Working
with Fractions
A
fraction (part of a whole), written one number above another, the
top number is called the numerator and the bottom number is called
the denominator. Example:
is
read three fourth obtained by dividing an item into four equal parts
and using 3 of the 4 parts.When the numerator and
the denominator are the same, the fraction is 1.
1 written as a fraction is extremely useful when performing the
addition or subtraction of two fraction with different denominators.
Example:
When
the numerator is smaller than the denominator, the fraction is less
than 1, is called a proper fraction. For example, 7/8 is a proper
fraction, since 7/8 < 1.
When the
numerator is larger than the denominator, the fraction is greater than
1, is called an improper fraction. For example, 5/3 is an improper
fraction, since 5/3 > 1.
Calculation
with fractions:
1. Addition and subtraction of fraction
(a) With the same denominator:
To add or subtract fractions with the same
denominator, just add or subtract their numerators and keep their
denominators
Example:
(b)
With unlike denominators:
To add or subtract fractions
with different denominators, you must first change each fraction
to an equivalent fraction with least common denominator (LCD) as
the common denominator and then proceed as in part (a).
Example
1:
Example
2:
2. Multiplication of fractions
When multiplying two or more fractions
together, first cancel all pairs of common factors from both numerator
and denominator, and then multiplying their respective remaining
numerators and denominators.
Example:
Multiply:
3. Division of fractions
To divide one fraction by another means
to multiply the reciprocal of its divisor
Example:
Divide:
