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Grade 5 (age 10-11)

Decimal Multiplication & Division

Decimal Multiplication & Division

Multiplying decimals means multiplying as if the numbers were whole and then adding the decimal places to position the point, so 0.3 times 0.4 is 0.12, which is really an area. Dividing shifts both points equally into a whole-number division, just as a 2.4 meter ribbon cut into 0.6 meter pieces gives 4. Slide the two numbers to watch the area model, number line, and length bars build each step.

Decimal Multiplication
📐 Decimal multiplication = finding area
①What is the area of a rectangle 1.5m × 1.2m?
②1.5 × 1.2 = 1.80 (digits after the point add up!)
③The area model shows the answer instantly!
15
12
Decimal Division
✂️ Decimal division = how many groups fit
①Cut a 2.4m ribbon into 0.6m pieces → 4 pieces
②Shift the decimal to make whole-number division
③24 ÷ 6 = 4 and 2.4 ÷ 0.6 = 4 give the same answer!
24
6
Summary
Decimal Point Rule (Mul)
Total decimals after the point = decimals in result
0.3 × 0.4 = 0.12 (1+1 = 2 digits)
Key Idea (Div)
Shift decimals equally → whole-number division
2.4 ÷ 0.6 → 24 ÷ 6 = 4
🎯 Key Points
①Multiply like whole numbers, then place the decimal
②Division: make divisor a whole number
③Multiplying by < 1 may make result smaller
④Dividing by < 1 may make result larger
⑤Practice converting decimals ↔ fractions!
Examples and Unit Test
Example 1
Calculate 0.3 × 0.4.
1
Ignore the decimal points and multiply like whole numbers: 3 × 4 = 12.
2
Place the point by the total decimals (1+1=2): 0.12.
▸ 0.12
Decimals in the product = sum of decimals in the two factors.
Example 2
Calculate 2.4 ÷ 0.6.
1
Shift the point one place to make the divisor a whole number: 24 ÷ 6.
2
24 ÷ 6 = 4. (Shifting both points equally keeps the answer the same.)
▸ 4
For division, shift both decimal points equally to make a whole-number division.
Unit Test
What is the value of 1.5 × 1.2?
①1.7
②1.8
③18
④0.18
▸ ② 1.8
1
First compute 15 × 12 = 180.
2
Total decimals is 2, so 1.80, which is 1.8.
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Mixed Number Add/Sub
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Congruence & Symmetry