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 \( \frac{a}{b} \div \frac{c}{d} \), 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 convert an improper fraction to a mixed number?

Back

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder over the original denominator is the fractional part.

Front

What is the result of \( \frac{1}{3} \div \frac{5}{7} \)?

Back

The result is \( \frac{7}{15} \).

Front

What is the result of \( \frac{8}{9} \cdot \frac{1}{5} \)?

Back

The result is \( \frac{8}{45} \).

Front

What is the result of \( \frac{7}{9} \div \frac{3}{4} \)?

Back

The result is \( \frac{28}{27} \).

Front

How do you simplify the fraction \( \frac{10}{9} \)?

Back

The fraction \( \frac{10}{9} \) is already in simplest form, but it can also be expressed as the mixed number \( 1 \frac{1}{9} \).

Front

What is the first step in dividing fractions?

Back

The first step is to find the reciprocal of the second fraction.

Front

What does it mean to simplify a fraction?

Back

Simplifying a fraction means reducing it to its lowest terms, where the numerator and denominator have no common factors other than 1.

Front

What is the result of dividing a fraction by a whole number, such as \( \frac{5}{6} \div \frac{3}{4} \)?

Back

To divide a fraction by a whole number, convert the whole number to a fraction (e.g., \( 3 \) becomes \( \frac{3}{1} \)) and then multiply by the reciprocal.