Fractions — Division

Fraction division asks 'how many?' 1/2 ÷ 1/4 = 2: how many quarters fit in a half? Two. The keep-change-flip rule is magical at first, then obvious. Indirect aim: algebraic reasoning, reciprocals, preparation for rational equations.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Fractions
• Level: Ages 8-10

Objectives

• Understand 'how many of a fraction fit in another'
• Use the keep-change-flip rule
• Justify the rule via multiplication
• Apply to real problems

Materials

• Fraction Insets
• Problem slips
• Control chart
• Worked examples

Instructions

1. Write: 1/2 ÷ 1/4. 2. Ask: how many 1/4 pieces fit in 1/2? 3. Fill 1/2 with 1/4 pieces: 2 fit. 4. So 1/2 ÷ 1/4 = 2. 5. Rule: keep first, change ÷ to ×, flip second. 1/2 × 4/1 = 4/2 = 2. 6. Why? Because dividing by a fraction = multiplying by its reciprocal. 7. Compute 2/3 ÷ 1/6 = 2/3 × 6 = 12/3 = 4. 8. Verify with insets.

Educator tip

The 'how many fit' interpretation anchors the rule. Without it, keep-change-flip feels like magic.

Assessment

Observe rule application, verification with insets, and extension to complex cases.

More from Mathematics

• Decimal Multiplication
• Decimal Division
• Perimeter — Various Polygons
• Angles and Protractor Use
• Ratio and Proportion
• Integer Operations — Signed Number Arithmetic
• Word Problems — Distance, Rate, Time
• Geometry Chart 1 — Basic Figures