Suppose that 3<a<4 and 4<b<5 find all possible answers of: a/b

Answer 1

Greetings Alisa T...thank you for connecting with a Wyzant tutor.

This is an interesting and dependent upon what your teacher wants to help you know about is to 'think' and not every math problem has a specific answer in the form of a number or value.

I will help you to begin thinking about this and then it will be upon you to expand that. Here you go...if you have other questions you are welcome to drop me a line.

Let's begin with each of the two statements: 3 < a < 4 and 4 < b < 5

Now, take each statement so that you understand what each of them means (and so you understand what they mean)

Let's start with the first part: 3 < a < 4

Break it into: 3 < a and we can rewrite this a > 3 Understand...make sure you do.

And then : a < 4

So, what can you then determine from each of these two statements:

You should understand that the value of 'a' is any value more than 3, BUT NOT EQUAL TO 3 and that a is any value less than 4 BUT NOT EQUAL TO 4.

Do you understand?

This about that...ANY VALUE BETWEEN 3 and 4 but NOT EQUAL TO 3 or 4.

Do you know how many values there are between 3 and 4.

Do you think you can count them?

Here's an idea, let's begin with think about some numbers between 3 and 4, but not including 3 and 4. There is 3.01, 3.00001, 3.00000000001, oh...and there is many, many, many more. See where I'm going.

Now let's see if we can imagine some values, numbers less than 4, but not equal to 4.

There is 3.999999, 3.9999998, 3.9999992, just to name a few.

So what I'm trying to help you notice [just like your teacher] there seems like perhaps a ga-zillion numbers which would fit the statement: 3 < a < 4

How might you be able to put that into a math statement? What do you think?

Now that is just the numerator component of the ratio a/b

It would be the same understanding for the denominator: 4 < b < 5

One last thing to think about...now if you had the same value in the numerator and the same value in the denominator...what might that give you...

consider a/a = ? is what?

If 3.000012/3.000012 = ? what would that equal?

I am here to help.

Contact me if you need further assistance.

Answer 2

Start by defining some extremes:

The absolute maximum for a/b would be at the maximum a and minimum b. This is 4/4 = 1

The minimum for a/b is 3/5

Are these both allowed values? NO! Each case is a limit which cannot be reached, because the a and b values must stop short of the limits. The answer appears to be:

3/5 < a/b < 1 (0.6 < a/b < 1)

Test: a = 3.999, and b = 4.001 a/b = 0.995 (OK)

I think more tests will also confirm the solution.....