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 $$\frac{3}{4}$$ , 3 is the numerator and 4 is the denominator.

To add fractions with different denominators, first find a common denominator, convert each fraction to an equivalent fraction with that denominator, and then add the numerators.

The least common denominator (LCD) is the smallest multiple that two or more denominators share. It is used to add or subtract fractions.

To subtract fractions, ensure they have the same denominator. If they don't, find the least common denominator, convert the fractions, and then subtract the numerators.

Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as $$\frac{5}{4}$$ .

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

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator.

1. Find the least common denominator (24). 2. Convert $$\frac{1}{3}$$ to $$\frac{8}{24}$$ and $$\frac{1}{8}$$ to $$\frac{3}{24}$$ . 3. Add: $$\frac{8}{24} + \frac{3}{24} = \frac{11}{24}$$ .

1. Find the least common denominator (20). 2. Convert $$\frac{2}{5}$$ to $$\frac{8}{20}$$ and $$\frac{1}{4}$$ to $$\frac{5}{20}$$ . 3. Subtract: $$\frac{8}{20} - \frac{5}{20} = \frac{3}{20}$$ .