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What is 1/3 - 10/12?

What is 1/3 - 10/12?

Here's how to subtract 10/12 from 1/3:

1
3
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 1 by 12, and get 12.

Then we multiply 10 by 3, and get 30.

Next we give both terms new denominators -- 3 × 12 = 36.

So now our fractions look like this:

12
36
30
36

Step 2

Since our denominators match, we can subtract the numerators.

12 − 30 = -18

So the answer is:

-18
36

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:

-18
36
÷ 2 =
-9
18

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:

-9
18
÷ 3 =
-3
6

Let's try dividing by 3 again...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

-3
6
÷ 3 =
-1
2

Let's try dividing by 3 again...

No good. 3 is larger than -1. So we're done reducing.

There you have it! The final answer is:
1
3
10
12
=
1
2

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10/12 - 1/2
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