Lesson 3: Dividing Mixed Numbers

Property

To divide a mixed number by a fraction, first convert the mixed number to an improper fraction. Then, multiply the improper fraction by the reciprocal of the divisor.

Examples

• $3 \frac{1}{2} \div \frac{1}{4} = \frac{7}{2} \div \frac{1}{4} = \frac{7}{2} \times \frac{4}{1} = \frac{28}{2} = 14$
• $2 \frac{2}{5} \div \frac{3}{4} = \frac{12}{5} \div \frac{3}{4} = \frac{12}{5} \times \frac{4}{3} = \frac{48}{15} = \frac{16}{5} = 3 \frac{1}{5}$

Explanation

This process combines your knowledge of mixed numbers and fraction division. The first step is always to convert the mixed number dividend into an improper fraction. Once you have two fractions, you apply the rule for division by multiplying by the reciprocal of the second fraction. Finally, simplify your answer and convert it back into a mixed number if it is an improper fraction.

Property

To divide mixed numbers:
(1) Convert each mixed number to an improper fraction using $a\frac{b}{c} = \frac{ac + b}{c}$;
(2) multiply by the reciprocal of the divisor: $\frac{p}{q} \div \frac{r}{s} = \frac{p}{q} \times \frac{s}{r}$;
(3) simplify the result;
(4) convert back to mixed number form if the result is an improper fraction.

Examples

Property

When evaluating expressions with multiple operations, follow the order of operations (PEMDAS). Before calculating, convert all mixed numbers to improper fractions.

1. Parentheses
2. Exponents
3. Multiplication and Division (from left to right)
4. Addition and Subtraction (from left to right)

Property

Solve real-world and mathematical problems involving division of fractions. This requires translating a real-world scenario into a mathematical expression using division of rational numbers, then applying the rule: divide by a fraction by multiplying by its reciprocal.

Examples