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Horizontal Line Test Money Formula for Percentage Simplifying Fractions, Estimating Fractions Polynomial Fractions Fractions Intro Adding/Subtracting FractionsWhat is Ratio Scale

The *Ratio Introduction* page introduced the
concept of ratios, with examples of how they can be simplified from groups larger than the numbers
in the actual ratio.

With ratio scale, ratios can be appropriately scaled up or down when necessary, with the use of division and multiplication.

To give the information you want.

__Examples__

__(1.1)__

A sweet shop sold Chocolate and Candy one week in a ratio of:

**Chocolate : Candy** => **1 : 6**

If the shop sold **60** Chocolate bars that week, how many Candy bars were sold?

__Solution__

We know **60** Chocolate bars were sold => **60 : Candy**

We know the Candy bars sold will be 6 times more, so multiplication can complete this ratio being scaled up.

**60** x **6** = **360** => **60 : 360**

**360** Candy bars were sold that week.

__(1.2)__

The ratio of bees to wasps in a garden is **8 : 1**.

If there are **72** bees, how many wasps are there?

__Solution__

We know **72** bees are in the garden => **72**** : Wasps**

The number of wasps in the garden is **8** times less, this now calls for division of **72** by **8**.

**72** ÷ **8**
= **9** => **72 : 9**

**9** wasps are in the garden.

__(1.3)__

A man works a **10** hour shift, and earns **$200** for doing so.

How many dollars did he earn an hour for the **10** hour shift?

__Solution__

We can set up the ratio as **Hours : Dollars**. **10 : 200**

Division by **10** will scale the ratio down so that the hours part is just
**1**.

**10** ÷ **10**
= **1 , 200** ÷ **10**
= **20** => **1 : 20**

The man earned **$20** in one hour during the
**10** hour shift.

In Ratio Math, a ratio can also be in **3** parts as well as **2**.

When **3** or more quantities are involved in a ratio, it is called a "continued ratio".

The ratio is continuing beyond **2** quantities.

__Examples__

__(2.1)__

Split $10'000 into the ratio **2 : 3 : 5**.

__Solution__

The ratio **2 : 3 : 5** is **10** parts in total.

**$10'000 ****÷ ****10**** **= **$1000**

**2 **x** $1000** = **$2000**

**3 **x** $1000** = **$3000**

**5 **x** $1000** = **$5000**

**2 : 3 : 5** = **$2000 : $3000 : $5000**

__(2.2)__

A Gold Mining company has 3 mines, A, B and C.

One year 5 million dollars (**$5'000'000**) was mined from all 3 mines combined.

The ratio of the Gold taken from each mine was,

A : B : C => **4**** : 2 : 2**.

How much Gold did each individual mine produce?

__Solution__

The ratio **4**** : 2 : 2** is 8 parts in total.

**$5'000'000 ****÷ 8 **= **$625'000**

MINE A) **4 **x** $625'000** = **$2'500'000**

MINE B) **2 **x** $625'000** = **$1'250'000**

MINE C) **2 **x** $625'000** = **$1'250'000**

The ratio for mines A, B and C is,

**$2'500'000 : $1'250'000 : $1'250'000**.

Mine's share =

So the calculations would be:

MINE A) =

MINE B) =

MINE C) =

In some situations, it can be required to be put  2 or more ratios into a continued ratio.

Say  3 different shops made a combined profit of

Their combined profit is divided up betwen the shops in ratios such that:

How much profit did each individual shop make?

To properly compare these  3 different profits, we look to put them into a continued ratio.

To do this, we can lay out the shops in a

Then write down the ratios between the shops that we currently know underneath, set up in the following way.

Now we can multiply these numbers in the following way, from left to right.

Writing the multiplication results in order below will give us a continued ratio.

This new ratio represents the  3 different shop profits in a continued ratio.

Now we can take either of the approaches shown from the gold mines example

Sum of Ratios =

SHOP 1) =

SHOP 2) =

SHOP 3) =

Of the **$36'000** of total profits.

**Shop 1** made **$12'000**, **shop 2** made **$16'000**
and **shop 3** made **$8'000**.

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