math help

What is 97/75 - 5/6?

What is 97/75 - 5/6?

Here's how to subtract 5/6 from 97/75:

97
75
 −
5
6

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 97 by 6, and get 582.

Then we multiply 5 by 75, and get 375.

Next we give both terms new denominators -- 75 × 6 = 450.

So now our fractions look like this:

582
450
 −
375
450

Step 2

Since our denominators match, we can subtract the numerators.

582 − 375 = 207

So the answer is:

207
450

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

207
450
 ÷ 3 =
69
150

Let's try dividing by 3 again...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

69
150
 ÷ 3 =
23
50

Let's try dividing by 3 again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

No good. 29 is larger than 23. So we're done reducing.

There you have it! The final answer is:
97
75
 −
5
6
 =
23
50

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