// Numbas version: exam_results_page_options {"name": "Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "advice": "", "name": "Percentages", "preamble": {"js": "", "css": ""}, "variables": {"factorsofhun": {"definition": "shuffle([[2,50],[4,25],[5,20]])", "group": "Ungrouped variables", "description": "", "name": "factorsofhun", "templateType": "anything"}, "d": {"definition": "mult*mult2", "group": "Ungrouped variables", "description": "", "name": "d", "templateType": "anything"}, "amount3": {"definition": "random(2..12)*factorsofhun[2][1]", "group": "Ungrouped variables", "description": "", "name": "amount3", "templateType": "anything"}, "number": {"definition": "random(12..78)", "group": "Ungrouped variables", "description": "", "name": "number", "templateType": "anything"}, "percent": {"definition": "random(1..99 except list(0..100#5))", "group": "Ungrouped variables", "description": "", "name": "percent", "templateType": "anything"}, "ans3": {"definition": "percent3*amount3/100", "group": "Ungrouped variables", "description": "", "name": "ans3", "templateType": "anything"}, "percent3": {"definition": "random(2..19)*factorsofhun[2][0]", "group": "Ungrouped variables", "description": "", "name": "percent3", "templateType": "anything"}, "dec3": {"definition": "random(1..5#0.01)", "group": "Ungrouped variables", "description": "", "name": "dec3", "templateType": "anything"}, "mult": {"definition": "random(3,7,9,11)", "group": "Ungrouped variables", "description": "", "name": "mult", "templateType": "anything"}, "amount2": {"definition": "random(2..12)*factorsofhun[0][1]", "group": "Ungrouped variables", "description": "", "name": "amount2", "templateType": "anything"}, "nicelist": {"definition": "shuffle(map(2^a*5^b,[a,b],[[0,1],[0,2],[1,0],[2,0],[3,0],[4,0],[5,0],[6,0],[1,1],[2,1],[3,1],[4,1],[1,2]]))\n", "group": "Ungrouped variables", "description": "", "name": "nicelist", "templateType": "anything"}, "a": {"definition": "random(1..b-1)", "group": "Ungrouped variables", "description": "", "name": "a", "templateType": "anything"}, "mult2": {"definition": "random(4,5)", "group": "Ungrouped variables", "description": "", "name": "mult2", "templateType": "anything"}, "dec1": {"definition": "random(0.1..0.9#0.01)", "group": "Ungrouped variables", "description": "", "name": "dec1", "templateType": "anything"}, "ans2": {"definition": "percent2*amount2/100", "group": "Ungrouped variables", "description": "", "name": "ans2", "templateType": "anything"}, "c": {"definition": "mult*random(1..mult2-1)", "group": "Ungrouped variables", "description": "", "name": "c", "templateType": "anything"}, "dec2": {"definition": "random(0.1..0.9#0.001 except list(0.1..0.9#0.01))", "group": "Ungrouped variables", "description": "", "name": "dec2", "templateType": "anything"}, "percent2": {"definition": "random(2..19)*factorsofhun[0][0]", "group": "Ungrouped variables", "description": "", "name": "percent2", "templateType": "anything"}, "b": {"definition": "random([50,4,25,5,20])", "group": "Ungrouped variables", "description": "", "name": "b", "templateType": "anything"}}, "rulesets": {}, "functions": {}, "parts": [{"steps": [{"type": "information", "scripts": {}, "showCorrectAnswer": true, "showFeedbackIcon": true, "marks": 0, "prompt": "

'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:

\\[34\\%=\\frac{34}{100}=0.34\\]

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

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

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

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

This question requires you know how to multiply fractions and/or decimals. If using a fraction, it will help to simplify it.

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:

{percent2}% of {amount2} is [[0]]

{percent3}% of {amount3} is [[1]]

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 $\\frac{4}{5}$.

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:

\\[\\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]]%

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

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

11% by adding 10% and 1%, that is $1.2+0.12=1.32$
9% by doing 10% minus 1%, that is $1.2-0.12=1.08$
30% by doing 3 times 10%, that is $3\\times 1.2=3.6$
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

10% of {number} is [[0]]

1% of {number} is [[1]]

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

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Move the decimal point to the right two places.

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

\\[34\\%=\\frac{34}{100}=34\\div 100=0.34\\]

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

\\[0.34=34\\div 100=\\frac{34}{100}=34\\%\\]

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:

{dec1} = [[0]]%

{dec2} = [[1]]%

{dec3} = [[2]]%

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

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