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# Rational Numbers Operation

Concept:

A rational number can be represented in the form of a/b, where a and b are integers, and b is not zero.

For example, a/b is called a fraction, where a is the numerator of the fraction and b is the denominator of the fraction.

Concept:

Two fraction are said to be equivalent if they have the same value but different forms.

Example:

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

Concept:

Two fractions are equivalent, if their cross products are equal.

Concept:

Addition and subtraction of fractions

Concept:

The least common denominator, or LCD

Example 1:

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

Example 2:

Solution:

Writing the denominators in factored form, 18 = 3 × 3 × 2 = 3^{2} × 2 and 27 = 3 × 3 × 3 = 3^{3}

so that, the LCD of the fractions is 3^{3} × 2 = 54

Concept:

Multiplication and Division of Fractions