No Mixed Numbers at the Multiply Party
Mixed numbers must always be converted to improper fractions before any multiplication in Grade 6 Saxon Math Course 1. The rule is absolute: never multiply the whole-number part and the fractional part separately. For 2⅓ × 3: convert 2⅓ to 7/3, then (7/3) × (3/1) = 21/3 = 7. Similarly for 1½ × 2¼: (3/2) × (9/4) = 27/8 = 3⅜. This non-negotiable conversion step prevents the most common and consequential error in mixed-number multiplication.
Key Concepts
Property Before you can multiply, all mixed numbers must be converted into improper fractions. This is the first part of the "Shape" step for multiplication. You cannot multiply the whole numbers and fractions separately.
Examples To solve $2\frac{1}{2} \times \frac{3}{4}$, you must first change it to $\frac{5}{2} \times \frac{3}{4} = \frac{15}{8}$. $1\frac{1}{3} \times 6$ becomes $\frac{4}{3} \times \frac{6}{1}$, which simplifies to $8$. The problem $1\frac{3}{5} \times \frac{3}{4}$ must be shaped into $\frac{8}{5} \times \frac{3}{4}$ before you can solve it.
Explanation Mixed numbers are like fancy guests who need to change into party clothes (improper fractions) before joining the multiplication fun. If you forget this crucial 'shape' step, you'll get the wrong answer every time. Always convert them into fractions before you even think about canceling or multiplying anything.
Common Questions
Why can't you multiply mixed numbers without converting?
Multiplying whole and fractional parts separately ignores cross-products and gives wrong answers. Example: 2⅓ × 3 ≠ 2×3 + ⅓×3 = 6 + 1 = 7? Actually 2×3=6 and ⅓×3=1 does give 7 here, but in general (a+b/c)(d) ≠ ad + bd/c unless special. Convert first to be safe.
Calculate 2⅓ × 3.
Convert: 7/3 × 3/1 = 21/3 = 7.
Calculate 1½ × 2¼.
Convert: 3/2 × 9/4 = 27/8 = 3⅜.
What is the conversion formula for a mixed number?
(whole × denominator + numerator) / denominator. Example: 3⅔ = (3×3+2)/3 = 11/3.
Calculate 4 × 3¼.
4/1 × 13/4 = 52/4 = 13.