Lesson 6: Divide Mixed Numbers

Property

To divide a mixed number by a mixed number, first convert both to improper fractions. Then, multiply the first fraction by the reciprocal of the second fraction.

Examples

• $3\frac{1}{2} \div 1\frac{1}{4} = \frac{7}{2} \div \frac{5}{4} = \frac{7}{2} \times \frac{4}{5} = \frac{28}{10} = \frac{14}{5} = 2\frac{4}{5}$
• $5\frac{1}{3} \div 2\frac{2}{3} = \frac{16}{3} \div \frac{8}{3} = \frac{16}{3} \times \frac{3}{8} = \frac{48}{24} = 2$

Explanation

This process combines two key steps for dividing fractions. First, you must rewrite both mixed numbers as improper fractions. Then, apply the rule for dividing fractions, which is to multiply the dividend by the reciprocal of the divisor. Finally, simplify your result and convert it back to a mixed number or whole number if needed.

Property

To divide a whole number by a mixed number, write the whole number as a fraction with a denominator of 1 and the mixed number as an improper fraction. Then, multiply by the reciprocal of the improper fraction.

Examples

• $6 \div 1\frac{1}{2} = \frac{6}{1} \div \frac{3}{2} = \frac{6}{1} \times \frac{2}{3} = \frac{12}{3} = 4$
• $5 \div 2\frac{1}{4} = \frac{5}{1} \div \frac{9}{4} = \frac{5}{1} \times \frac{4}{9} = \frac{20}{9} = 2\frac{2}{9}$

Explanation

This skill combines two key concepts from the lesson. First, convert the whole number into a fraction by placing it over 1. Second, convert the mixed number divisor into an improper fraction. Once both numbers are in fraction form, you can perform the division by multiplying the first fraction by the reciprocal of the second. The final answer can be simplified or converted back to a mixed number if necessary.

Property

To divide a mixed number by a whole number, convert the mixed number to an improper fraction and write the whole number as a fraction with a denominator of 1. Then, multiply by the reciprocal of the whole number.

Examples

• $2\frac{1}{2} \div 5 = \frac{5}{2} \div \frac{5}{1} = \frac{5}{2} \times \frac{1}{5} = \frac{5}{10} = \frac{1}{2}$
• $3\frac{1}{3} \div 2 = \frac{10}{3} \div \frac{2}{1} = \frac{10}{3} \times \frac{1}{2} = \frac{10}{6} = \frac{5}{3} = 1\frac{2}{3}$

Explanation

To divide a mixed number by a whole number, you must first convert both numbers into fractional form. Change the mixed number into an improper fraction. Write the whole number as a fraction by placing it over a denominator of 1. Finally, multiply the first fraction by the reciprocal of the second fraction and simplify the result.