Divide Unit Fractions and Whole Numbers

Grade 5 Math – Notes & Formulae

Divide Unit Fractions by Whole Numbers

• The unit fraction (\(\frac{1}{b}\)) is divided into n groups.
• Formula: \( \frac{1}{b} \div n = \frac{1}{b \times n} \)
• Example: \( \frac{1}{5} \div 2 = \frac{1}{10} \)
• Use area models or number lines to show how the denominator increases (smaller pieces).

Divide Whole Numbers by Unit Fractions

• How many of the unit fraction fit into the whole number?
• Formula: \( n \div \frac{1}{b} = n \times b \)
• Example: \( 4 \div \frac{1}{6} = 24 \)
• The answer gets bigger because breaking into smaller parts increases the count.
• Use repeated grouping or area/array models for support.

General Division: Unit Fractions & Whole Numbers

• Whichever comes first (unit fraction/whole), use the matching formula above.
• Word problems: "How much is each share?" or "How many shares can you make?"
• Draw diagrams, number line, or set up repeated addition/subtraction for clarity.

Word Problems: Dividing Unit Fractions & Whole Numbers

• Read carefully to see if you need to divide the fraction or the whole.
• Choose which formula fits (see above).
• Always label your answer and check that the result fits your context.

Quick Reference

• \(\frac{1}{b} \div n = \frac{1}{b \times n}\) → gets smaller.
• \( n \div \frac{1}{b} = n \times b \) → gets larger.
• Model with area, number line, or group diagrams.
• Word problems: clarify which is being shared and which is the divisor.