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FRACTION

By Mushadi Iksan, M.Ed.

3.1 FRACTION
A fraction is a number that represents a part of a whole. It is written as , where a and b are whole numbers and b 0. is read as “ a over b”
Example:
1. is read as “three over four” or “ three quarter”
2. is read as “ one over three” or “one third”.

3.1.1 Representing Fractions with Diagrams
· Fractions can be represented with diagrams and number lines.
In the left diagram, the shaded parts are 1 out of 4 equal parts, that is Example:


· In any fraction, the top number is called the numerator and the bottom number is called the denominator.
Example:
Denominator
Numerator

· The numerator represents the number of equal parts that are shaded and the denominator represents the total number of equal parts in one whole.

· When the numerator is the same as the denominator, the value of the fraction is equal to 1.
Example:


3.1.2 Equivalent Fractions
· Equivalent fractions are fractions having the same value.
Example:
=






=



· Equivalent fractions can be obtained by multiplying the numerator and denominator by the same whole numbers (greater than 1).

Example:


Since,
, , , and

· To determine whether two given fractions are equivalent or not, we can use calculation.
Fractions and are equivalent if ad = bc

Example :
Determine whether and are equivalent.

Solution:
Cross-multiplying
The products are the same
Therefore, and are equivalent


3.1.3 Comparing the Values of Two Fractions
· When comparing two fractions having the same denominator, the fraction with the bigger numerator is greater in value.
Example:
and
has greater value, because 7 > 5 and their denominator are the same.

· When comparing two fractions having the same numerator, the fraction with the smaller denominator is greater in value.
Example:
and
has greater value, because 12 <>

· Alternative method of comparing two fractions having different numerators and denominators.
Fractions and ;
If ad > bc then >
If ad <> Þ >


3.1.4 Simplifying Fraction
· A fraction is in its lowest terms if the numerator and denominator have no common factor except 1.
· To simplify a fraction to its lowest term, divide the numerator and the denominator by their HCF.
· All answer must be given in their lowest term.

Example:
Simplify to its lowest terms.
Solution:
13 is the HCF of 13 and 39








3.2 PROPER FRACTIONS, IMPROPER FRACTION AND MIXED NUMBERS
3.2.1 Proper Fractions and Improper Fractions
· A proper fraction has a numerator which is smaller than the denominator.
Example:


· An improper fraction has a numerator which is the same as or greater than the denominator.
Example:


3.2.2 Converting Whole Numbers to Improper Fractions
· All whole numbers are improper fractions with 1 as their denominators.
Example:
, ,

· Whole numbers can be converted to improper fractions with other denominators.
Example:
= =

3.2.3 Mixed Number
· A mixed number is a number consisting of a whole number and a fraction.
· All mixed numbers are greater than.
Example:
, , ,

3.2.4 Converting Mixed Numbers to Improper Fractions.
· To change a mixed number to an improper fraction, multiply the whole number by the denominator and then add the product to the numerator. The denominator remains the same.
Example:
a.
b.


3.2.5 Converting Improper Fractions to Mixed Numbers
· To change an improper fraction to a mixed number, divide the numerator by the denominator.
· The quotient obtained is the whole number part and the remainder is the numerator of the fractional part.
Example:
Þ Remainder = 2
Therefore,

· Where possible, simplify the improper fraction to its lowest terms before converting it to the mixed number.
Example: