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 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 the result over the original denominator. For example, \( 3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \).

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. For example, \( 6 \div \frac{1}{2} = 6 \times 2 = 12 \).

Front

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

Back

Dividing a fraction by a whole number involves multiplying the denominator of the fraction by that whole number. For example, \( \frac{1}{2} \div 5 = \frac{1}{2 \times 5} = \frac{1}{10} \).

Front

What is the division of \( \frac{7}{10} \div \frac{1}{5} \)?

Back

The division of \( \frac{7}{10} \div \frac{1}{5} \) is calculated as \( \frac{7}{10} \times 5 = \frac{35}{10} = 3 \frac{1}{2} \).

Front

How do you simplify the fraction \( \frac{35}{10} \)?

Back

To simplify \( \frac{35}{10} \), divide both the numerator and the denominator by their greatest common divisor, which is 5. Thus, \( \frac{35 \div 5}{10 \div 5} = \frac{7}{2} \) or \( 3 \frac{1}{2} \).

Front

What is the relationship between division and multiplication in fractions?

Back

Division of fractions can be transformed into multiplication by using the reciprocal. For example, \( a \div b = a \times \frac{1}{b} \).

Front

What is the result of \( 3 \div \frac{1}{6} \)?

Back

The result of \( 3 \div \frac{1}{6} \) is \( 3 \times 6 = 18 \).

Front

What is the result of \( 8 \div \frac{1}{3} \)?

Back

The result of \( 8 \div \frac{1}{3} \) is \( 8 \times 3 = 24 \).