math help

What is 28/100 - 10/12?

What is 28/100 - 10/12?

Here's how to subtract 10/12 from 28/100:

28
100
 −
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 28 by 12, and get 336.

Then we multiply 10 by 100, and get 1000.

Next we give both terms new denominators -- 100 × 12 = 1200.

So now our fractions look like this:

336
1200
 −
1000
1200

Step 2

Since our denominators match, we can subtract the numerators.

336 − 1000 = -664

So the answer is:

-664
1200

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:

-664
1200
 ÷ 2 =
-332
600

Let's try dividing by 2 again...

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

-332
600
 ÷ 2 =
-166
300

Let's try dividing by 2 again...

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

-166
300
 ÷ 2 =
-83
150

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...

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...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

Nope! So now we try the next greatest prime number, 83...

Nope! So now we try the next greatest prime number, 89...

No good. 89 is larger than -83. So we're done reducing.

There you have it! The final answer is:
28
100
 −
10
12
 = −
83
150

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10/12 - 7/12
10/12 + 8/12
10/12 - 8/12
10/12 + 9/12
10/12 - 9/12
10/12 + 10/12
10/12 - 10/12
10/12 + 11/12
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