Fractions

Fraction

A fraction is a way to represent a part of a whole or a part of a group. It helps us express numbers that are not whole numbers.

Imagine you have a pizza and you want to share it with your friend. Each slice you cut the pizza into is like a fraction — a part of the whole pizza. You and your friend (2 persons) eat 1 slice which is half of the pizza.

Imagine you have a pizza and you want to share it with your three friends. Each slice you cut the pizza into is like a fraction — a part of the whole pizza. You and your three friends (4 persons) eat 1 slice which is one-fourth of the pizza.

Here, 12 and 14 are fractions.

Parts of a Fraction

A fraction has two parts:

a. Numerator: The number on top of the fraction that tells you how many parts you have.
b. Denominator: The number at the bottom of the fraction that tells how many equal parts are in the whole.

The figure shows the numerator and denominator in a fraction.

Examples:

→ In the fraction12, "1" is the numerator (you have one part), and "2" is the denominator (the whole is divided into two equal parts).
→ In the fraction25, "2" is the numerator (you have one part), and "5" is the denominator (the whole is divided into two equal parts).

Types of Fractions

Types of Fractions are:

a. Unit Fractions: Fractions which have 1 as their numerators are called unit fractions.
For example: 12, 13,14, 15,19, etc.

b. Proper Fractions: When the numerator is smaller than the denominator. For example: 12, 23, 34,45, 79, etc.

c. Improper Fractions: When the numerator is greater than the denominator.
For example: 32, 43, 75, 97, 98, etc.

d. Mixed Numbers: A combination of a whole number and a proper fraction For example: 112, 223, 325, 547, 378, etc.

Example: Which of the following is a unit fraction?

a) 7/9 
b) 5/9
c) 3/9
d) 1/9

Answer: d) 1/9

Explanation: Fractions which have 1 as their numerators are called unit fractions. Hence, 1/9 is a unit fraction.

Lowest Form of Fraction

The lowest form of a fraction is when the numerator and denominator have only one common factor (a number that divides them both) of 1.

To get a fraction into its lowest form, we need to find a common number that can divide both the numerator and the denominator. If there is, we divide both parts by that common number.

Let's take the fraction 129.

→ Both 12 and 9 can be divided by 3.
→ When we divide 12 by 3, we get 4.
→ When we divide 9 by 3, we get 3.

The lowest form of the fraction 129= 43

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value when simplified to their lowest form.

To find equivalent fractions, we need to multiply or divide both the numerator and denominator of a fraction by the same number.

For example: 515, 412, 39 and 26 are equivalent fractions as their lowest term is 13.

Comparing the Fractions with the Same Denominator

Like fractions are fractions that have the same denominator.

For example: 17, 27, 37, 47 and 57 are like fractions.

When comparing like fractions, the one with the smaller numerator is considered a smaller fraction than the fraction with the larger numerator. 

For examples: In the like fractions 1/5 and 3/5, 1 is less than 3. Thus, we can say that 1/5 is smaller than 3/5.

 1 < 3 ⇒ 1/5 < 3/5

In the like fractions 17/3 and 11/3, 11 is less than 17. Thus, we can say that 11/3 is smaller than 17/3.

11 < 17 ⇒ 11/3 < 17/3

Unlike fractions are fractions that have different denominators.

For example: 17, 23, 35, 411 and 513 are unlike fractions.

Comparison of unlike fractions will be taught in the higher classes.

Addition of Fractions

To add like fractions, follow these steps:

Step 1: Make sure the bottom numbers (denominators) are the same.

Step 2: Add the top numbers (numerators) and put that answer over the denominator.

Step 3: If necessary, make the fraction simpler.

For example, if you want to add 5/7 and 4/7, both fractions have the same denominator (7), so just add the numerators. 5 + 4 = 9. So, the result is 9/7.

Unlike fractions, addition is complex and can be taught in the higher classes.

Example: What is the sum of 5/7, 2/7 and 1/7?

a) 2²⁄₇
b) 1²⁄₇
c) 2¹⁄₇
d) 1¹⁄₇

Answer: d) 1¹⁄₇

Explanation: If the denominators are the same, then add the numerators and put that answer over the denominator.

Sum = ⁵⁄₇ + ²⁄₇ + ¹⁄₇

= ⁵⁺²⁺¹⁄₇ = ⁸⁄₇

Sum in  mixed fraction = ⁸⁄₇
                                  = (7+1) ÷ 7
                                   = 1+¹⁄₇
                                    = 1¹⁄₇

Example: If 2/9 of the apples were rotten, what fraction of the apples was fresh?

a) 1/9
b) 5/9
c) 7/9
d) 11/9

Answer: c) 7/9

Explanation: Fraction of rotten apples = 2/9

In the figure, the shaded region represents rotten apples.

Hence, the unshaded region represents fresh apples.

Therefore, Fraction of fresh apples = 7/9