Adding Fractions with Unlike Denominators

Front

What is a fraction?

Back

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

Front

What does it mean to have unlike denominators in fractions?

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 a common denominator?

Back

A common denominator is a number that is a multiple of the denominators of two or more fractions. It allows you to add or subtract the fractions.

Front

What is the first step in adding \( \frac{1}{3} \) and \( \frac{1}{4} \)?

Back

The first step is to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.

Front

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

Back

To convert \( \frac{1}{3} \) to a fraction with a denominator of 12, multiply the numerator and denominator by 4: \( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \).

Front

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

Back

To convert \( \frac{1}{4} \) to a fraction with a denominator of 12, multiply the numerator and denominator by 3: \( \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \).

Front

What is the sum of \( \frac{4}{12} \) and \( \frac{3}{12} \)?

Back

The sum is \( \frac{4 + 3}{12} = \frac{7}{12} \).

Front

What is the formula for adding fractions?

Back

The formula for adding fractions is: \( \frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + b \cdot c}{b \cdot d} \) where \( a \) and \( c \) are the numerators and \( b \) and \( d \) are the denominators.

Front

What is the result of adding \( \frac{1}{2} \) and \( \frac{3}{8} \)?

Back

First, find a common denominator (which is 8). Convert \( \frac{1}{2} \) to \( \frac{4}{8} \). Then add: \( \frac{4}{8} + \frac{3}{8} = \frac{7}{8} \).