math help

What is 28/100 - 9/12?

What is 28/100 - 9/12?

Here's how to subtract 9/12 from 28/100:

28
100
 −
9
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 9 by 100, and get 900.

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

So now our fractions look like this:

336
1200
 −
900
1200

Step 2

Since our denominators match, we can subtract the numerators.

336 − 900 = -564

So the answer is:

-564
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:

-564
1200
 ÷ 2 =
-282
600

Let's try dividing by 2 again...

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

-282
600
 ÷ 2 =
-141
300

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:

-141
300
 ÷ 3 =
-47
100

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...

No good. 53 is larger than -47. So we're done reducing.

There you have it! The final answer is:
28
100
 −
9
12
 = −
47
100

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