**TOPIC 2: FRACTIONS**

**A fraction** is a number which is expressed in the form of a/b where a – is the top number called numerator and b– is the bottom number called denominator.

Proper, Improper and Mixed Numbers

**A Fraction**

Describe a fraction

A fraction is a number which is expressed in the form of a/b where a – is the top number called numerator and b– is the bottom number called denominator.

**Consider the diagram below**

The shaded part in the diagram above is 1 out of 8, hence mathematically it is written as 1/8

**Example 1**

(a) 3 out of 5 ( three-fifths) = 3/5

**Example 2**

(b) 7 0ut of 8 ( i.e seven-eighths) = 7/8

**Example 3**

5/12=(5 X 3)/(12 x 3) =15/36

3/8 =(3 x 2)/(8 X 2) = 6/16

Dividing the numerator and denominator by the same number (This method is used to simplify the fraction)

Difference between Proper, Improper Fractions and Mixed Numbers

Distinguish proper, improper fractions and mixed numbers

**Proper fraction** –is a fraction in which the numerator is less than denominator

**Example 4**

4/5, 1/2, 11/13

**Improper fraction** -is a fraction whose numerator is greater than the denominator

**Example 5**

12/7, 4/3, 65/56

Mixed fraction –is a fraction which consist of a whole number and a proper fraction

**Example 6**

(a) To convert mixed fractions into improper fractions, use the formula below

(b)To convert improper fractions into mixed fractions, divide the numerator by the denominator

Example 7

Convert the following mixed numbers into improper fractions

**Comparison of Fractions**

In order to find which fraction is greater than the other, put them over a common denominator, and then the greater fraction is the one with greater numerator.

A Fraction to its Lowest Terms

Simplify a fraction to its lowest terms

**Example 8**

For the pair of fractions below, find which is greater

Solution

**Equivalent Fractions**

Identify equivalent fractions

Equivalent Fraction – Are equal fractions written with different denominators

They are obtained by two methods

<!– [if !supportLists]–>(a) <!–[endif]–>Multiplying the numerator and denominator by the same number

<!– [if !supportLists]–>(a) <!–[endif]–>Dividing the numerator and denominator by the same number (This method is used to simplify the fraction

**NOTE****:** The fraction which cannot be simplified more is said to be in its lowest form

**Example 9**

Simplify the following fractions to their lowest terms

Solution

**Fractions in Order of Size**

Arrange fractions in order of size

**Example 10**

Arrange in order of size, starting with the smallest, the fraction

Solution

Put them over the same denominator, that is find the L.C.M of 3, 7, 8 and 9

**Operations and Fractions**

**Addition of Fractions**

Add fractions

**Operations on fractions involves **

1. Addition,

2. Subtraction,

3. Multiplication

4. Division

**Addition and subtraction of fractions** is done by putting both fractions under the same denominator and then add or subtract

**Multiplication of fractions** is done by multiplying the numerator of the first fraction with the numerator of the second fraction, and the denominator of the first fraction with the denominator the second fraction.

For mixed fractions, convert them first into improper fractions and then multiply

**Division of fractions** is done by taking the first fraction and then multiply with the reciprocal of the second fraction

For mixed fractions, convert them first into improper fractions and then divide

**Example 11**

Find

Solution

**Subtraction of Fractions**

Subtract fractions

**Example 12**

Evaluate

Solution

**Multiplication of Fractions**

Multiply fractions

**Example 13**