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{person} {thing[0]} {number} {thing[2]} per {integer} {unit}s. This is equivalent to {thing[1]} [[0]] {thing[2]} per {unit}.

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Note: If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)

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The word 'per' can be replaced with the operation of division.

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These questions are very similar to equivalent fractions.

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Suppose you are told 'Daniel eats 61 berries per 3 hours'. The following three methods are equivalent but might appear different.

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  1. We are given 61 berries / 3 hours. Divide both sides of the rate by 3 (so that we are dealing with 'per hour' not 'per 3 hours'). This gives 61/3 berries/hour.
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  3. \\[\\text{61 berries/3 hours}=\\frac{61\\text{ berries}}{3 \\text{ hours}}=\\frac{61}{3}\\frac{\\text{berries}}{\\text{hour}}=\\frac{61}{3} \\,\\text{berries/hour}.\\]
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  5. \\[\\text{61 berries/3 hours}=\\frac{61\\text{ berries}}{3 \\text{ hours}}=\\frac{61\\text{ berries }\\div 3}{3 \\text{ hours }\\div 3}=\\frac{61\\div 3\\text{ berries }}{1 \\text{ hour }}=\\frac{61}{3} \\,\\text{berries/hour}.\\]
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A {vehicle} travels {distance} km per {amount} L of petrol.  

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How many kilometres can be travelled by using {niceamount} L? [[1]] km

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How many litres of petrol are needed to travel {nicedistance} km? [[0]] L

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Note: If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)

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Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0).

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Suppose you have 'a motorbike travels 245 km per 13 L of petrol'. Note, this can be written as 245 km / 13 L.

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To determine kilometres per 20 L, first determine how many kilometres per 1 L, and then multiply by 20. That is, 

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245 km / 13  L  = $\\frac{345}{13}$ km/L =  $\\frac{345}{13}\\times 20$ km / 20 L.

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To determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,

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245 km / 13 L = 1 km / $\\frac{13}{245}$ L = 50 km / $\\frac{13}{245}\\times 50$ L.

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Note, 245 km per 13 L could also be written as 13 L / 245 km. It might be simpler to do the second question this way:

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 To determine litres per 50 km, first determine how many litres per 1 km, and then multiply by 50. That is,

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13 L / 245 km = $\\frac{13}{245}$ L / km = $\\frac{13}{245}\\times 50$ L / 50 km.

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A rate of {num1} {firstunit[0]}s / {num2} {secondunit[0]}s is equivalent to [[0]] {firstunit[1]}s / {secondunit[1]}.

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Note: If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)

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Just like a fraction, we can multiply or divide both sides of the rate by any number (except 0). Do one thing at a time to avoid making a mistake.

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For example, suppose we need to convert 24 milliseconds / 4 litres into an equivalent rate in minutes / kilolitre. We need to do the following steps:

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  1. convert milliseconds to minutes,
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  3. convert litres to kilolitres,
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  5. make it per kilolitre. 
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  1. There are 60,000 milliseconds in a minute so to convert from millisecond to minutes we divide the milliseconds by 60,000. We now have 0.0004 minutes / 4 litres.
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  3. There are 1,000 litres in a kilolitre so to convert from litres to kilolitres, you need to divide the litres by 1,000. We now have 0.0004 minutes / 0.004 litres. 
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  5. To make it per litre we recall that 0.0004 minutes / 0.004 litres is equivalent to 0.0004/0.004 minutes / litre (this is the same as dividing both sides by 0.004). 
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So our final answer is 0.1 minutes / litre.

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plural, singular, object

"}, "amount": {"definition": "if(vehicle='car',random(35..60),if(vehicle='motorbike',random(11..20)))", "templateType": "anything", "group": "fuel", "name": "amount", "description": ""}, "person": {"definition": "Random(['Aaron', 'Alex', 'Ben', 'Claire', 'Charlotte', 'Daniel', 'Deb', 'Ethan', 'Elizabeth', 'Grace', 'Hunter', 'Julia', 'Isaac', 'Xavier', 'Victoria', 'Sophie', 'Abbey', 'Annie', 'Noah'])", "templateType": "anything", "group": "Ungrouped variables", "name": "person", "description": ""}, "niceamount": {"definition": "random(list(10..50#5) except amount)", "templateType": "anything", "group": "fuel", "name": "niceamount", "description": ""}, "nicedistance": {"definition": "random(list(50..200#10))", "templateType": "anything", "group": "fuel", "name": "nicedistance", "description": ""}, "vehicle": {"definition": "random(['car','motorbike'])", "templateType": "anything", "group": "fuel", "name": "vehicle", "description": ""}, "integer": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "integer", "description": ""}, "secondunit": {"definition": "if(seed[1]='cap',random([\"millilitre\",\"kilolitre\",1000000],[\"millilitre\",\"megalitre\",1000000000]),\nif(seed[1]='mass',random([\"gram\",\"tonne\",1000000],[\"milligram\",\"tonne\",1000000000],[\"milligram\",\"kilogram\",1000000]),\nif(seed[1]='time',random([\"millisecond\",\"hour\",3600000],[\"minute\",\"day\",1440],[\"second\",\"day\",86400],[\"millisecond\",\"day\",24*3600000]),\nif(seed[1]='distance',random([\"millimetre\",\"kilometre\", 1000000], [\"centimetre\", \"kilometre\",100000],[\"millimetre\",\"metre\",1000])))))", "templateType": "anything", "group": "part c", "name": "secondunit", "description": ""}, "seed": {"definition": "shuffle(['cap','time','mass','distance'])[0..2]", "templateType": "anything", "group": "part c", "name": "seed", "description": ""}, "unit": {"definition": "random(['hour', 'minute', 'day', 'month'])", "templateType": "anything", "group": "Ungrouped variables", "name": "unit", "description": ""}}, "metadata": {"description": "

Unit rates and converting rates.

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