Understand Fraction Division

Grade 5 Math – Notes & Formulae

Relate Division and Fractions

• Every fraction can be seen as a division: \(\frac{a}{b}\) means "a divided by b".
• Formula: \( a \div b = \frac{a}{b} \)
• Example: \( 5 \div 8 = \frac{5}{8} \)
• Word problems: "7 pizzas for 4 kids" → \( \frac{7}{4} = 1.75 \) pizzas each

Divide Unit Fractions by Whole Numbers

• Split a unit fraction (like \(\frac{1}{b}\)) into n equal groups.
• Formula: \( \frac{1}{b} \div n = \frac{1}{b \times n} \)
• Example: \( \frac{1}{4} \div 3 = \frac{1}{12} \)
• Model: Partition a picture into more pieces (area, number line).

Divide Whole Numbers by Unit Fractions

• How many times does \(\frac{1}{b}\) fit into a whole number?
• Formula: \( n \div \frac{1}{b} = n \times b \)
• Example: \( 5 \div \frac{1}{2} = 10 \)
• Model: Area diagrams and number lines show repeated grouping.

Divide Fractions by Fractions

• Dividing fractions: multiply by reciprocal.
• Formula: \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \)
• Example: \( \frac{3}{4} \div \frac{2}{3} = \frac{3}{4} \times \frac{3}{2} = \frac{9}{8} = 1\frac{1}{8} \)
• Area models help visualize the meaning of "groups of" a fraction.

Models & Number Lines for Fraction Division

• Draw area models or use a number line to show equal partitioning or repeated grouping.
• Use for unit fractions, whole numbers, or general fractions.
• Visuals help justify and check work for all division cases!

Quick Reference

• Fractions are division: \( a \div b = \frac{a}{b} \)
• Unit fractions divided by whole: denominator × whole for new denominator.
• Whole divided by unit: multiply whole × denominator.
• Fraction ÷ fraction: multiply by reciprocal.
• Draw models for clear understanding.