Subtract: 17.46 - 11.034A. 6.372 B. 6.426 C. 6.012 D. 6.12
When it comes to subtracting decimals, it's essential to understand the concept and apply the correct steps to arrive at the correct answer. In this article, we'll delve into the world of decimal subtraction and explore the correct method to solve the given problem.
Understanding Decimals
Decimals are a way of representing numbers in a more precise and accurate manner. They consist of a whole number part and a fractional part, separated by a decimal point. For example, 17.46 is a decimal number that can be broken down into 17 (whole number part) and 0.46 (fractional part).
Subtracting Decimals: The Correct Method
To subtract decimals, we need to follow a specific method. Here are the steps:
- Line up the decimal points: The first step is to line up the decimal points of the two numbers. This ensures that we're subtracting the correct number of decimal places.
- Subtract the whole numbers: Next, we subtract the whole number parts of the two numbers. In this case, we have 17 (whole number part of 17.46) and 11 (whole number part of 11.034).
- Subtract the fractional parts: After subtracting the whole number parts, we need to subtract the fractional parts. To do this, we need to line up the decimal points and subtract the corresponding decimal places.
- Borrow if necessary: If the fractional part of the number being subtracted is larger than the fractional part of the number being subtracted from, we need to borrow from the whole number part.
Solving the Problem: 17.46 - 11.034
Now that we've understood the correct method for subtracting decimals, let's apply it to the given problem: 17.46 - 11.034.
Step 1: Line up the decimal points
| 17.46 | - | 11.034 | |
|---|---|---|---|
| 17.46 | 11.034 |
Step 2: Subtract the whole numbers
| 17.46 | - | 11.034 | |
|---|---|---|---|
| 17.46 | 11.034 | ||
| 6.426 |
Step 3: Subtract the fractional parts
| 17.46 | - | 11.034 | |
|---|---|---|---|
| 17.46 | 11.034 | ||
| 6.426 |
To subtract the fractional parts, we need to line up the decimal points and subtract the corresponding decimal places.
| 17.46 | - | 11.034 | |
|---|---|---|---|
| 17.46 | 11.034 | ||
| 6.426 |
We can see that the fractional part of the number being subtracted (11.034) is larger than the fractional part of the number being subtracted from (17.46). Therefore, we need to borrow from the whole number part.
Step 4: Borrow if necessary
| 17.46 | - | 11.034 | |
|---|---|---|---|
| 17.46 | 11.034 | ||
| 6.426 |
To borrow from the whole number part, we need to subtract 1 from the whole number part of the number being subtracted from (17.46). This gives us 16.46.
| 17.46 | - | 11.034 | |
|---|---|---|---|
| 16.46 | 11.034 | ||
| 6.426 |
Now, we can subtract the fractional parts.
| 16.46 | - | 11.034 | |
|---|---|---|---|
| 16.46 | 11.034 | ||
| 5.426 |
Step 5: Final answer
| 16.46 | - | 11.034 | |
|---|---|---|---|
| 16.46 | 11.034 | ||
| 5.426 |
The final answer is 5.426.
Conclusion
Subtracting decimals requires a specific method to ensure accuracy and precision. By following the steps outlined in this article, we can confidently solve decimal subtraction problems. Remember to line up the decimal points, subtract the whole numbers, subtract the fractional parts, and borrow if necessary. With practice and patience, you'll become proficient in subtracting decimals in no time.
Common Mistakes to Avoid
When subtracting decimals, it's essential to avoid common mistakes. Here are a few to watch out for:
- Not lining up the decimal points: Failing to line up the decimal points can lead to incorrect answers.
- Not borrowing if necessary: Failing to borrow from the whole number part when necessary can also lead to incorrect answers.
- Rounding incorrectly: Rounding numbers incorrectly can also lead to incorrect answers.
Practice Problems
To reinforce your understanding of decimal subtraction, try solving the following practice problems:
- 23.17 - 14.95
- 17.32 - 11.67
- 25.49 - 18.27
Remember to follow the steps outlined in this article to ensure accuracy and precision.
Final Thoughts
In this article, we'll address some of the most common questions and concerns related to decimal subtraction. Whether you're a student, teacher, or simply looking to brush up on your math skills, this article is for you.
Q: What is decimal subtraction?
A: Decimal subtraction is the process of subtracting one decimal number from another. It involves lining up the decimal points, subtracting the whole numbers, and then subtracting the fractional parts.
Q: Why do I need to line up the decimal points?
A: Lining up the decimal points is essential to ensure that you're subtracting the correct number of decimal places. If the decimal points are not lined up, you may end up with an incorrect answer.
Q: What if the fractional part of the number being subtracted is larger than the fractional part of the number being subtracted from?
A: If the fractional part of the number being subtracted is larger than the fractional part of the number being subtracted from, you need to borrow from the whole number part. This involves subtracting 1 from the whole number part of the number being subtracted from.
Q: Can I round the numbers before subtracting?
A: No, it's not recommended to round the numbers before subtracting. Rounding can lead to incorrect answers and may not accurately reflect the original numbers.
Q: What if I'm subtracting a negative number?
A: When subtracting a negative number, you need to change the sign of the number being subtracted. For example, if you're subtracting -3.14, you would change the sign to +3.14 and then proceed with the subtraction.
Q: Can I use a calculator to subtract decimals?
A: Yes, you can use a calculator to subtract decimals. However, it's essential to understand the concept of decimal subtraction and how to perform it manually. This will help you to avoid common mistakes and ensure accuracy.
Q: What are some common mistakes to avoid when subtracting decimals?
A: Some common mistakes to avoid when subtracting decimals include:
- Not lining up the decimal points
- Not borrowing if necessary
- Rounding incorrectly
- Changing the sign of the number being subtracted incorrectly
Q: How can I practice decimal subtraction?
A: You can practice decimal subtraction by working through examples and exercises. You can also use online resources and calculators to help you practice and check your answers.
Q: What are some real-world applications of decimal subtraction?
A: Decimal subtraction has many real-world applications, including:
- Calculating discounts and sales tax
- Determining the cost of materials for a construction project
- Calculating the interest on a loan
- Determining the cost of a product with a discount
Conclusion
Decimal subtraction is a fundamental concept in mathematics that requires practice and patience to master. By understanding the concept and avoiding common mistakes, you'll become proficient in subtracting decimals in no time. Remember to line up the decimal points, subtract the whole numbers, subtract the fractional parts, and borrow if necessary. With practice and dedication, you'll become a decimal subtraction expert in no time.
Additional Resources
If you're looking for additional resources to help you practice decimal subtraction, here are a few suggestions:
- Online calculators and worksheets
- Math textbooks and workbooks
- Online math courses and tutorials
- Math apps and games
Final Thoughts
Decimal subtraction is a critical skill that requires practice and patience to master. By understanding the concept and avoiding common mistakes, you'll become proficient in subtracting decimals in no time. Remember to line up the decimal points, subtract the whole numbers, subtract the fractional parts, and borrow if necessary. With practice and dedication, you'll become a decimal subtraction expert in no time.