Dividing with Fractions and Mixed Numbers
Dividing with fractions and mixed numbers is a Grade 8 math skill from Yoshiwara Core Math (Chapter 4: Calculation). To divide by a fraction, multiply by its reciprocal — dividing by 2/3 becomes multiplying by 3/2. When mixed numbers are involved, first convert them to improper fractions, then apply the rule. For instance, 4½ ÷ ¾ becomes (9/2) × (4/3) = 6 mph. This skill appears in real-world speed, cutting, and portioning problems throughout Grade 8 math.
Key Concepts
Property To divide a number by a fraction, multiply the number by the reciprocal of the fraction. For example, to divide by $\frac{2}{3}$, you multiply by its reciprocal, $\frac{3}{2}$.
First, convert any mixed numbers to improper fractions. Then, apply the rule: $$ a \div \frac{b}{c} = a \times \frac{c}{b} $$.
Examples How many $\frac{3}{4}$ foot lengths of rope can be cut from a 6 foot rope? We calculate $6 \div \frac{3}{4} = 6 \times \frac{4}{3} = \frac{24}{3} = 8$ lengths.
Common Questions
How do you divide a whole number by a fraction?
Multiply the whole number by the reciprocal of the fraction. For example, 6 ÷ (3/4) = 6 × (4/3) = 8.
What is the reciprocal of a fraction?
The reciprocal of a fraction flips numerator and denominator. The reciprocal of 2/3 is 3/2.
How do you divide mixed numbers?
Convert each mixed number to an improper fraction first, then multiply by the reciprocal of the divisor.
Why do you multiply by the reciprocal when dividing fractions?
Multiplying by the reciprocal is mathematically equivalent to division — it is the multiplicative inverse.
How do you find speed when dividing distance by a fractional time?
Convert mixed numbers to improper fractions then divide. For example, 4½ miles in ¾ hour: (9/2) ÷ (3/4) = 6 mph.