Explain how to estimate the quotient using compatible numbers. 27 2/3 ÷ 3 9/10
The Correct Answer and Explanation is:
To estimate the quotient of 27 2/3 ÷ 3 9/10 using compatible numbers, you want to round both numbers to values that are easy to divide mentally. Compatible numbers are numbers that are close to the actual values but make the math simpler.
Step 1: Convert the mixed numbers to approximate whole numbers
- 27 2/3 is close to 28
- 3 9/10 is close to 4
These are compatible numbers because 28 is easily divisible by 4.
Step 2: Divide the compatible numbers
Now divide:28÷4=728 ÷ 4 = 728÷4=7
So, the estimated quotient is 7.
Explanation:
When estimating quotients, especially with mixed numbers or decimals, compatible numbers are a helpful tool. These are numbers that are easy to compute with and are close in value to the original numbers. In this problem, we are estimating the quotient of 27 2/3 ÷ 3 9/10.
First, we simplify both mixed numbers by rounding them to nearby whole numbers that make the division simpler. The number 27 2/3 is just slightly less than 28, so we round it up to 28. Meanwhile, 3 9/10 is close to 4, so we round it to 4.
Now, we perform the division using these compatible numbers:
28 ÷ 4 = 7
This estimated quotient of 7 gives us a good sense of the actual answer. It may not be exact, but it is close enough for mental math, quick checks, or when you do not need the precise decimal or fraction result.
Using compatible numbers is a common strategy in math to make complex problems easier to solve, especially when working without a calculator. It is particularly useful in real-world settings, like estimating prices, dividing items among people, or checking the reasonableness of an answer.
In summary, to estimate the quotient of 27 2/3 ÷ 3 9/10, round each mixed number to a compatible whole number and divide:
28 ÷ 4 = 7
So, the estimated answer is 7.
