math help

What is 57/7 - 4/6?

What is 57/7 - 4/6?

Here's how to subtract 4/6 from 57/7:

57
7
 −
4
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 57 by 6, and get 342.

Then we multiply 4 by 7, and get 28.

Next we give both terms new denominators -- 7 × 6 = 42.

So now our fractions look like this:

342
42
 −
28
42

Step 2

Since our denominators match, we can subtract the numerators.

342 − 28 = 314

So the answer is:

314
42

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...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

314
42
 ÷ 2 =
157
21

Let's try dividing by 2 again...

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

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...

No good. 23 is larger than 21. So we're done reducing.

There you have it! The final answer is:
57
7
 −
4
6
 =
157
21

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