Multiply Fractions and Whole Numbers

Grade 5 Math – Complete Notes & Formulae

Multiplying Fractions by Whole Numbers

• Multiply numerator by whole number, denominator stays the same.
• Formula: \( n \times \frac{a}{b} = \frac{n \times a}{b} \)
• Example: \( 5 \times \frac{2}{3} = \frac{10}{3} = 3\frac{1}{3} \)
• If the product is improper, convert to a mixed number.
• Use models or diagrams for visual understanding.

Find Fractions of a Number

• A fraction “of” a number means: multiply, then divide.
• Formula: \( \frac{a}{b} \text{ of } n = \frac{a \times n}{b} \)
• Example: \(\frac{3}{4} \text{ of } 20 = \frac{3\times 20}{4} = 15\)
• Word problems: “What is \(\frac{2}{5}\) of 30?” → \( \frac{2\times 30}{5} = 12 \)

Word Problems & Sorting

• Identify the key phrase “of” or “groups of” to multiply.
• Check if product is greater/less than a whole number for sorting tasks.
• For multi-step word problems, multiply, then interpret result (mixed number, simplification).

Multiples of Fractions

• To find the nth multiple of a fraction, multiply numerator by n.
• Formula: nth multiple of \(\frac{a}{b}\): \( \frac{n \times a}{b} \)
• Example: 4th multiple of \(\frac{1}{6}\): \( 4 \times \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \)

Quick Reference

• Multiply: numerator by whole number, denominator stays the same.
• Fraction of a number: multiply, then divide by denominator.
• Simplify product if possible & convert to mixed number if needed.
• Visuals (area/length diagrams) help reinforce meaning!
• “Of” in questions means multiplication.