Divide 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 a reciprocal?

Back

A reciprocal of a number is 1 divided by that number. For a fraction \( \frac{a}{b} \), the reciprocal 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 greatest common divisor (GCD)?

Back

The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides each of the integers without leaving a remainder.

Front

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

Back

Dividing a whole number by a fraction is equivalent to multiplying the whole number by the reciprocal of the fraction.

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, add the numerator, and place that result over the original denominator.

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a proper fraction, such as \( 2 \frac{1}{3} \).

Front

What is the result of \( 6 \frac{1}{9} \div \frac{7}{9} \)?

Back

The operation is incorrect; the correct answer is \( 6 \frac{1}{9} \times \frac{9}{7} = 7 \frac{2}{7} \).

Front

What is the result of \( 2 \div \frac{2}{8} \)?

Back

The result is 8, because dividing by a fraction is the same as multiplying by its reciprocal: \( 2 \times \frac{8}{2} = 8 \).

Front

What is the result of \( \frac{6}{9} \div \frac{8}{9} \)?

Back

The result is \( \frac{3}{4} \) after simplifying the fraction.