Lesson 5: Multiplying Mixed Numbers

Property

To convert a mixed number $A\frac{b}{c}$ to an improper fraction, use the formula:

Examples

• $2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}$
• $5\frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{23}{4}$

Explanation

A mixed number consists of a whole number and a fraction. To convert it to an improper fraction, first multiply the whole number part by the fraction''s denominator. Next, add the numerator to this product to get the new numerator. The denominator of the improper fraction remains the same as the original fraction''s denominator.

Property

To multiply mixed numbers, follow these steps:

1. Convert: Change each mixed number into an improper fraction using the formula $a\frac{b}{c} = \frac{(a \times c) + b}{c}$.
2. Multiply: Multiply the numerators, and multiply the denominators.
3. Simplify: Simplify the resulting fraction and convert it back to a mixed number if needed.

Examples