Find a fraction between 97/36 and 96/35 with smallest denominator

Find a fraction between 97/36 and 96/35 which has the smallest denominator. Since 97/36 > 96/35, I formed the following inequality

Now, appropriately so, we could write the given fractions with common denominators and thusly yield

Now this is where I am stuck. The correct answer is p = 19 and q = 7, which corresponds to the fraction 3420/1260.

Anyone got any idea?

Re: Find a fraction between 97/36 and 96/35 with smallest denominator

Quote:

Originally Posted by

**MathCrusader** Find a fraction between 97/36 and 96/35 which has the smallest denominator. Since 97/36 > 96/35, I formed the following inequality

Now, appropriately so, we could write the given fractions with common denominators and thusly yield

Now this is where I am stuck. The correct answer is p = 19 and q = 7, which corresponds to the fraction 3420/1260.

Anyone got any idea?

Hi MathCrusader! :)

To simplify a fraction, you need to know how the numerators and denominators factorize.

Can you create prime number factorizations of all the numbers you have?

Re: Find a fraction between 97/36 and 96/35 with smallest denominator

Re: Find a fraction between 97/36 and 96/35 with smallest denominator

Quote:

Originally Posted by

**MathCrusader** Find a fraction between 97/36 and 96/35 which has the smallest denominator. Since 97/36 > 96/35, I formed the following inequality

Now, appropriately so, we could write the given fractions with common denominators and thusly yield

Now this is where I am stuck. The correct answer is p = 19 and q = 7, which corresponds to the fraction 3420/1260.

Anyone got any idea?

Quote:

Originally Posted by

**MathCrusader**

Good!

So you have:

Now we are looking for a number between 3395 and 3456 that has as much factors in common as possible with 1260.

I think this is easiest with just trial and error, combining one or more prime factors into a numbers starting with the lowest possible.

Start with q=2, and see if you can find an acceptable value for p.

Then q=3, q=4, q=5, q=6, q=7... and there you go!