Multiplying Mixed Numbers
Multiplying mixed numbers requires converting each mixed number to an improper fraction first, then multiplying numerators together and denominators together. For 2 and 1/2 times 1 and 1/3: convert to 5/2 and 4/3, then multiply: (5 times 4) over (2 times 3) = 20/6 = 3 and 1/3. This Grade 7 math skill from Saxon Math, Course 2 avoids the common error of multiplying whole and fractional parts separately (which gives the wrong answer due to missing cross terms) and reinforces that converting to improper fractions is the reliable method for all mixed number multiplication.
Key Concepts
Property To multiply mixed numbers, first convert them into improper fractions.
Examples $3\frac{2}{3} \times 1\frac{1}{2} = \frac{11}{3} \times \frac{3}{2} = \frac{11}{2} = 5\frac{1}{2}$ $3 \times 2\frac{1}{2} = \frac{3}{1} \times \frac{5}{2} = \frac{15}{2} = 7\frac{1}{2}$.
Explanation Don't multiply the whole numbers and fractions separately! That's a trap. First, transform each mixed number into a top heavy improper fraction. This combines everything into a simple format. Now, you just multiply the numerators and multiply the denominators to find your answer. It is the best method.
Common Questions
How do I multiply mixed numbers?
Convert each mixed number to an improper fraction, then multiply numerators together and denominators together. For 1 and 1/2 times 2 and 2/3: convert to 3/2 and 8/3, multiply to get 24/6 = 4.
Why do I need to convert to improper fractions first?
Multiplying whole and fractional parts separately misses the cross-multiplication terms. For example, (2 + 1/2) times (1 + 1/3) needs all four products: 2x1, 2x1/3, 1/2x1, and 1/2x1/3. Converting to improper fractions handles this automatically.
Can I simplify before multiplying to make the numbers smaller?
Yes. Cross-cancel before multiplying: if any numerator and any denominator share a common factor, divide both by that factor first. This reduces the numbers and simplifies the final answer.
What is 2 and 1/4 times 1 and 1/3?
Convert: 2 and 1/4 = 9/4 and 1 and 1/3 = 4/3. Multiply: (9 times 4) over (4 times 3) = 36/12 = 3.
When do students learn to multiply mixed numbers?
Mixed number multiplication is typically introduced in Grade 5-6 and mastered in Grade 7. Saxon Math, Course 2 covers it in Chapter 7.
What are common mistakes when multiplying mixed numbers?
The most common mistake is multiplying without converting — for example, treating 2 and 1/2 as 2 times 1/2. Always convert to improper fractions before applying any multiplication.
How does multiplying mixed numbers connect to real-world problems?
Scaling recipes (2 and 1/2 times a recipe that calls for 1 and 1/3 cups of flour), calculating areas with fractional dimensions, and scaling diagrams all require multiplying mixed numbers.