Multiplying Mixed Numbers
Multiplying mixed numbers requires converting all mixed numbers and whole numbers to improper fractions before multiplying numerators and denominators separately. In Grade 6 Saxon Math Course 1, a b/c × d = (ac+b)/c × d/1. For 3¼ × 2⅔: convert to 13/4 × 8/3 = 104/12 = 26/3 = 8⅔. The property also applies when one factor is a whole number: 4 × 2½ = 4/1 × 5/2 = 20/2 = 10. Always convert first — multiplying whole and fractional parts separately produces incorrect results.
Key Concepts
Property To multiply mixed numbers, you must first write the mixed numbers and whole numbers as improper fractions. Then, multiply the numerators together and the denominators together. $$a\frac{b}{c} \times d = \frac{ac+b}{c} \times \frac{d}{1}$$.
Examples $2\frac{2}{3} \times 4 = \frac{8}{3} \times \frac{4}{1} = \frac{32}{3} = 10\frac{2}{3}$ $2\frac{1}{2} \times 1\frac{1}{3} = \frac{5}{2} \times \frac{4}{3} = \frac{20}{6} = 3\frac{1}{3}$ $3\frac{1}{2} \times 1\frac{2}{3} = \frac{7}{2} \times \frac{5}{3} = \frac{35}{6} = 5\frac{5}{6}$.
Explanation Never multiply the whole numbers and fractions separately—it's a trap! Think of it like a recipe: you can't just throw ingredients next to each other. You must prepare them first by converting everything into improper fractions. This blends all the parts together correctly, ensuring you get the delicious, accurate final product every single time.
Common Questions
What is the first step in multiplying mixed numbers?
Convert every mixed number (and whole number) to an improper fraction before multiplying.
Calculate 3¼ × 2⅔.
13/4 × 8/3 = 104/12 = 26/3 = 8⅔.
Calculate 4 × 2½.
4/1 × 5/2 = 20/2 = 10.
What is the formula to convert a mixed number?
(Whole × Denominator + Numerator) / Denominator. Example: 3¼ = (3×4+1)/4 = 13/4.
How do you verify your answer after multiplying mixed numbers?
Estimate: 3¼ is about 3 and 2⅔ is about 3, so the product should be near 9. The exact answer 8⅔ is close, confirming it is reasonable.