Multiplying with Mixed Numbers
Multiplying mixed numbers requires converting each mixed number to an improper fraction first, then multiplying numerators together and denominators together, and finally simplifying the result to a mixed number in lowest terms. In Grade 6 Saxon Math Course 1 (Chapter 7: Fractions and Geometric Concepts), students follow three steps: convert to improper fractions, cancel common factors if possible, then multiply. For 1 and 2/3 times 2 and 1/4: convert to 5/3 and 9/4; cancel (5 and 9 share no common factors; 3 and 9 share factor 3, giving 5/1 times 3/4 = 15/4 = 3 and 3/4).
Key Concepts
Property To multiply mixed numbers, first convert them into improper fractions. Then, you can cancel common factors and multiply.
Examples Example 1: $$2\frac{1}{2} \times 1\frac{3}{5} = \frac{5}{2} \times \frac{8}{5} = \frac{\stackrel{1}{\cancel{5}}}{\underset{1}{\cancel{2}}} \times \frac{\stackrel{4}{\cancel{8}}}{\cancel{5} 1} = \frac{4}{1} = 4$$ Example 2: $$3\frac{1}{3} \times \frac{9}{10} = \frac{10}{3} \times \frac{9}{10} = \frac{\stackrel{1}{\cancel{10}}}{\underset{1}{\cancel{3}}} \times \frac{\stackrel{3}{\cancel{9}}}{\cancel{10} 1} = \frac{3}{1} = 3$$ Example 3: $$1\frac{1}{4} \times 2\frac{2}{3} = \frac{5}{4} \times \frac{8}{3} = \frac{5}{\underset{1}{\cancel{4}}} \times \frac{\stackrel{2}{\cancel{8}}}{3} = \frac{10}{3} = 3\frac{1}{3}$$.
Explanation Mixed numbers are like party crashers in multiplication—they don't follow the rules! To handle them, you must first convert them into improper fractions. Once they're in the right format, they can join the canceling party with everyone else. It's the secret password to solving these problems easily, so don’t forget this important first step.
Common Questions
What are the steps for multiplying mixed numbers?
1. Convert each mixed number to an improper fraction. 2. Cancel common factors if possible. 3. Multiply numerators and denominators. 4. Simplify the result to a mixed number.
Convert 2 and 3/5 to an improper fraction.
(2 x 5) + 3 = 13. Result: 13/5.
Multiply 1 and 1/2 times 2 and 2/3.
Convert: 3/2 x 8/3. Cancel 3s: 1/2 x 8/1. Multiply: 8/2 = 4.
Why must you convert mixed numbers to improper fractions before multiplying?
The multiplication algorithm works only on fractions in numerator-over-denominator form. Attempting to multiply mixed numbers directly gives incorrect results.
Multiply 2 and 1/4 times 1 and 1/3.
Convert: 9/4 x 4/3. Cancel 4s: 9/1 x 1/3 = 9/3 = 3.