Multiplying and Dividing Fractions

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). For example, in the fraction \( \frac{3}{4} \), 3 is the numerator and 4 is the denominator.

Front

How do you multiply two fractions?

Back

To multiply two fractions, multiply the numerators together and the denominators together. For example, \( \frac{1}{2} \cdot \frac{3}{4} = \frac{1 \cdot 3}{2 \cdot 4} = \frac{3}{8} \).

Front

What is the result of multiplying a whole number by a fraction?

Back

To multiply a whole number by a fraction, convert the whole number to a fraction (by putting it over 1) and then multiply. For example, \( 2 \cdot \frac{3}{4} = \frac{2}{1} \cdot \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \).

Front

What is the process for dividing fractions?

Back

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, \( \frac{1}{2} \div \frac{3}{4} = \frac{1}{2} \cdot \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \).

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a fraction. For example, \( 1 \frac{1}{2} \) is a mixed number, which means 1 whole and 1/2.

Front

How do you convert a mixed number to an improper fraction?

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, \( 1 \frac{1}{2} = \frac{1 \cdot 2 + 1}{2} = \frac{3}{2} \).

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction is obtained by flipping the numerator and denominator. For example, the reciprocal of \( \frac{3}{4} \) is \( \frac{4}{3} \).

Front

How do you simplify a fraction?

Back

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify \( \frac{6}{8} \), divide both by 2 to get \( \frac{3}{4} \).

Front

What is the least common denominator (LCD)?

Back

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

Front

How do you add fractions with different denominators?

Back

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