MathBored

Essential Math Primer
← Back to Primer Overview
U07 • Lesson 25 of 105

Decimal Operations: Multiplication & Division

Extends multiplication and division to decimal numbers. Students explore why multiplying by decimals less than one produces a smaller product, use area models and place value reasoning to multiply decimals, and divide decimals by whole numbers, connecting quotient placement to place value understanding.

Upper Elementary • 3-5

Prerequisites: U02, U06

Key Concepts

  • multiplying decimals using place value and area models
  • placing the decimal point in products
  • dividing decimals by whole numbers
  • estimating to check decimal computation results

Decimal Operations: Multiplication and Division

Multiplying and dividing with decimals builds on what you know about whole-number multiplication and division. The new challenge is figuring out where the decimal point goes in the answer.

Multiplying Decimals

  1. Ignore the decimal points and multiply as if both numbers were whole numbers.
  2. Count the total number of decimal places in both factors.
  3. Place the decimal point in the product so it has that many decimal places.

Worked Example 1: Multiplying Decimals

Find 2.4 x 0.3.

  1. Multiply as whole numbers: 24 x 3 = 72.
  2. Count decimal places: 2.4 has 1 place, 0.3 has 1 place. Total: 2 places.
  3. Place the decimal: 72 becomes 0.72.
2.4 x 0.3 = 0.72

Important Insight

When you multiply by a decimal less than 1, the product is smaller than the other factor. This makes sense: 0.3 of something is less than the whole thing. So 2.4 x 0.3 = 0.72, which is less than 2.4.

Worked Example 2: Larger Decimal Multiplication

Find 3.15 x 4.2.

  1. Multiply as whole numbers: 315 x 42.
  2. 315 x 42: 315 x 2 = 630, and 315 x 40 = 12,600. Sum: 630 + 12,600 = 13,230.
  3. Count decimal places: 3.15 has 2 places, 4.2 has 1 place. Total: 3 places.
  4. Place the decimal: 13,230 becomes 13.230, which is 13.23.
3.15 x 4.2 = 13.23

Estimate check: 3 x 4 = 12. Our answer of 13.23 is close. Makes sense!

Dividing Decimals by Whole Numbers

Place the decimal point in the quotient directly above where it is in the dividend, then divide normally.

Worked Example 3: Dividing a Decimal by a Whole Number

Find 9.36 / 4.

  1. Set up long division: 4 ) 9.36. Place decimal point in the answer directly above.
  2. 4 goes into 9 twice (8). Subtract: 9-8=1. Bring down 3 to get 13.
  3. 4 goes into 13 three times (12). Subtract: 13-12=1. Bring down 6 to get 16.
  4. 4 goes into 16 four times (16). Subtract: 16-16=0.
9.36 / 4 = 2.34

Check: 2.34 x 4 = 9.36. Correct!

Using Area Models for Decimal Multiplication

Just as with whole numbers, you can break decimal multiplication into parts:

30.10.05
4120.40.20
0.20.60.020.01
12 + 0.4 + 0.20 + 0.6 + 0.02 + 0.01 = 13.23

Common Mistake

When counting decimal places, students sometimes count the digits instead of the decimal places. In 3.15, there are 2 decimal places (the 1 and the 5), not 3. The digit before the decimal does not count.

Real-World Connection

If gas costs $3.45 per gallon and you buy 8 gallons, the total is 3.45 x 8. Multiply 345 x 8 = 2,760. Two decimal places gives $27.60.

Practice Problems

1. Multiply: 0.6 x 0.7

Show Answer

6 x 7 = 42. Two decimal places total: 0.42.

2. Multiply: 2.5 x 1.4

Show Answer

25 x 14 = 350. Two decimal places: 3.50 or simply 3.5. Estimate: about 3 x 1 = 3. Reasonable.

3. Divide: 15.6 / 3

Show Answer

3 into 15 = 5. 3 into 6 = 2. Decimal stays in place: 5.2. Check: 5.2 x 3 = 15.6.

4. Divide: 8.45 / 5

Show Answer

5 into 8 = 1 R3. 5 into 34 = 6 R4. 5 into 45 = 9. Answer: 1.69. Check: 1.69 x 5 = 8.45.

5. A ribbon is 12.6 meters long. It is cut into 4 equal pieces. How long is each piece?

Show Answer

12.6 / 4 = 3.15 meters. Check: 3.15 x 4 = 12.6.

Lesson Summary

Overview