Adding Fractions

A fraction represents a part of a whole and is written as $$\frac{a}{b}$$ , 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, $$\frac{2}{5} + \frac{1}{5} = \frac{2+1}{5} = \frac{3}{5}$$ .

The least common denominator (LCD) is the smallest number that can be used as a common denominator for two or more fractions.

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.

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, $$\frac{1}{2}$$ is equivalent to $$\frac{2}{4}$$ .

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

A mixed number is a whole number combined with a 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 over the original denominator.

$$\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$ .

$$\frac{3}{5} + \frac{1}{5} = \frac{4}{5}$$ .