Multiplying Mixed Numbers
Multiplying mixed numbers in Grade 6 Saxon Math Course 1 requires converting every mixed number to an improper fraction first: multiply whole number by denominator, add numerator, keep denominator. Then multiply numerators and denominators separately and simplify. For 1¾ × 2½: convert to 7/4 × 5/2 = 35/8 = 4⅜. Trying to multiply whole and fractional parts separately is a common misconception that always produces wrong results.
Key Concepts
Property To multiply mixed numbers, you must first convert each mixed number into an improper fraction. After converting, multiply the numerators together and the denominators together.
Examples $1\frac{2}{3} \times 2\frac{2}{5} = \frac{5}{3} \times \frac{12}{5} = \frac{60}{15} = 4$ $1\frac{1}{2} \times 2\frac{1}{3} = \frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = \frac{7}{2}$ $2\frac{1}{4} \times 1\frac{1}{5} = \frac{9}{4} \times \frac{6}{5} = \frac{54}{20} = \frac{27}{10}$.
Explanation Multiplying mixed numbers is a two step dance! First, you must change your partners by converting each mixed number into its improper fraction costume. Only then can they dance. Multiply the numerators together and the denominators together. Trying to multiply them before they change costumes will lead to a dance disaster and a completely wrong answer!
Common Questions
How do you convert a mixed number to an improper fraction?
Multiply whole number × denominator + numerator over the same denominator. Example: 2¾ = (2×4+3)/4 = 11/4.
Calculate 1¾ × 2½.
7/4 × 5/2 = 35/8 = 4⅜.
Can you multiply whole parts and fraction parts separately?
No — this is incorrect. You must first convert all mixed numbers to improper fractions before multiplying.
What is 3 × 2⅓?
Convert 2⅓ = 7/3. Multiply: 3/1 × 7/3 = 21/3 = 7.
How do you simplify 35/8?
35 ÷ 8 = 4 remainder 3, so 35/8 = 4⅜. Alternatively check if GCF(35,8)=1; since it does, it is already in lowest terms as an improper fraction.