math help

What is 99/7 - 10/12?

What is 99/7 - 10/12?

Here's how to subtract 10/12 from 99/7:

99
7
 −
10
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 10 by 7, and get 70.

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

So now our fractions look like this:

1188
84
 −
70
84

Step 2

Since our denominators match, we can subtract the numerators.

1188 − 70 = 1118

So the answer is:

1118
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:

1118
84
 ÷ 2 =
559
42

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...

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

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

No good. 43 is larger than 42. So we're done reducing.

There you have it! The final answer is:
99
7
 −
10
12
 =
559
42

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