# Simplifying Ratios

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Let’s say we want to make some of our favourite Peanut Butter Cookies, which normally requires the ingredients shown above.

However, when we check in the fridge, we only have one egg.

To make our cookies with only one egg, we will need to halve the recipe by dividing all of the ingredients by two.

Eg. Use 1 egg, 1 packet of butter, 1/2 a cup of Peanut Butter, and so on.

This way we keep the ratios, or proportions, of the ingredients the same, and so our cookies should still work out okay.

Breaking down big ratios into smaller simplified ratios is what we will be working on in this lesson.

Ratios and Factors

Simplifying Number Ratios is a lot like simplifying fractions.

We need to find the biggest factor number which goes into both parts of our Ratio.

The biggest number which goes into a pair of number values is called:

the “Greatest Common Factor” (GCF) or

the “Highest Common Factor” (HCF).

GCF and HCF are the exact same thing.

If you are not sure how to find the greatest common factor (GCF) of two numbers, then watch the following videos.

Simplifying Number Ratios

The steps we need to do to simplify a Ratio into smallest number form are as follows.

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The following Examples show how to simplify some ratios, by following these steps.

Image Copyright 2012 by Passy’s World

Image Copyright 2012 by Passy’s World

Units and Simplifying Ratios

It is essential that both ratio numbers are in the same units before simplifying.

If they are in different units, then convert both numbers to the smaller sized unit.

This is shown in the following example.

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Simplifying Fractions and Decimals

There are extra working out steps when we need to simplify Fraction and Decimal Ratios.

Watch the following simplifying ratios video.

In this video, Professor Perez shows how to simplify fraction and decimal ratios.

Simplifying Fractions Ratios

The steps required are as follows.

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The following example shows how we do these steps.

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Simplifying Decimal Ratios

We need to do an extra step at the start of these questions.

This step involves getting both of the decimals into whole numbers.

We do this by multiplying both decimals by either 10, 100, 1000, etc depending on the number of decimal place digits after the point.

If there is only one digit after the point, multiply by 10

If there are two numbers after the point, multiply by 100

If there are three numbers after the point, multiply by 1000

If we have a mixture of different amounts of digits after the decimal point, then we need to multiply by the biggest 10, 100, 1000, number that we obtain.

The following examples show how to simplify Decimal Ratios.

Image Copyright 2012 by Passy’s World

Image Copyright 2012 by Passy’s World

If we have a mixture of different amounts of digits after the decimal point, then we need to multiply by the biggest 10, 100, 1000, number that we obtain.

Eg. In the following example we have values with 1 decimal place (1dp), and 2 dp’s.

We need to multiply both sides by 100 to move the point on the two decimal place item. We MUST multiply by 100 to both sides of the Ratio to preserve its accuracy. (Just like multiplying the top and bottom of a fraction by the exact same number when we create a common denominator).

In this final example, we also end up with big numbers to reduce down and simplify.

When this happens it is sometimes necessary to do the simplification in more than one step.

First divide by the biggest number which goes into both of the big numbers.

Then see what goes into the resulting numbers, and reduce down to the final answer.

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Ratio Blaster Game

In this game we move our bottom of screen blaster gun left to right using the arrow keys, and shoot at the Equivalent Ratio using the Space Bar.

the target ratios are written in fraction form: eg. 4/8 means 4 to 8 which is equivalent to 1 to 2. (Eg. Reduce down by dividing both values by their Highest Common Factor of “4”.

Simplifying Ratios Worksheets

Click the links below for some free printable simplifying ratios worksheets, with answers available as well.

http://www.helpingwithmath.com/printables/worksheets/ratio_proportion/wor0601ratio03.htm

http://www.helpingwithmath.com/printables/worksheets/ratio_proportion/wor0601ratio04.htm

Online Ratios Practice

The following web page has a number of activities related to working with Ratios.

It is strongly recommended that you try these out as a self-test on simplifying ratios.

http://math.rice.edu/~lanius/proportions/index.html

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