Adding and Subtracting Fractions

BASIC CONCEPTS

A fraction is a mathematical expression that represents a part of a whole and is composed of two parts: the numerator and the denominator. The numerator is the number above the line, indicating how many parts we have, and the denominator below the line shows into how many equal parts the whole is divided.

ADDING FRACTIONS

Adding fractions requires the denominators to be the same. If we have two fractions with different denominators, we must first find a common denominator.

1. FIND A COMMON DENOMINATOR: The common denominator is the least common multiple (LCM) of the denominators of the fractions.
2. ADJUST THE FRACTIONS: Adjust the fractions so that they have the same (common) denominator. This involves multiplying the numerator and denominator of each fraction by the appropriate factor to achieve the common denominator.
3. ADD THE NUMERATORS: Add the numerators of the adjusted fractions.
4. WRITE THE RESULT: Write the result as a fraction with the new (common) denominator. Simplify the resulting fraction if possible.

SUBTRACTING FRACTIONS

Subtracting fractions is similar to adding them, except that instead of adding the numerators, we subtract them.

1. FIND A COMMON DENOMINATOR: Just as with addition, first find a common denominator.
2. ADJUST THE FRACTIONS: Adjust the fractions to the common denominator.
3. SUBTRACT THE NUMERATORS: Subtract the numerators of the adjusted fractions.
4. WRITE THE RESULT: Write the result as a fraction with the new (common) denominator. Simplify the resulting fraction if possible.