Adding Fractions (Unlike Denominators)

Front

What is a fraction?

Back

A fraction represents a part of a whole and consists of a numerator (top number) and a denominator (bottom number).

Front

What does it mean to have unlike denominators?

Back

Unlike denominators are denominators that are not the same. For example, in the fractions \(\frac{1}{3}\) and \(\frac{1}{4}\), the denominators 3 and 4 are unlike.

Front

How do you add fractions with unlike denominators?

Back

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

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that two or more denominators share. It is used to find a common denominator for adding fractions.

Front

Example: Find the LCD of 3 and 4.

Back

The LCD of 3 and 4 is 12.

Front

Convert \(\frac{1}{3}\) to an equivalent fraction with a denominator of 12.

Back

\(\frac{1}{3} = \frac{4}{12}\) (Multiply both the numerator and denominator by 4).

Front

Convert \(\frac{1}{4}\) to an equivalent fraction with a denominator of 12.

Back

\(\frac{1}{4} = \frac{3}{12}\) (Multiply both the numerator and denominator by 3).

Front

Add \(\frac{1}{3} + \frac{1}{4}\) using the LCD.

Back

\(\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}\)

Front

What is an improper fraction?

Back

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

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a proper fraction, such as 1 \(\frac{1}{4}\).