Question

Divide and write your answer as a mixed number, if necessary. a. \(3 \frac{2}{7} \div 1 \frac{9}{14}\) b. \(-1 \frac{7}{8} \div \frac{3}{4}\) c. \(4 \frac{2}{9} \div 8 \frac{1}{3}\) d. \(\frac{-12 \frac{2}{3}}{-3 \frac{1}{6}}\)

Short answer

Question: Solve the following division problems involving mixed numbers and/or fractions: a. \(3 \frac{2}{7} \div 1 \frac{9}{14}\) b. \(-1 \frac{7}{8} \div \frac{3}{4}\) c. \(4 \frac{2}{9} \div 8 \frac{1}{3}\) d. \(\frac{-12 \frac{2}{3}}{-3 \frac{1}{6}}\) Answer: a. 2 b. -2 1/2 c. 1/12 d. 3

Step-by-step solution

Convert the mixed numbers to improper fractions.

To convert the mixed numbers into improper fractions, use the formula: \(\frac{(whole\ number \times denominator) + numerator}{denominator}\). So we get: \(3 \frac{2}{7} = \frac{(3 \times 7) + 2}{7} = \frac{23}{7}\) \(1 \frac{9}{14} = \frac{(1 \times 14) + 9}{14} = \frac{23}{14}\) Now the division looks like this: \(\frac{23}{7} \div \frac{23}{14}\)

Invert the second fraction.

We now find the reciprocal of the second fraction, which is \(\frac{14}{23}\).

Multiply the first fraction by the inverted second fraction.

Multiply \(\frac{23}{7}\) by \(\frac{14}{23}\): \(\frac{23}{7} \times \frac{14}{23} = \frac{23 \times 14}{7 \times 23}\)

Simplify the fraction.

The fraction simplifies to \(\frac{14}{7}\), as the 23's cancel out each other.

Convert the answer back to a mixed number, if necessary.

Since the result is a simple fraction, we can just divide: \(\frac{14}{7}=2\). So, the final answer is 2. b. \(-1 \frac{7}{8} \div \frac{3}{4}\)

Convert the mixed numbers to improper fractions.

Convert the mixed number to an improper fraction: \(-1 \frac{7}{8} = -\frac{(1 \times 8) + 7}{8} = -\frac{15}{8}\) Now the division looks like this: \(-\frac{15}{8} \div \frac{3}{4}\)

Invert the second fraction.

The reciprocal of the second fraction is \(\frac{4}{3}\).

Multiply the first fraction by the inverted second fraction.

Multiply \(-\frac{15}{8}\) by \(\frac{4}{3}\): \(-\frac{15}{8} \times \frac{4}{3} = -\frac{15 \times 4}{8 \times 3}\)

Simplify the fraction.

The fraction simplifies to \(-\frac{5}{2}\).

Convert the answer back to a mixed number, if necessary.

Convert the improper fraction to a mixed number: \(-\frac{5}{2}=-2\frac{1}{2}\). So, the final answer is -2 1/2. c. \(4 \frac{2}{9} \div 8 \frac{1}{3}\) Follow the same process from steps 1-5. The end result will be \(\frac{1}{12}\). d. \(\frac{-12 \frac{2}{3}}{-3 \frac{1}{6}}\) Follow the same process from steps 1-5. The end result will be 3.