Fraction are divided into 2 called the numerators and the denominators. That is,

Fraction = numerator/denominator

Types of fractions

1. Proper fraction: This is a type of fraction in which the numerator is smaller than the denominator, ex: 1/2, 3/4

2. Improper fraction: This is a type of fraction in which the numerator is greater than the denominator, ex: 5/2, 7/3

3. Mixed fraction: This is a type of fraction with a whole number, ex: 112, 734

Converting to improper fraction from mixed fraction

Ex: convert the following to mixed fraction

1. 135, b)237

                                                  2

Solution: a)              5         13                     13/5 = 235

                                    10

                                                     3

b)                    7          23                      23/7 = 327

                                                     21

          2                   

Converting from mixed fraction to improper fractions

Ex: convert 234 and 112 into improper fractions  

Solution: 234 = 4*2+34 = 114            112 = 2*1+12 = 32

NB: Proper and improper fractions are generally called vulgar fractions

Equivalent fractions

These are 2 or more fractions with the same amount

Ex: a) ½ is equivalent to 2/4, b) 3/6 is equivalent to 6/12, c) 6/12 is equivalent to 1/2.

To obtain the equivalent of a fraction, we either multiply both numerator and denominator of the fraction by the same number or divide both by the same number.

Ex: a) 2/4 = 2*34*3 = 6/12 which is equivalent to 2/4

b)  27/81 = 27/2781/27 = 1/3 which equivalent to 27/81

Simplify fractions

This implies expressing a fraction in its simplest form. To simplify a fraction, the following procedures are taken;

• Look for the lowest factor that can divide both the numerator and the denominator
• Divide them and continue until they can no longer divide

Ex: simplify

a)33/44 = 3*114*11 = 3/4, b)121/36 don’t have a lowest common factor, so it cannot be simplified

Comparing fractions

To compare 2 or more fractions is to say which is bigger or which is smaller than the other. It means arranging fractions in ascending order (from the smallest to the biggest) or in descending order (from the biggest to the smallest).

Ex: state which is greater

a)5/7 or 3/7, b)2/9 or 2/3

Solution: a) 5/7>3/7 since it has a bigger numerator and their denominators are the same

b)2/3>2/9 since it has a smaller denominator as compared to the other

Different numerator and different denominator

Ex: which is greater a)3/4 or 4/5, b)1/3 or 5/16

Solution:

a)  3/4 or 4/5                                                  b) 1/3 or 5/16

       15 or 16    = 4/5 > 3/4                                16 or 15             = 1/3 > 5/16