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Grade 5 (age 10-11)

grade 5 Decimal Multiplication & Division

Decimal Multiplication & Division

Multiplying decimals means multiplying as if the numbers were whole and then placing the point by the sum of the decimal places. A rectangle 1.5 meters by 1.2 meters has area 1.80 m², and 1.80 is the same as 1.8; 0.3 times 0.4 is 0.12, which is also 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 and the area model, the number line, and the length bars build each step.

Decimal Multiplication

📐 Decimal multiplication = finding area
①A 1.5 m by 1.2 m rectangle has area 1.80 m². 1.80 is the same as 1.8
②1.5 × 1.2 = 1.80 (place the point by the total decimals)
③The area model shows the product at once
🔢 What the slider shows
The slider already shows the decimal: 15 means 1.5.
1.5
1.2

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!
2.4
0.6

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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Fraction Multiplication & Division
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Mixed Number Operations