\times \\frac{\\var{amount2}}{1}\\\\&= \\frac{\\var{percent2}\\times \\var{amount2}}{100}\\\\&=\\frac{\\var{percent2*amount2}}{100}\\\\&=\\var{ans2}\\end{align}

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It is often useful to determine $10\\%$ and $1\\%$ of an amount so you can combine them to get other percentages. For example,

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$10\\%$ of $\\var{number}$ is [[0]],

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$1\\%$ of $\\var{number}$ is [[1]],

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and by using the above we can say $\\var{q}\\%$ of $\\var{number}$ is  [[2]].

Move the decimal point once to the left to get 10%, move it one more time to the left to get 1%. Add and subtract multiples of these as required.

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Notice

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\$10\\%=\\frac{10}{100}=\\frac{1}{10}=1\\div 10 = 0.1\$

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and

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\$1\\%=\\frac{1}{100}=1\\div 100 = 0.01\$

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This means that

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$10\\%$ of $\\var{number}$ is $\\var{number/10}$,

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$1\\%$ of $\\var{number}$ is $\\var{number/100}$,

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and from this we can calculate $\\var{q}\\%$ of $\\var{number}$ is

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$9\\%=10\\%-1\\%=\\var{number/10}-\\var{number/100}=\\var{q*number/100}$.
$11\\%=10\\%+1\\%=\\var{number/10}+\\var{number/100}=\\var{q*number/100}$.
$20\\%=10\\%+10\\%=\\var{number/10}+\\var{number/10}=\\var{q*number/100}$.
$90\\%=100\\%-10\\%=\\var{number}-\\var{number/10}=\\var{q*number/100}$.
$99\\%=100\\%-1\\%=\\var{number}-\\var{number/100}=\\var{q*number/100}$.

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