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Mathematics

Fractions

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A group of related sciences, including algebra, geometry, and calculus, concerned with the study of number, quantity, shape, and space and their interrelationships by using a specialized notation

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 29

(a) 3 out of 5 ( three-fifths) = 3/5

Example 30

(b) 7 0ut of 8 ( i.e seven-eighths) = 7/8

Example 31

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 Numbers

Distinguish proper, improper fractions and mixed numbers

Proper fraction -is a fraction in which the numerator is less than denominator

Example 32

Proper fractions; 4/5, 1/2, 11/13

Improper fraction -is a fraction whose numerator is greater than the denominator

Example 33

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 34

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 35

Convert the following mixed numbers into improper fractions

Solution:

Example 36

Change 7/4 into a mixed number

Solution:

7/4 = 1¾

Example 37

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 38

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 39

Simplify the following fractions to their lowest terms

Solution

Fractions in Order of Size

Arrange fractions in order of size

Example 40

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 41

Find