Question

Estimate the quotient of eight and seven over eight divided by one and one over nine using compatible numbers. What is the quotient?

8

9

4

2

Answer 1

What are compatible numbers? Compatible numbers are numbers that look nice or friendly with each other when we do mental calculation to estimate a product, but especially a division.

Some examples of compatible numbers when doing division are 400 and 10, 36 and 6, 2400 and 12, and 64 and 8

2400 and 12 are compatible because when doing this division (2400/12), we can quickly divide 24 by 12 to get 2 and put two zeros at the end to get 200

Some examples of compatible numbers when doing multiplication are 200 and 40, 1100 and 40, 25 and 4.

1100 and 40 are compatible because we can quickly do this multiplication by multipling 11 and 4 to get 44 and add three zeros at the end to get 44000.

http://www.basic-mathematics.com/what-are-compatible-numbers.html

Answer 2

Well, I did not know the phrase "compatible numbers" in this context so I had to look it up.

Let's see if we can apply the idea to the posted problem.

Answer 3

After reading all that, I realized that there was no reference to dividing mixed numbers.

So, here is what I think.

(8 and 7/8) divided by (1 and 1/9)

7/8 is close to 1 so (8 and 7/8) can be estimated to be 9.

(1 and 1/9)

1/9 is close to zero so (1 and 1/9) is estimated at 1.

So, estimate (8 and 7/8) divided by (1 and 1/9) as 9/1 = 9.

But, (8 and 7/8) divided by (1 and 1/9) when computed cranks out to 7.9885.

That makes the 9 look bad especially when there is an option of 8.

If it were my work, I'd go with the 8. This compatitible number approach is a little sketchy, too sketchy, for me.

You might want to read over that section in your text.

But, for me, I'm going with 8. Yet, I cannot say that I am certain 8 is the desired answer.

Sorry to be so wordy.