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 fractions?

Back

To multiply fractions, multiply the numerators together and the denominators together. For example, \( \frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \).

Front

How do you divide fractions?

Back

To divide fractions, multiply the first fraction by the reciprocal of the second fraction. For example, \( \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6} \).

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, \( 1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} \).

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

What is the result of multiplying a fraction by 1?

Back

Multiplying a fraction by 1 does not change its value. For example, \( \frac{3}{5} \times 1 = \frac{3}{5} \).

Front

What is the result of dividing a fraction by itself?

Back

Dividing a fraction by itself equals 1, as long as the fraction is not zero. For example, \( \frac{3}{4} \div \frac{3}{4} = 1 \).

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, \( \frac{8}{12} \) simplifies to \( \frac{2}{3} \) because the GCD of 8 and 12 is 4.

Front

What is the least common denominator (LCD)?

Back

The least common denominator is the smallest multiple that two or more denominators share. For example, the LCD of 3 and 4 is 12.