Operations on Rational Numbers

A rational number can be represented in the form of a/b, where a and b are integers, and b is not zero
a/b is called a fraction, where a is the numerator of the fraction and b is the denominator of the fraction.
Two fraction are said to be equivalent if they have the same value but different forms.
For example, 2/3, 4/6, -6/-9.
We denote two equivalent fractions by writing an equal sign between them, 2/3 = 4/6 = -6/-9
Two fractions are equivalent, if their cross products are equal.
cross products
cross products
lowest terms
the rules of signs for fractions
the rules of signs for fractions
Addition and subtraction of fractions
rules of addition of fractions
rules of subtraction of fractions
addition of unlike fraction
subtraction of unlike fractions
The least common denominator, or LCD
Example 1:
the least common denominator
Solution
The denominators are factored as : 15 = 3 × 5 and 6 = 2 × 3
The prime factors are 3, 5, 2, and therefore the LCD of the fractions is 3 × 5 × 2 = 30
find the least common denominator
Example 2:
find the Common Least Denominator
Solution
Writing the denominators in factored form, 18 = 3 × 3 × 2 = 32 × 2 and 27 = 3 × 3 × 3 = 33
so that, the LCD of the fractions is 33 × 2 = 54
find the least common denominator
Multiplication and Division of Fractions
multiplication of fractions
division of fractions