Decimal Division

To divide by a decimal, multiply both by 10 until the divisor is whole. 1.5 ÷ 0.3 becomes 15 ÷ 3 = 5. Indirect aim: algebraic manipulation, preparation for rational expressions.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Decimal Fractions
• Level: Ages 9-11

Objectives

• Divide decimals: move decimal point in divisor to make integer
• Move point equally in dividend
• Execute long division
• Verify with multiplication

Materials

• Racks and Tubes with decimal extension
• Long division worksheet
• Calculator for verification
• Money for real problems

Instructions

1. Write 1.5 ÷ 0.3. 2. Multiply both by 10: 15 ÷ 3 = 5. 3. Verify: 0.3 × 5 = 1.5. 4. Write 2.4 ÷ 0.06. 5. Multiply both by 100: 240 ÷ 6 = 40. 6. Verify. 7. Long division with decimals: place decimal in quotient directly above dividend's. 8. Apply: $24 ÷ $0.50/item = 48 items.

Educator tip

The move-both-decimals trick is a consequence of the identity a/b = (10a)/(10b). Show that connection.

Assessment

Observe correct decimal movement, accurate division, verification.

More from Mathematics

• 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
• Congruence and Similarity
• Geometric Symmetry — Reflection, Rotation, Translation