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Basics, percentage of an amount, converting to fractions and decimals.

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'Percent' means 'out of 100'. So we can write 34% as $\\frac{34}{100}$. Since this is the same as $34\\div 100$ we can write this as a decimal by moving the decimal point two places (the number of zeroes in 100). So 34 (which has a decimal point after the 4) becomes 0.34. In summary:

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\$34\\%=\\frac{34}{100}=0.34\$

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{percent}% means {percent} out of [[0]].

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This means we can write {percent}% as the fraction [[1]] .

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And so we can write {percent}% as the decimal [[2]].

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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 and/or decimals. If using a fraction, it will help to simplify it.

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For example, 40% of 55 is $40\\%\\times 55=\\frac{40}{100}\\times 55$, which equals $\\frac{2}{5}\\times 55$ by simplifying the fraction, next there is a factor of 5 which can be cancelled to give $2\\times 11=22$. So we have 40% of 55 is 22.

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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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{percent2}% of {amount2} is [[0]]

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{percent3}% of {amount3} is [[1]]

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Recall that $\\frac{2}{3}$ means '2 out of 3', and so going the other way, expressions like '4 out of 5' are equivalent to $\\frac{4}{5}$.

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To convert a fraction into a percentage, make an equivalent fraction with a denominator of 100, then the numerator will be the percentage. For example, given $\\frac{4}{5}$ we can multiply the top and bottom by 20 to get it over 100 (we could have multiplied by 2 and then 10 as well since this is the same thing). Our working could look like this:

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\$\\frac{4}{5}=\\frac{4\\times 20}{5\\times 20}=\\frac{80}{100}=80\\%\$

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{a} out of {b} as a fraction is [[0]]. What is this equal to as a percentage? [[1]]%

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{c} out of {d} as a fraction is [[2]]. What is this equal to as a percentage? [[3]]%

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 10% of 12 is 1.2 and 1% of 12 is 0.12. From this we can calculate many simple percentages:

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• 11% by adding 10% and 1%, that is $1.2+0.12=1.32$
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• 9% by doing 10% minus 1%, that is $1.2-0.12=1.08$
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• 30% by doing 3 times 10%, that is $3\\times 1.2=3.6$
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• 99% by doing 100% minus 1%, that is $12-0.12=11.88$
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It is often useful to determine 1% of an amount and 10% of an amount so you can combine them to get other percentages. For example

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10% of {number} is [[0]]

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1% of {number} is [[1]]

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therefore 11% of {number} is  [[2]], 9% of {number} is [[3]] and 20% of {number} is [[4]].

Move the decimal point to the right two places.

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To get from a percentage to a decimal we ultimately moved the decimal place twice to the left. Recall

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\$34\\%=\\frac{34}{100}=34\\div 100=0.34\$

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That means to go the other way (from a decimal to a percentage) we need to move the decimal place twice to the right, in other words

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\$0.34=34\\div 100=\\frac{34}{100}=34\\%\$

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Often it is useful to remember that 1 represents 100%, this can help you to check if your answer makes sense.

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Rewrite the following decimals as percentages:

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{dec1} = [[0]]%

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{dec2} = [[1]]%

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{dec3} = [[2]]%