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Simplifying ratios

rebelmaths

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To express a ratio in its simplest form you always multiply or divide all parts by the same number.

In this case you need to divide the ratios by a common factor. Can both numbers be divided by 2? Or maybe 3 or 4? Keep dividing both sides until you think it can't get any simpler.

Alternatively you could find the highest common factor and divide by that.

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Express the ratio $\\var{num11}$ : $\\var{num12}$ in its simplest form.

[[0]]:[[1]]

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Express this ratio in its simplest form as above. Divide the $\\var{student}$ students into this ratio.

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In a class there are $\\var{boy}$ boys and $\\var{girl}$ girls. Find the ratio of boys to girls in the class in its simplest form.

[[0]]boys : [[1]]girls

If the whole year group of $\\var{student}$ students is in the same ratio, how many girls are there in the year?

[[2]]

This time we want to get rid of the fractions. To do this we will multiply all the parts by a number. Find the Lowest Common Multiple of the denominators (if its difficult to find you can always multiply the three denominators and use that). Multiply all the fractions by this number. Simplify your answer ratio into its simplest form as above.

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Express $\\frac{1}{\\var{number0}}:\\frac{5}{\\var{number1}}:\\frac{7}{\\var{number2}}$ as a ratio in whole numbers.

[[0]] : [[1]] : [[2]]

Solve the following ratio questions:

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Watch the following video to understand ratios better!

Ratios Video

(a)

The highest common factor of $\\var{num11}$ and $\\var{num12}$ is $\\var{gcd(num11,num12)}$.

Divide both numbers by $\\var{gcd(num11,num12)}$ gives the simplest ratio as $\\var{num11/gcd(num11,num12)}:\\var{num12/gcd(num11,num12)}$

(b)

The highest common factor of $\\var{girl}$ and $\\var{boy}$ is $\\var{l}$. Divide both the number of boys and girls by this to give:

Ratio = $\\frac{\\var{boy}}{\\var{l}}$ : $\\frac{\\var{girl}}{\\var{l}}=\\var{ans21}$ : $\\var{ans22}$

To work out the number of girls we note that there are $\\var{ans21}+\\var{ans22}=\\var{ans21+ans22}$ parts in total.

We can divide the total number of pupils by $\\var{ans21+ans22}$ to give $\\var{student}\\div\\var{ans21+ans22} = \\var{student/(ans21+ans22)}$. So each part of the ratio is worth $\\var{student/(ans21+ans22)}$ pupils.

Since girls make up $\\var{ans22}$ parts of the ratio, then the total number of girls is:

$\\var{ans22}\\times\\var{student/(ans21+ans22)} = \\var{ans23}$

(c)

First find the lowest common denominator = $\\var{low}$

Now we can multiply each fraction by $\\var{low}$ and we will end up with a whole number:

$(\\frac{1}{\\var{number0}}) \\times \\var{low} = \\var{ans31}$

$(\\frac{5}{\\var{number1}}) \\times \\var{low} = \\var{ans32}$

$(\\frac{7}{\\var{number2}}) \\times \\var{low} = \\var{ans33}$

So the ratio is $\\var{ans31}:\\var{ans32}:\\var{ans33}$

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