Sharing Using Ratios

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The following example shows how we can use Ratios for sharing out amounts.

Also shown is the standard approach and working out steps for doing these types of mathematics questions.

Ratios Sharing One
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As agreed by the three friends, the winnings of $ 120 000 need to be shared amongst them in the same ratio as the money they each contributed towards the ticket.

Ratios Sharing Two
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We now work out from the 20 parts total, how much “One Part” is worth.

After we know what one part is, it is then just simple multiplication to work out what share of the total amount each person gets.

Ratios Sharing Three
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We have our sharing amount answers, and it is always a good idea to check these answers to make sure that they are correct.

There are two levels of checking we can do.

These involve checking the Total of the Amounts, and then checking the Ratio of the Amounts.

Ratios Sharing Four
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Ratios Sharing Five
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Because both checks have been successful, we can be 100% sure that our sharing Answers are correct.


Video about Ratio Sharing

Watch the following video which is about sharing out items in given ratios.

This video uses the notion of “rounds” which might appear a bit different to our example lottery question, but is actually the same.

The total “rounds” are simply the “Total Parts”, and so the video presenter gives so many rounds to each person depending on their share of the ratio.


Steps for Working Out Sharing Questions

The previous example has shown the steps that we need to do to work out a Ratios question which involves sharing amounts.

We use these exact same steps for working out questions that involve dividing up amounts.

Ratio Sharing Six
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Steps for Checking Sharing Questions

As shown at the end of the Lottery example, there were two checks that we need to do for Ratios Sharing Questions.

The first check involves checking that the answer amounts all add up to exactly match the original amount being shared.

The second check involves checking that the Ratio of the answer amounts exactly matches the original sharing ratio.

Ratio Sharing seven
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Ratios Sharing Examples

The following examples show how to do questions which involve dividing up amounts, or sharing amounts.

In each example we follow the standard working out steps:

– Find the Total Number of Parts in the Ratio
(Do this by adding up all the number values in the given Ratio to get a Total

– Amount for One Part = (Total Amount being shared) / Total Number of Parts in Ratio

(This tells us what one part is worth)

– Each Share = its Ratio Number x Amount for One Part.


Although not shown on all of our examples, remember that checking our amswer amounts is just as important as doing the working out steps.

The standard Answer Checking Steps are as follows:

– Check all the shares add up to the original given Amount

– Check the Ratio of the Shares simplifies to be the same as the Original Given Ratio.


Ratio Sharing Eight
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Ratio Sharing Nine
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Ratio Sharing Ten
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Related Items

Introduction to Ratios
Simplifying Ratios
Calculating Ratio Amounts
Increasing and Decreasing Using Ratios
Fibonacci Sequence in Music


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