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A quick practice set of problems for education students to take in preparation for their numeracy test.

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A two-stroke fuel is mixed using the fuel to oil ratio $\\var{twostrokefuel}:1$.

This is equivalent to the ratio [[0]] $: \\var{twostrokeoil}$.

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These questions are similar to equivalent fractions. To create an equivalent ratio, you need to multiply (or divide) by the same number on both sides.

In particular, to go from $\\var{twostrokefuel}:1$ to an equivalent ratio that looks like $?:\\var{twostrokeoil}$ we need to multiply both of the original amounts by $\\var{twostrokeoil}$ to give the ratio $\\var{ans1}:\\var{twostrokeoil}$.

For another example, suppose your ratio is $4:5$ and you are asked to find an equivalent ratio that looks like $?:30$. To get from a 5 to a 30 we can multiply by 6, but to keep the ratio equivalent we need to do the same to the other side of the ratio. So we multiply 4 by 6 and get 24 and we can say the ratios $4:5$ and $24:30$ are equivalent.

A fixed-gear bike is set up so that one revolution of the pedals moves the bike {onedistance} metres. How many pedal revolutions of the pedals are required to ride the bike {requireddistance} metres?

[[0]] revolutions.

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)

These questions are similar to equivalent fractions. To create an equivalent ratio, you need to multiply (or divide) by the same number on both sides.

In particular, the ratio of pedal revolutions to distance travelled is $\\var{1}:\\var{onedistance}$. To go from this ratio to an equivalent ratio that looks like $?:\\var{requireddistance}$ we need to divide both the original amounts by $\\var{onedistance}$ and then multiply by $\\var{requireddistance}$ (note, this is the same as multiplying by $\\frac{\\var{requireddistance}}{\\var{onedistance}}$) to give the ratio $\\var[fractionNumbers]{requireddistance/onedistance}:\\var{requireddistance}$.

For another example, suppose we need to find an equivalent ratio of $4:5$ in the form $31:\\,?$. We need to get from a 4 to a 31 by multiplying or dividing. The easiest way to do this is probably to divide by 4 and then multiply by 31 (note, this is the same as multiplying by $\\frac{31}{4}$). We need to do the same thing to the other side of the ratio. So we multiply 5 by $\\frac{31}{4}$ and get $\\frac{155}{4}$ and we can say the ratios $4:5$ and $31:\\frac{155}{4}$ are equivalent.

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Cordial is mixed using the syrup-to-water ratio $\\var{cordialratio[0]}:\\var{cordialratio[1]}$. You need to make $\\var{totalcordial}$ litres. How many litres of syrup do you need?

[[0]] L

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)

Determine the total number of parts used in the ratio. Find what one part corresponds to and then multiply by the required number of parts.

Amounts in the ratio $\\var{cordialratio[0]}:\\var{cordialratio[1]}$ need to add up to $\\var{totalcordial}$ litres. The ratio has $\\var{sum(cordialratio)}$ parts ($\\var{cordialratio[0]}+\\var{cordialratio[1]}$). One part corresponds to $\\frac{\\var{totalcordial}}{\\var{sum(cordialratio)}}$ litres. This means $\\var{cordialratio[0]}$ parts correspond to $\\var{cordialratio[0]}\\times\\frac{\\var{totalcordial}}{\\var{sum(cordialratio)}}=\\var[fractionNumbers]{cordialratio[0]*totalcordial/sum(cordialratio)}$ L.

For another example, suppose you need to divide $490$ kg into the ratio $2:5$. The ratio has $7$ parts ($2+5$). One part corresponds to $\\frac{490}{7}=70$ kg. This means $2$ parts correspond to $2\\times 70=140$ kg, and $5$ parts correspond to $5\\times 70=350$ kg. Therefore, $490$ kg divided into the ratio $2:5$ is $140$ kg $:$ $350$ kg.

Three people split $\\$\\var{totaldollars}$ amongst themselves in the ratio $\\var{part1}:\\var{part2}:\\var{part3}$. How much money does the {position[0]} person get?

\\$ [[0]] (to the nearest cent)

Determine the total number of parts used in the ratio. Find what one part corresponds to and then multiply by the required number of parts.

$\\$\\var{totaldollars}$ amongst themselves in the ratio $\\var{part1}:\\var{part2}:\\var{part3}$. The ratio has $\\var{totalparts}$ parts ($\\var{part1}+\\var{part2}+\\var{part3}$). One part corresponds to $\\$\\frac{\\var{totaldollars}}{\\var{totalparts}}$. This means $\\var{position[1]}$ parts correspond to $\\var{position[1]}\\times \\$\\frac{\\var{totaldollars}}{\\var{totalparts}}=\\$\\var[fractionNumbers]{position[1]*totaldollars/totalparts}$.

For another example, suppose you need to divide $800$ kg into the ratio $2:5:1$. The ratio has $8$ parts ($2+5+1$). One part corresponds to $\\frac{800}{8}=100$ kg. This means $2$ parts corresponds to $2\\times 100=200$ kg and $5$ parts correspond to $5\\times 100=500$ kg. Therefore, $800$ kg divided into the ratio $2:5:1$ is $200 \\text{ kg } : 500 \\text{ kg }: 100 \\text{ kg}$.