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What is 78/92 - 3/12?

What is 78/92 - 3/12?

Here's how to subtract 3/12 from 78/92:

78
92
3
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 78 by 12, and get 936.

Then we multiply 3 by 92, and get 276.

Next we give both terms new denominators -- 92 × 12 = 1104.

So now our fractions look like this:

936
1104
276
1104

Step 2

Since our denominators match, we can subtract the numerators.

936 − 276 = 660

So the answer is:

660
1104

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:

660
1104
÷ 2 =
330
552

Let's try dividing by 2 again...

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

330
552
÷ 2 =
165
276

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:

165
276
÷ 3 =
55
92

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...

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...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

No good. 59 is larger than 55. So we're done reducing.

There you have it! The final answer is:
78
92
3
12
=
55
92