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 NumbersA FractionDescribe a fractionA 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 belowThe 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) = 3/5Example 2(b) 7 0ut of 8 ( i.e seven-eighths) = 7/8Example 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 NumbersDistinguish proper, improper fractions and mixed numbersProper fraction –is a fraction in which the numerator is less than denominatorExample 44/5, 1/2, 11/13Improper fraction -is a fraction whose numerator is greater than the denominatorExample 512/7, 4/3, 65/56Mixed fraction –is a fraction which consist of a whole number and a proper fractionExample 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 7Convert the following mixed numbers into improper fractions
Comparison of FractionsIn 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 TermsSimplify a fraction to its lowest termsExample 8For the pair of fractions below, find which is greater
Solution
Equivalent FractionsIdentify equivalent fractionsEquivalent 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 formExample 9Simplify the following fractions to their lowest terms
Solution
Fractions in Order of SizeArrange fractions in order of sizeExample 10Arrange in order of size, starting with the smallest, the fraction
SolutionPut them over the same denominator, that is find the L.C.M of 3, 7, 8 and 9
Operations and FractionsAddition of FractionsAdd fractionsOperations 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 11Find
Solution
Subtraction of FractionsSubtract fractionsExample 12Evaluate
Solution
Multiplication of FractionsMultiply fractionsExample 13
Division of FractionsDivide fractionsExample 14
Mixed Operations on FractionsPerform mixed operations on fractionsExample 15
Example 16
Word Problems Involving FractionsSolve word problems involving fractionsExample 17
- Musa is years old. His father is 3¾times as old as he is. How old is his father?
- 1¾of a material are needed to make suit. How many suits can be made from
