Adding and Subtracting Fractions

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number). For example, in the fraction 1/2, 1 is the numerator and 2 is the denominator.

To add fractions with the same denominator, keep the denominator the same and add the numerators. For example, $$\frac{1}{4} + \frac{2}{4} = \frac{1+2}{4} = \frac{3}{4}$$ .

To subtract fractions with the same denominator, keep the denominator the same and subtract the numerators. For example, $$\frac{5}{8} - \frac{3}{8} = \frac{5-3}{8} = \frac{2}{8} = \frac{1}{4}$$ .

The least common denominator (LCD) is the smallest number that can be used as a common denominator for two or more fractions. For example, the LCD of $$\frac{1}{3}$$ and $$\frac{1}{4}$$ is 12.

To add fractions with different denominators, first find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD, and then add the numerators. For example, $$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$ .

To subtract fractions with different denominators, find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD, and then subtract the numerators. For example, $$\frac{5}{6} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$$ .

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. For example, $$\frac{7}{4}$$ is an improper fraction.

A mixed number is a whole number combined with a proper fraction. For example, $$1 \frac{1}{2}$$ is a mixed number.

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator over the original denominator. For example, $$\frac{9}{4} = 2 \frac{1}{4}$$ .

To simplify a fraction, divide both the numerator and the denominator by their greatest common factor (GCF). For example, $$\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$$ .