Find two numbers the quotient is between. Then estimate the quotient 284 divided by 5
The Correct Answer and Explanation is:
Problem:
Find two numbers the quotient is between. Then estimate the quotient for 284 ÷ 5.
Solution:
First, find two numbers that 284 is between, which are easy to divide by 5.
Looking at nearby multiples of 5:
- 280 ÷ 5 = 56
- 285 ÷ 5 = 57
Therefore, 284 ÷ 5 is between 56 and 57.
Now, estimate the quotient. Since 284 is closer to 285, the estimate is about 57.
Explanation:
When dividing numbers, especially those that do not divide evenly, estimating the quotient can make calculations easier and quicker. The process starts by finding two nearby multiples of the divisor that the dividend falls between.
In this case, the problem is 284 divided by 5. The first step is to think about multiples of 5 close to 284. Multiplying 5 by 56 gives 280, and multiplying 5 by 57 gives 285. Since 284 lies between 280 and 285, it follows that the quotient of 284 ÷ 5 must be between 56 and 57.
To estimate the quotient, it helps to see how close 284 is to each multiple. Because 284 is only 1 away from 285 but 4 away from 280, it is closer to 285. Therefore, the estimate for the quotient is 57.
Estimation allows for a quick approximation of the answer without performing exact long division. This method is helpful in everyday situations where an exact answer is not necessary but a close estimate is sufficient for making decisions or solving problems quickly.
For verification, performing the actual division:
284 ÷ 5 = 56.8
This shows that the estimate of 57 is very close to the actual quotient.
Final answer:
The quotient is between 56 and 57. The estimate is 57.
