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    MATHEMATICS: FORM ONE: Topic 2 – FRACTIONS

    Msomi BoraBy 5 Comments4 Mins Read

    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
    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
    Proper fractions; 4/5, 1/2, 11/13
    Improper fraction -is a fraction whose numerator is greater than the denominator
    Example 5
    Example of improper fractions are; 12/7, 4/3, 65/56
    Mixed fraction –is a fraction which consist of a whole number and a proper fraction
    Example 6
    Mixed fractions
    (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
    Solution:
    Example 8
    Change 7/4 into a mixed number
    Solution:
    7/4 = 1¾
    Example 9
    Write the following fractions in order of size beginning with the smallest; 2/3, 5/6, 1/2, 3/4
    Solution:
    Change the fractions into decimals

    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 10
    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
    Multiplying the numerator and denominator by the same number
    Give equivalent fractions to 1/4
    .
    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 11
    Simplify the following fractions to their lowest terms
    Solution
    Fractions in Order of Size
    Arrange fractions in order of size
    Example 12
    Arrange in order of size, starting with the smallest, the fraction
    Solution
    Change the fractions into decimals

    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 13
    Find
    Solution
    Example 14
    Subtraction of Fractions
    Subtract fractions
    Example 15
    Evaluate
    Solution
    Example 16
    Multiplication of Fractions
    Multiply fractions
    Example 17
    Division of Fractions
    Divide fractions
    Example 18
    Mixed Operations on Fractions
    Perform mixed operations on fractions
    Example 19
    Example 20
    Word Problems Involving Fractions
    Solve word problems involving fractions
    Abdiel takes 2/3 of an hour to read 30 pages of a story book. How long does he take to read 1 page?
    Solution:
    1 page will take?
    Example 21
    Musa is 12 years old. His father is 3¾ times as old as he is. How old is his father?
    Solution:
    Example 22
    1¾ metres of a material are needed to make a suit. How many suits can be made from 63 metres?
    Solution:
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