## 22 Jun Study the concept of ratios though our chemistry tuition

Ratios are an essential part of mathematics and everyday life. They are essentially mathematical tools that are used to show how a specific number of things are shared amongst a specific number categories i.e. people. This makes it easier to calculate the fraction of the whole that an individual/category got.

## Notation

Ratios use the sign ‘:’ in between numbers as the ratio notation.

** Example 1**: If we have 10 sweets that are shared between LEE and DEE and Lee gets 4 and Dee gets 6,

the ratio of the sweets can be written as 4:6.

That is the ratio of Lee’s sweets to Dee’s.

The first number is the smallest number in the ratio and the numbers progress going to the right. Ratios can be between as many individuals as possible as long as each individual is getting something from the total number of things that are being shared

** Example 2**: If 60 sweets are shared between Tanya, John, Peter and Angela such that Tanya gets 5 sweets, John gets 10, Peter gets 15, and Angela gets 20. The ratio can be written as;

5:10:15:20

Ratios can be simplified in a similar way that fractions are simplified using the highest common factor of all the numbers in the ratio

** Example 3**: In example 1 the highest common factor is 2 and if we divide the whole expression by 2 our ratio will be equal to 2:3

Similarly, for example, 2 if we divide the whole expression with 5, which is the highest common factor of all the number in the ratio, our ratio will be equal to;

1:2:3:4

This is simpler than the initial bloated figures and it is relatively easier to calculate using smaller numbers.

Ratios can be written using fractions and decimals and, in most cases, it is advisable to first convert the fractions or decimals to whole numbers to make further calculations easier

** Example 4**: The ratio 1/4:1/2 can be converted to a whole number ratio by multiplying both elements of the expression by a number that will result in the smallest whole number. In this case, the number is 4 and if we multiply the expression with 4, it becomes;

1:2 which is relatively easier to work with than fractions.

### Typical Calculations

Ratios can be used to calculate the amount that is unknown shared between individuals.

** Example 5**: Angela and Tanya share 30 drinks in the ratio 5:10. Calculate the number of sweets each of them get.

The first step is to add the numbers in the ratio to get the total number of items shared.

5+10 = 15

Once we have this number, we use it as our common denominator and we use the individual numbers in the ratio as our numerators;

5/15 and 10/15

Once we have these, we multiply with the total number of drinks to get the total number of drinks shared amongst the individuals

- 5/15 x 30 =10 sweets for Angela
- 10/15 x30 =20 sweets for Tanya

### Practical Application of Ratios

Ratios have practical uses especially in construction and map work where they use scales to represent a large area on a smaller area to make it easy to calculate. The scale is a prime example of the practicality of ratios

*Example*

- a) A scale on a map is 1cm: 100m, calculate the actual distance of 3 cm
- b) Calculate the distance on the map of 450m

We multiply the represented distance we are given with the actual distance on the scale

3 x 100 = 300m

For b, we divide the given actual distance with actual distance on our scale and multiply by the representation distance on the scale

450/100 x1 = 4,5cm

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