Definition, Types, and Conversion of Fractions.

FRACTIONS DEFINITION.

A single unit can be broken into equal parts called fractions example 1/4, ½, 1/5.

If for example, the unit is broken into five equal parts and two parts are then taken, the fraction is written as 2/5.

The 5 is called the denominator and the 2 is called the numerator.

TYPES OF FRACTIONS.

There are three types of fractions

a) A proper fraction.

Is a fraction which has its numerator less than its denominator e.g. 2/5.

b) Improper fraction

Is a fraction which has its numerator more than its denominator e.g. 7/2.

c) A mixed number fractions.

This is made up of a whole number and a proper fraction e.g. 2 1/2.

CONVERSION OF FRACTIONS.

Changing a mixed number to an improper fraction.

In changing a mixed number to an improper fraction we have to do the following:

Example: Change 2 1/3 into an improper fraction.

Solution.

i) Multiply the whole number 2 by the denominator 3

2×3=6

2) Then add 6 to the numerator 1 to get the numerator of the improper fraction. 6+1=7

3) Write it with 7 as the numerator and 2 as the denominator

2 1/3=7/3

EXERCISE

Change the following mixed numbers into improper fractions:

a) 4 2/3

Solution

4 2/3 = [(3×4) +2]/3 =14/3

Try these

b) 11 3/13

c) 23 1/4

Changing improper fractions into mixed numbers.

Example: Change 17/3 into a mixed number.

Solution

Dividing 17 by 3 we get 5 and a remainder 2. Therefore 5 becomes the whole number, 2 the numerator and 3 the denominator of the mixed number.

Hence,17/3= 5 2/3

Exercise

Change the following improper fractions into mixed numbers.

a) 33/5

Solution

33/5 = (30+3)/5 = 30/5 + 3/5 = 6 3/5

Try these

b) 73/12

c) 120/7

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