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Contributor: Katie Schnabel. Lesson ID: 14191
Your favorite band…in concert…LIVE! You have to be there to hear your favorite songs! But how many friends can you bring with you? Use long division to divide a decimal to find out.
Your favorite band is coming to town, and you have $39 to spend on tickets for you and your friends. But here’s the catch: each ticket costs $9.75.
Dive into how to use division with decimals to find out exactly who’s rocking out with you!
Dividing by a decimal might seem tricky, but don’t let that decimal throw off your groove! It’s simpler than it looks if you follow these steps.
Start by setting up your problem: $39 ÷ $9.75.
| 9. | 7 | 5 | 3 | 9. |
First, move the decimal in the divisor all the way to the right to make it a whole number. In this example, you’ll move it two places.
| 9 | 7 | 5. | 3 | 9. | |||||
| → | → |
Next, do the same with the dividend, moving its decimal two places to the right. If there aren’t enough digits, add zeros as placeholders.
| 9 | 7 | 5. | 3 | 9 | 0 | 0. | |||
| → | → |
Now, it’s just like a regular long-division problem!
Dive in.
These are some big numbers. You may not know right away. Start with an estimate. 975 is close to 1,000, and 3,900 is near 4,000.
Try multiplying 975 by 4.
| 9 | 7 | 5 | ||||
| x | 4 | |||||
| 3 | 9 | 0 | 0 |
Great—3,900 exactly!
Now, return to the division problem. Place the 4 on top and write 3,900 underneath the dividend.
When you subtract, there’s no remainder. Don’t forget to place the decimal in the correct spot.
| 4. | |||||||||
| 9 | 7 | 5. | 3 | 9 | 0 | 0. | |||
| - | 3 | 9 | 0 | 0 | |||||
| 0 |
Four tickets! You can bring yourself and three friends to the concert.
Try another example.
Set up the problem like this.
| 3. | 7 | 5 | 4 | 8. |
You're right. You have to move the decimal all the way to the right.
Move it two places to the right—same with the dividend.
| 3 | 7 | 5. | 4 | 8 | 0 | 0. | |||
| → | → | → | → |
Now, divide 4800 by 375.
Just once. Write a 1 on top, and place 375 underneath. Subtract.
| 1 | |||||||||
| 3 | 7 | 5. | 4 | 8 | 0 | 0. | |||
| - | 3 | 7 | 5 | ||||||
| 1 | 0 | 5 |
480 - 375 leaves you with 105. Bring down the next number.
Twice! Write a 2 on top, place 750 underneath, and subtract.
| 1 | 2 | ||||||||
| 3 | 7 | 5. | 4 | 8 | 0 | 0. | |||
| - | 3 | 7 | 5 | ↓ | |||||
| 1 | 0 | 5 | 0 | ||||||
| - | 7 | 5 | 0 | ||||||
| 3 | 0 | 0 |
Now you have 300. Since 375 can’t go into 300, bring down a zero.
| 1 | 2 | ||||||||
| 3 | 7 | 5. | 4 | 8 | 0 | 0. | 0 | ||
| - | 3 | 7 | 5 | ↓ | |||||
| 1 | 0 | 5 | 0 | ↓ | |||||
| - | 7 | 5 | 0 | ↓ | |||||
| 3 | 0 | 0 | 0 |
If you estimate, it looks like around 8 times. Try multiplying: 375 x 8.
| 3 | 7 | 5 | ||||
| x | 8 | |||||
| 3 | 0 | 0 | 0 |
Perfect! 375 x 8 = 3000.
Place the 8 on top, write 3000 underneath, and subtract to get zero. Last step: bring up the decimal.
| 1 | 2. | 8 | |||||||
| 3 | 7 | 5. | 4 | 8 | 0 | 0. | 0 | ||
| - | 3 | 7 | 5 | ||||||
| 1 | 0 | 5 | 0 | ||||||
| - | 7 | 5 | 0 | ||||||
| 3 | 0 | 0 | 0 | ||||||
| - | 3 | 0 | 0 | 0 | |||||
| 0 |
Final answer: 12.8.
Head to the Got It? section for fun activities and games to practice long division with decimal divisors!
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