Multiply Fractions

Grade 5 Math – Notes & Formulae

Multiplying Two Fractions

• Multiply numerators together, multiply denominators together.
• Formula: \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \)
• Example: \( \frac{2}{3} \times \frac{5}{7} = \frac{10}{21} \)
• Simplify fraction if possible after multiplying.

Word Problems & Applications

• Recognize when to multiply fractions (e.g., “part of a part,” “area of fraction”).
• Example: If \(\frac{3}{4}\) of a cake is left, and you eat \(\frac{2}{3}\) of what is left:
  \(\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}\) of whole cake.

Multiply Three Fractions and Whole Numbers

• Multiply all numerators together, all denominators together.
• Example: \(2 \times \frac{3}{4} \times \frac{1}{5} = \frac{2 \times 3 \times 1}{1 \times 4 \times 5} = \frac{6}{20} = \frac{3}{10}\)
• Simplify your answer if possible.
• Can use models or repeated multiplication approach.

Complete Fraction Multiplication Sentences

• Fill missing number by using inverse operation or setting up equation.
• Example: \( ? \times \frac{2}{7} = \frac{10}{21} \)
  Solve: \( ? = \frac{5}{3} \)

Multiplication and Area of Fractions

• Area of a rectangle with fraction lengths:
  Area = Length × Width
• Example: Length = \(\frac{2}{3}\)m, Width = \(\frac{1}{2}\)m
  Area = \( \frac{2}{3} \times \frac{1}{2} = \frac{2}{6} = \frac{1}{3} \)m²
• Area/Array models visually show fraction multiplication.

Quick Reference

• Multiply fractions: numerator × numerator, denominator × denominator.
• Simplify answers if possible.
• Use models/area for interpretation.
• Three fractions: multiply all numerators, all denominators, then simplify.
• Multiplication applies to area, probability, and “part of a part.”