Dividing Fractions

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, to divide \( \frac{a}{b} \div \frac{c}{d} \), you calculate \( \frac{a}{b} \times \frac{d}{c} \).

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \).

Front

How do you simplify a fraction?

Back

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).

Front

What is the GCD of 8 and 12?

Back

The GCD of 8 and 12 is 4.

Front

What is the result of \( \frac{4}{4} \div \frac{1}{4} \)?

Back

The result is 16, as \( \frac{4}{4} \times \frac{4}{1} = 16 \).

Front

How do you divide a fraction by a whole number?

Back

To divide a fraction by a whole number, multiply the fraction by the reciprocal of the whole number. For example, \( \frac{2}{5} \div 4 = \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10} \).

Front

What is the result of \( \frac{2}{5} \div 3 \)?

Back

The result is \( \frac{2}{15} \), as \( \frac{2}{5} \times \frac{1}{3} = \frac{2}{15} \).

Front

What is the quotient of \( \frac{4}{5} \div 2 \)?

Back

The quotient is \( \frac{2}{5} \), as \( \frac{4}{5} \div 2 = \frac{4}{5} \times \frac{1}{2} = \frac{4}{10} = \frac{2}{5} \).

Front

What does it mean to express a fraction in lowest terms?

Back

Expressing a fraction in lowest terms means simplifying it so that the numerator and denominator have no common factors other than 1.

Front

What is the result of dividing two fractions in lowest terms?

Back

The result of dividing two fractions in lowest terms is the simplest form of the quotient, where the numerator and denominator are coprime.