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Fractions

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Summary: 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

fr1 1440418792613

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

  1. 5/12=(5 X 3)/(12 x 3) =15/36
  2. 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

f2mix 1440420509480

(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

21 1440496099904

Example 7

Convert the following mixed numbers into improper fractions

12 1440496399148

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

greater 1455525709198

Solution

soln 1455525814980

Equivalent Fractions

Identify equivalent fractions

Equivalent Fraction

  • Are equal fractions written with different denominators
  • They are obtained by two methods

(a) Multiplying the numerator and denominator by the same number

fraction 1455524877902

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

Fraction 2 1455524990641

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

example 1455525146816

Solution

solution 1455525390054

Fractions in Order of Size

Arrange fractions in order of size

Example 10

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

size 1455525995009

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 addition, subtraction, multiplication and 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

addition 1455526364559

Solution

adsol 1455526475181

Subtraction of Fractions

Subtract fractions

Example 12

Evaluate

subtract 1455526667395

Solution

subsol 1455526808496

Multiplication of Fractions

Multiply fractions

Example 13

mult 1455527009798

Division of Fractions

Divide fractions

Example 14

div 1455527123586

Mixed Operations on Fractions

Perform mixed operations on fractions

Example 15

mix1 1455527238665

Example 16

divmult 1455527363294

Word Problems Involving Fractions

Solve word problems involving fractions

Example 17

  1. Musa is years old. His father is 3¾times as old as he is. How old is his father?
  2. 1¾of a material are needed to make suit. How many suits can be made from
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