Fractions & Ratios

Many teachers complain that students often find it very difficult to understand fractions and ratios. The main reason behind that is they are taught how to solve fractions without knowing exactly the exact reason behind those steps in solving them. In this section, we’ll be looking at fractions and ratios and the basic concept behind them.

What is a Fraction?

A fraction is a numerical quantity that is not a whole number. Take for example, ½ is a fraction, which gives you the result 0.5. In other words, a fraction can be described as how many parts of a specified size there are.

Look at this picture below:

fractions

Here you can see the pizza is cut into 8 pieces and 1 piece out of the 8 is taken, which gives the fraction as 1/8.

In a fraction, there is a top part and a bottom part where the top portion is called the numerator and bottom part is called the denominator. If the numerator is lesser than the denominator, then it is called a proper fraction. Otherwise if the denominator is greater, then it called an improper fraction. When you add or subtract fractions with the same denominator, then you only add or subtract the numerator and leave the denominator as is.

How to Reduce a Fraction

A fraction can be easily reduced into its simplest form and to do that, divide both the numerator and denominator by the greatest common factor or divide with a common factor many times until you get 1.

Example 1 – Reduce 8 / 2

Find the greatest common factor of 2 and 8.

2: 1, 2
8: 1, 2, 4, 8

Divide the numerator and denominator by 2.

(8 ÷2) / (2 ÷2) = 4 / 1 = 4

Example 2 – Reduce 15 / 20

Find the greatest common factor of 15 and 20.

15: 1, 3, 5, 15
20: 1, 2, 4, 5, 10, 20

Divide the numerator and denominator by 5.

(15 ÷ 5) / (20 ÷ 5) = 3 / 4

Ratios

Ratios can be best described as a relationship between the given two numbers. In other words, ratio depicts how much one number is contained in another word. Take for example, a bowl containing 10 chocolates and 5 biscuits, then the ratio to chocolates and biscuits in the bowl is 10 to 5. This ratio can also be represented as 10:5, that is also equivalent to 2:1.

The numbers in a ratio can be anything including weight, quantities, numbers, time etc., but the only thing is that both numbers must be of a positive value. Ratios can be represented in many ways including either 3:1 or 3 to 1 or even as a fraction 3/1.

Let’s look at another example to understand it more easily:

A cake recipe specifies that you need 3 cups of flour and 2 cups of milk. Hence, the ratio here is

3:2 of flour to milk.

So, if you want to make 3 pancakes, you might want to add 3 times the actual recipe, so we multiply the ratio numbers by 3. Hence:

3 x 3 : 2 x 3 = 9:6

In other words, you might need 9 cups of flour and 6 cups of milk.

Example 1 – A sandwich consists of 2 buns, 1 lettuce, 2 turkey slices, and 1 slice of cheese. What is the ratio of buns to turkey slices?

Determine the number of each part required.

Number of buns – 2
Number of turkey slices – 2
buns: slices = 2:2 or 2/2 = 1

Example 2 – In a classroom, there are 15 boys, 13 girls, and 2 teachers. What are the ratios:

a. boys to girls
b. girls to boys
c. students to teachers

Boys to girls – 15:13
Girls to boys: 13:15

Students to teachers: (15 +13) : 2 = 28 : 2 or 28 /2 = 14

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