Grade 6 (age 11-12)

Decimal Division

Decimal division gets easy once the divisor is a whole number. Dividing 2.4 by 0.6, multiply both by 10 to get 24 divided by 6; the shifted decimal keeps the answer. It is like cutting a 2.4 meter ribbon into 0.6 meter pieces and counting. Here you hop along a number line and sliders count the jumps.

Principle of Decimal Division

📏 Shift Decimal → Whole Number!

①2.4 ÷ 0.6 is hard directly

②×10 both sides → 24 ÷ 6 = 4

③Same shift on both sides keeps the answer!

Check on a Number Line

Dividend (×0.1)24

Divisor (×0.1)6

💡 2.4 contains 0.6 4.00 times

①Jumps of 0.6 on the line

②4 full jumps

③Answer is 4.00

Summary

Key Strategy

Make the divisor a whole number, then divide!

Decimal divisor → shift decimal points equally to the right

Check

Quotient × Divisor = Dividend

Multiply back to verify

🎯 Key Points

①Shift decimals until divisor is whole

②Then do whole-number division

③Watch the decimal place in the quotient

④Decimal divisor can give a quotient larger than the dividend

⑤Always check by multiplying back!

Examples & Unit Review

Example 1

Calculate 7.5 ÷ 0.5.

Multiply both numbers by 10 so the divisor becomes a whole number: 7.5 ÷ 0.5 = 75 ÷ 5.

75 ÷ 5 = 15.

▸ 15

Multiplying dividend and divisor by the same number keeps the quotient unchanged.

Example 2

Calculate 4.8 ÷ 0.12.

Multiply both by 100 to clear two decimal places: 4.8 ÷ 0.12 = 480 ÷ 12.

480 ÷ 12 = 40.

▸ 40

Multiply by 10, 100, or 1000 to match the number with more decimal places.

Unit Review

What is 9.6 ÷ 0.8?

①12

②1.2

③120

④8.8

▸ ① 12

Multiply both numbers by 10: 9.6 ÷ 0.8 = 96 ÷ 8.

96 ÷ 8 = 12.

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Fraction Division

Ratio & Rate