Multiply Mixed Numbers

Grade 5 Math – Complete Notes & Formulae

Estimate Products of Mixed Numbers

• Round each mixed number to nearest whole (ignore fraction part for a fast estimate).
• Example: \( 2\frac{3}{5} \times 1\frac{1}{4} \approx 3 \times 1 = 3 \)
• Use benchmarks: If fraction part is close to 1, round up further.

Multiply Mixed Numbers × Whole Numbers

• Convert mixed number to improper fraction:
• Formula: \( w\frac{a}{b} = \frac{w \times b + a}{b} \)
• Then multiply by whole number:
• Formula: \( n \times \frac{x}{y} = \frac{n \times x}{y} \)
• Convert improper product to mixed number if needed.
• Example: \( 3\frac{2}{5} \times 4 = \frac{17}{5} \times 4 = \frac{68}{5} = 13\frac{3}{5} \)

Multiply Mixed Numbers × Fraction

• Convert mixed number to improper fraction.
• Multiply as with any two fractions:
• Formula: \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \)
• Convert to mixed number if needed.
• Example: \( 1\frac{2}{3} \times \frac{3}{4} = \frac{5}{3} \times \frac{3}{4} = \frac{15}{12} = 1\frac{3}{12} = 1\frac{1}{4} \)

Multiply Two Mixed Numbers

• Convert both to improper fractions.
• Multiply fractions using: numerator × numerator, denominator × denominator.
• Convert result to mixed number and simplify.
• Example: \( 1\frac{1}{2} \times 2\frac{1}{3} = \frac{3}{2} \times \frac{7}{3} = \frac{21}{6} = 3\frac{1}{2} \)

Multiply Mixed Numbers, Fractions, & Whole Numbers

• Convert all numbers to improper fractions as needed.
• Multiply all numerators together, all denominators together.
• Simplify and convert to mixed number if possible.
• Example: \( 2\frac{1}{2} \times \frac{4}{9} \times 3 = \frac{5}{2} \times \frac{4}{9} \times \frac{3}{1} = \frac{5 \times 4 \times 3}{2 \times 9 \times 1} = \frac{60}{18} = \frac{10}{3} = 3\frac{1}{3} \)

Area Models & Word Problems

• Draw an area/array showing the products of whole × whole, whole × fraction, fraction × whole, fraction × fraction.
• For recipes/multi-step: Always convert, multiply, and simplify stepwise for final answer!
• Always label your answer for word problems and check for reasonableness.

Quick Reference

• Estimate by rounding mixed numbers to whole numbers.
• Convert all mixed numbers to improper fractions before multiplying.
• Multiply numerators, multiply denominators, simplify.
• Convert the result to a mixed number and reduce fractions if possible.
• For multi-step: do each multiplication in order, labeling units and checking answer type.