Decimal Multiplication

Grade 5 · decimals · 92 practice problems · read aloud

🔊 Listen to this explanation

Multiplying Decimals

Multiplying decimals is just like multiplying whole numbers, with one extra step! We use it all the time for money, measurements, and figuring out discounts. 🛍️

How to Multiply Decimals: Step-by-Step

  1. Multiply: Ignore the decimal points and multiply the numbers as if they were whole numbers.
  2. Count the Places: Count the total number of decimal places in both of the original numbers.
  3. Place the Decimal: In your answer, place the decimal point so that it has the same number of decimal places you counted in step 2.

Worked Examples

Example 1: 0.8 × 3

1. Multiply: 8 × 3 = 24

2. Count: 0.8 has 1 decimal place. 3 has 0. Total = 1 decimal place.

3. Place: 24 → 2.4

Answer: 2.4

Example 2: 1.25 × 0.4

1. Multiply: 125 × 4 = 500

2. Count: 1.25 has 2 decimal places. 0.4 has 1. Total = 3 decimal places.

3. Place: 500 → 0.500 (or just 0.5)

Answer: 0.5

⚠️ Common Mistakes to Avoid

  • Lining up the decimals: Don't line up the decimal points when multiplying! Only line them up when you are adding or subtracting.
  • Forgetting the decimal: Always count the total decimal places before you place the decimal in your answer.
  • Wrong place value: If your final answer doesn't have enough digits, add zeros to the left! (Like in Example 2, we needed to make 500 into 0.500).

🌟 Tips & Tricks

  • Estimate First! Round the decimals to the nearest whole number and multiply. This helps you know if your final answer is reasonable. For 1.25 × 0.4, you'd think "about 1 × 0.4 = 0.4," so an answer of 0.5 makes sense!
  • Count on Your Fingers: Physically count the decimal places in the problem on your fingers to keep track.
  • Money Helper: Remember that $1.25 is 125 cents. Thinking in cents can make the problem feel easier!

How to Practice

To become a decimal multiplication master:

  • Start with flashcards for single-digit decimals.
  • Solve real-life problems: "If one candy bar costs $0.75, how much do 4 bars cost?"
  • Ask a friend or parent to give you problems and check your work.
  • Remember, practice makes progress! ✨

Practice problems

6 of the 92, worked through step by step — try them before opening the answer.

1 3.75 × 8 = ?

Hint: When multiplying a decimal by a whole number, multiply as if both were whole numbers, then place the decimal point correctly in the final answer.

Show the answer

Answer: 30

  1. Understand the number 3.75. 3.75 is the same as 3 + 0.75, and 0.75 is the fraction 3/4.
  2. Multiply 3.75 by 8 by breaking it into two parts. 3.75 × 8 = (3 + 0.75) × 8
  3. Use the distributive property: = (3 × 8) + (0.75 × 8)
  4. Calculate 3 × 8 = 24.
  5. Calculate 0.75 × 8. Since 0.75 = 3/4, we can compute: 3/4 × 8 = (3 × 8) / 4 = 24 / 4 = 6.
  6. Add the two results: 24 + 6 = 30. Final Answer: 30

Let's solve 3.75 × 8 step-by-step.

2 2.75 × 8 = ?

Hint: Think of the decimal as money - if you had 3 dollars and 75 cents, how would you multiply that by a whole number?

Show the answer

Answer: 22

  1. Understand the decimal. 2.75 means 2 whole parts and 75 hundredths. So 2.75 = 2 + 0.75.
  2. Break the multiplication into parts. 2.75 × 8 = (2 + 0.75) × 8.
  3. Use the distributive property. (2 × 8) + (0.75 × 8).
  4. Multiply the whole number part. 2 × 8 = 16.
  5. Multiply the decimal part. 0.75 means 75/100, so 0.75 × 8 = (75/100) × 8. First, 75 × 8 = 600. Then divide by 100: 600 / 100 = 6.
  6. Add the two results. 16 + 6 = 22. Final answer: 22.

Let's solve 2.75 × 8 step-by-step.

3 2.75 × 4 = ?

Hint: Think of the decimal as money. If you had four items that each cost a certain amount of dollars and cents, how would you find the total cost?

Show the answer

Answer: 11

  1. Understand the number 2.75. 2.75 is the same as 2 + 0.75. Also, 0.75 is the same as 75/100, which simplifies to 3/4.
  2. Multiply 2.75 by 4 using the distributive property. 2.75 × 4 = (2 + 0.75) × 4 = (2 × 4) + (0.75 × 4)
  3. Calculate 2 × 4. 2 × 4 = 8
  4. Calculate 0.75 × 4. 0.75 = 3/4, so 0.75 × 4 = (3/4) × 4 = (3 × 4) / 4 = 12 / 4 = 3
  5. Add the two results. 8 + 3 = 11
  6. Conclusion. Therefore, 2.75 × 4 = 11.

Let's solve 2.75 × 4 step-by-step.

4 4.25 × 6 = ?

Hint: Think of this as 4.25 added together 6 times. You can break it into whole numbers and decimals to make it easier.

Show the answer

Answer: 25.5

  1. Write the multiplication: 4.25 × 6
  2. Multiply the whole number part: 4 × 6 = 24
  3. Multiply the decimal part: 0.25 × 6 = 1.5
  4. Add the results: 24 + 1.5 = 25.5
  5. Place the decimal point in the answer: 25.5 The final answer is 25.5.

5 3.25 × 12 = ?

Hint: Think of multiplying a decimal by a whole number. You can break it into parts: multiply the whole number part and the decimal part separately, then combine.

Show the answer

Answer: 39

  1. Multiply 3.25 by 12
  2. First, multiply the whole number part: 3 × 12 = 36
  3. Then multiply the decimal part: 0.25 × 12 = 3
  4. Add the results: 36 + 3 = 39
  5. The answer is 39.

6 4.25 × 12 = ?

Hint: Think of multiplying the decimal by the whole number as repeated addition of the decimal value.

Show the answer

Answer: 51

  1. Write the multiplication: 4.25 × 12
  2. Multiply 4.25 by 10: 4.25 × 10 = 42.5
  3. Multiply 4.25 by 2: 4.25 × 2 = 8.5
  4. Add the two results: 42.5 + 8.5 = 51
  5. The answer is 51.
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