Estimate $87.54 \div 7.8$ Using Compatible Numbers.A. About 11 B. About 12 C. About 10 D. About 13
Introduction
Estimating division with compatible numbers is a useful technique in mathematics that helps us approximate the result of a division operation. This method is particularly helpful when dealing with large or complex numbers. In this article, we will explore how to estimate the division of two numbers using compatible numbers and apply this technique to the given problem: $87.54 \div 7.8$.
What are Compatible Numbers?
Compatible numbers are numbers that are close to each other and can be used to estimate the result of a mathematical operation. They are often used in mental math and estimation problems. In the context of division, compatible numbers are numbers that are close to the dividend (the number being divided) and the divisor (the number by which we are dividing).
How to Estimate Division with Compatible Numbers
To estimate division with compatible numbers, we need to follow these steps:
- Identify the dividend and divisor: The dividend is the number being divided, and the divisor is the number by which we are dividing.
- Find compatible numbers: Look for numbers that are close to the dividend and the divisor. These numbers should be easy to work with and provide a good estimate of the result.
- Divide the compatible numbers: Divide the compatible number that is close to the dividend by the compatible number that is close to the divisor.
- Check the estimate: Compare the estimated result with the actual result to see how close they are.
Estimating $87.54 \div 7.8$
Let's apply the steps above to estimate the division of $87.54 \div 7.8$.
Step 1: Identify the Dividend and Divisor
The dividend is $87.54$, and the divisor is $7.8$.
Step 2: Find Compatible Numbers
We can use the following compatible numbers:
- Dividend: $90$ (a number close to $87.54$)
- Divisor: $8$ (a number close to $7.8$)
Step 3: Divide the Compatible Numbers
Now, let's divide the compatible numbers:
Step 4: Check the Estimate
To check the estimate, we can calculate the actual result of the division:
As we can see, the estimated result ($11.25$) is very close to the actual result ($11.21$).
Conclusion
Estimating division with compatible numbers is a useful technique that helps us approximate the result of a division operation. By following the steps outlined above, we can estimate the division of two numbers using compatible numbers. In this article, we applied this technique to estimate the division of $87.54 \div 7.8$ and obtained a result that is very close to the actual result.
Answer
Based on our estimate, the correct answer is:
- A. about 11
Introduction
Estimating division with compatible numbers is a useful technique in mathematics that helps us approximate the result of a division operation. In our previous article, we explored how to estimate the division of two numbers using compatible numbers and applied this technique to the given problem: $87.54 \div 7.8$. In this article, we will answer some frequently asked questions about estimating division with compatible numbers.
Q&A
Q: What are compatible numbers?
A: Compatible numbers are numbers that are close to each other and can be used to estimate the result of a mathematical operation. They are often used in mental math and estimation problems.
Q: How do I find compatible numbers?
A: To find compatible numbers, look for numbers that are close to the dividend (the number being divided) and the divisor (the number by which we are dividing). These numbers should be easy to work with and provide a good estimate of the result.
Q: What is the difference between an estimate and an actual result?
A: An estimate is an approximate result of a mathematical operation, while an actual result is the exact result of the operation. In the context of estimating division with compatible numbers, the estimate is the result we obtain by dividing the compatible numbers, and the actual result is the exact result of the division operation.
Q: Why is it important to check the estimate?
A: It is essential to check the estimate to ensure that it is close to the actual result. This helps us to verify the accuracy of our estimate and to make any necessary adjustments.
Q: Can I use any numbers as compatible numbers?
A: No, not any numbers can be used as compatible numbers. The numbers should be close to the dividend and the divisor, and they should be easy to work with. Using numbers that are too far apart or too difficult to work with can lead to inaccurate estimates.
Q: How do I know if my estimate is accurate?
A: To determine if your estimate is accurate, compare it with the actual result. If the estimate is close to the actual result, then it is likely to be accurate. However, if the estimate is far from the actual result, then it may be necessary to re-evaluate the estimate and make any necessary adjustments.
Q: Can I use estimating division with compatible numbers for all types of division problems?
A: No, estimating division with compatible numbers is not suitable for all types of division problems. This technique is best used for problems where the dividend and divisor are close to each other and can be easily estimated. For more complex division problems, it may be necessary to use other techniques or tools.
Q: How can I practice estimating division with compatible numbers?
A: To practice estimating division with compatible numbers, try the following:
- Start with simple division problems and gradually move on to more complex problems.
- Use real-world examples, such as calculating the cost of items or the amount of time it takes to complete a task.
- Practice estimating division with compatible numbers regularly to develop your skills and build your confidence.
Conclusion
Estimating division with compatible numbers is a useful technique that helps us approximate the result of a division operation. By following the steps outlined in this article and practicing regularly, you can develop your skills and become more confident in your ability to estimate division with compatible numbers.
Tips and Resources
- For more information on estimating division with compatible numbers, check out the following resources:
- Khan Academy: Estimating Division with Compatible Numbers
- Mathway: Estimating Division with Compatible Numbers
- IXL: Estimating Division with Compatible Numbers
- To practice estimating division with compatible numbers, try the following online resources:
- Math Playground: Estimating Division with Compatible Numbers
- Coolmath: Estimating Division with Compatible Numbers
- Hooda Math: Estimating Division with Compatible Numbers