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Percentage of an amount

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

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

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

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

This question requires you to 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).

In particular, \\begin{align}\\var{percent2}\\% \\text{ of } \\var{amount2} &= \\frac{\\var{percent2}}{100}\\times \\var{amount2} \\\\[2mm]&=\\frac{\\var{percent2}}{100}\\times \\frac{\\var{amount2}}{1}\\\\[2mm]&= \\frac{\\var{percent2}\\times \\var{amount2}}{100}\\\\[2mm]&=\\frac{\\var{percent2*amount2}}{100}\\\\[2mm]&=\\var{ans2}\\end{align}

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

$10\\%$ of $\\var{number}$ is [[0]],

$1\\%$ of $\\var{number}$ is [[1]],

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

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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.

Notice

\\[10\\%=\\frac{10}{100}=\\frac{1}{10}=1\\div 10 = 0.1\\]

and

\\[1\\%=\\frac{1}{100}=1\\div 100 = 0.01\\]

This means that

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

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

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

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

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