Understand Fraction Multiplication

Grade 5 Math – Short Notes & Formulae

Multiply Fractions by Whole Numbers

• Multiply the numerator by the whole number, keep the denominator the same.
• Formula: \( n \times \frac{a}{b} = \frac{n \times a}{b} \)
• Example: \( 4 \times \frac{2}{5} = \frac{8}{5} = 1\frac{3}{5} \)
• Model: Use number lines, arrays, or diagrams to visualize repeated groups.

Fractions of a Number

• Find \(\frac{a}{b}\) of n: Divide n by denominator, then multiply by numerator.
• Formula: \( \frac{a}{b} \text{ of } n = \frac{a \times n}{b} \)
• Example: \(\frac{3}{4}\) of 20 = \( \frac{3\times 20}{4} = 15 \)
• Visual: Shade parts of shapes/arrays or use division, then multiplication.

Multiply Fractions Using Models

• Area/array model: Partition a rectangle for two fractions, overlap shows product.
• Number line: Partition segments and show jumps or repeated addition.
• Model can help visualize the meaning of fraction multiplication.
• Example using array/area: \(\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}\) (shaded overlap out of 6 parts).

Multiply Two Fractions

• Multiply the numerators together, multiply denominators together.
• Formula: \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \)
• Example: \( \frac{3}{5} \times \frac{2}{7} = \frac{6}{35} \)

Multiply Fractions Greater Than One

• If given a mixed number, convert to improper fraction first.
• Multiply as you would with regular fractions.
• Example: \(1\frac{2}{3} \times \frac{3}{4} = \frac{5}{3} \times \frac{3}{4} = \frac{15}{12} = 1\frac{3}{12} = 1\frac{1}{4}\)

Multiples of Fractions & Missing Numbers

• Find products by multiplying fractions repeatedly (e.g. 2 × \(\frac{4}{7}\) = \(\frac{8}{7}\)).
• Find the value that matches a missing product by writing an equation and solving for the unknown.
• Use models to show pattern of repeated addition or multiplication of fractions.

Quick Reference

• Multiply fractions by whole numbers: numerator × whole, denominator stays.
• Multiply fractions: numerator × numerator, denominator × denominator.
• Simplify results when possible.
• Use area models or number lines for understanding and visualization.
• Convert mixed numbers to improper fractions before multiplying.
• Fraction of a number: multiply numerator, then divide by denominator.