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What is 9/34 - 10/12?

What is 9/34 - 10/12?

Here's how to subtract 10/12 from 9/34:

9
34
 −
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 9 by 12, and get 108.

Then we multiply 10 by 34, and get 340.

Next we give both terms new denominators -- 34 × 12 = 408.

So now our fractions look like this:

108
408
 −
340
408

Step 2

Since our denominators match, we can subtract the numerators.

108 − 340 = -232

So the answer is:

-232
408

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:

-232
408
 ÷ 2 =
-116
204

Let's try dividing by 2 again...

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

-116
204
 ÷ 2 =
-58
102

Let's try dividing by 2 again...

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

-58
102
 ÷ 2 =
-29
51

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...

No good. 31 is larger than -29. So we're done reducing.

There you have it! The final answer is:
9
34
 −
10
12
 = −
29
51

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