math help

What is 99/7 - 6/12?

What is 99/7 - 6/12?

Here's how to subtract 6/12 from 99/7:

99
7
 −
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 99 by 12, and get 1188.

Then we multiply 6 by 7, and get 42.

Next we give both terms new denominators -- 7 × 12 = 84.

So now our fractions look like this:

1188
84
 −
42
84

Step 2

Since our denominators match, we can subtract the numerators.

1188 − 42 = 1146

So the answer is:

1146
84

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:

1146
84
 ÷ 2 =
573
42

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:

573
42
 ÷ 3 =
191
14

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...

No good. 17 is larger than 14. So we're done reducing.

There you have it! The final answer is:
99
7
 −
6
12
 =
191
14

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