math help

What is 53/9 - 6/12?

What is 53/9 - 6/12?

Here's how to subtract 6/12 from 53/9:

53
9
 −
6
12

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 53 by 12, and get 636.

Then we multiply 6 by 9, and get 54.

Next we give both terms new denominators -- 9 × 12 = 108.

So now our fractions look like this:

636
108
 −
54
108

Step 2

Since our denominators match, we can subtract the numerators.

636 − 54 = 582

So the answer is:

582
108

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:

582
108
 ÷ 2 =
291
54

Let's try dividing by 2 again...

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:

291
54
 ÷ 3 =
97
18

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...

No good. 19 is larger than 18. So we're done reducing.

There you have it! The final answer is:
53
9
 −
6
12
 =
97
18

6/12 + 1/2
6/12 - 1/2
6/12 + 1/3
6/12 - 1/3
6/12 + 2/3
6/12 - 2/3
6/12 + 1/4
6/12 - 1/4
6/12 + 2/4
6/12 - 2/4
6/12 + 3/4
6/12 - 3/4
6/12 + 1/5
6/12 - 1/5
6/12 + 2/5
6/12 - 2/5
6/12 + 3/5
6/12 - 3/5
6/12 + 4/5
6/12 - 4/5
6/12 + 1/6
6/12 - 1/6
6/12 + 2/6
6/12 - 2/6
6/12 + 3/6
6/12 - 3/6
6/12 + 4/6
6/12 - 4/6
6/12 + 5/6
6/12 - 5/6
6/12 + 1/7
6/12 - 1/7
6/12 + 2/7
6/12 - 2/7
6/12 + 3/7
6/12 - 3/7
6/12 + 4/7
6/12 - 4/7
6/12 + 5/7
6/12 - 5/7
6/12 + 6/7
6/12 - 6/7
6/12 + 1/8
6/12 - 1/8
6/12 + 2/8
6/12 - 2/8
6/12 + 3/8
6/12 - 3/8
6/12 + 4/8
6/12 - 4/8
6/12 + 5/8
6/12 - 5/8
6/12 + 6/8
6/12 - 6/8
6/12 + 7/8
6/12 - 7/8
6/12 + 1/9
6/12 - 1/9
6/12 + 2/9
6/12 - 2/9
6/12 + 3/9
6/12 - 3/9
6/12 + 4/9
6/12 - 4/9
6/12 + 5/9
6/12 - 5/9
6/12 + 6/9
6/12 - 6/9
6/12 + 7/9
6/12 - 7/9
6/12 + 8/9
6/12 - 8/9
6/12 + 1/10
6/12 - 1/10
6/12 + 2/10
6/12 - 2/10
6/12 + 3/10
6/12 - 3/10
6/12 + 4/10
6/12 - 4/10
6/12 + 5/10
6/12 - 5/10
6/12 + 6/10
6/12 - 6/10
6/12 + 7/10
6/12 - 7/10
6/12 + 8/10
6/12 - 8/10
6/12 + 9/10
6/12 - 9/10
6/12 + 1/11
6/12 - 1/11
6/12 + 2/11
6/12 - 2/11
6/12 + 3/11
6/12 - 3/11
6/12 + 4/11
6/12 - 4/11
6/12 + 5/11
6/12 - 5/11
6/12 + 6/11
6/12 - 6/11
6/12 + 7/11
6/12 - 7/11
6/12 + 8/11
6/12 - 8/11
6/12 + 9/11
6/12 - 9/11
6/12 + 10/11
6/12 - 10/11
6/12 + 1/12
6/12 - 1/12
6/12 + 2/12
6/12 - 2/12
6/12 + 3/12
6/12 - 3/12
6/12 + 4/12
6/12 - 4/12
6/12 + 5/12
6/12 - 5/12
6/12 + 6/12
6/12 - 6/12
6/12 + 7/12
6/12 - 7/12
6/12 + 8/12
6/12 - 8/12
6/12 + 9/12
6/12 - 9/12
6/12 + 10/12
6/12 - 10/12
6/12 + 11/12
6/12 - 11/12