Adding and Subtracting Fractions

A fraction represents a part of a whole and is written as 'a/b', where 'a' is the numerator (the number of parts) and 'b' is the denominator (the total number of equal parts).

To add fractions with the same denominator, keep the denominator the same and add the numerators. For example, $$\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5} = \frac{3}{5}$$ .

To add fractions with different denominators, first find a common denominator, convert the fractions, and then add the numerators. For example, $$\frac{1}{4} + \frac{1}{2} = \frac{1}{4} + \frac{2}{4} = \frac{3}{4}$$ .

A common denominator is a shared multiple of the denominators of two or more fractions, allowing them to be added or subtracted.

To subtract fractions with the same denominator, keep the denominator the same and subtract the numerators. For example, $$\frac{5}{8} - \frac{2}{8} = \frac{5-2}{8} = \frac{3}{8}$$ .

To subtract fractions with different denominators, find a common denominator, convert the fractions, and then subtract the numerators.

An equivalent fraction is a fraction that represents the same value as another fraction, even though the numerator and denominator may be different. For example, $$\frac{1}{2} = \frac{2}{4}$$ .

The simplest form of a fraction is when the numerator and denominator have no common factors other than 1. For example, $$\frac{4}{8}$$ simplifies to $$\frac{1}{2}$$ .

To simplify a fraction, divide the numerator and denominator by their greatest common factor (GCF). For example, to simplify $$\frac{6}{9}$$ , divide both by 3 to get $$\frac{2}{3}$$ .

$$\frac{3}{8} + \frac{4}{8} = \frac{7}{8}$$ .