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What is 30/14 - 64/16?

What is 30/14 - 64/16?

Here's how to subtract 64/16 from 30/14:

30
14
64
16

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 30 by 16, and get 480.

Then we multiply 64 by 14, and get 896.

Next we give both terms new denominators -- 14 × 16 = 224.

So now our fractions look like this:

480
224
896
224

Step 2

Since our denominators match, we can subtract the numerators.

480 − 896 = -416

So the answer is:

-416
224

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:

-416
224
÷ 2 =
-208
112

Let's try dividing by 2 again...

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

-208
112
÷ 2 =
-104
56

Let's try dividing by 2 again...

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

-104
56
÷ 2 =
-52
28

Let's try dividing by 2 again...

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

-52
28
÷ 2 =
-26
14

Let's try dividing by 2 again...

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

-26
14
÷ 2 =
-13
7

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...

No good. 11 is larger than 7. So we're done reducing.

There you have it! The final answer is:
30
14
64
16
=
13
7

64/16 + 1/2
64/16 - 1/2
64/16 + 1/3
64/16 - 1/3
64/16 + 2/3
64/16 - 2/3
64/16 + 1/4
64/16 - 1/4
64/16 + 2/4
64/16 - 2/4
64/16 + 3/4
64/16 - 3/4
64/16 + 1/5
64/16 - 1/5
64/16 + 2/5
64/16 - 2/5
64/16 + 3/5
64/16 - 3/5
64/16 + 4/5
64/16 - 4/5
64/16 + 1/6
64/16 - 1/6
64/16 + 2/6
64/16 - 2/6
64/16 + 3/6
64/16 - 3/6
64/16 + 4/6
64/16 - 4/6
64/16 + 5/6
64/16 - 5/6
64/16 + 1/7
64/16 - 1/7
64/16 + 2/7
64/16 - 2/7
64/16 + 3/7
64/16 - 3/7
64/16 + 4/7
64/16 - 4/7
64/16 + 5/7
64/16 - 5/7
64/16 + 6/7
64/16 - 6/7
64/16 + 1/8
64/16 - 1/8
64/16 + 2/8
64/16 - 2/8
64/16 + 3/8
64/16 - 3/8
64/16 + 4/8
64/16 - 4/8
64/16 + 5/8
64/16 - 5/8
64/16 + 6/8
64/16 - 6/8
64/16 + 7/8
64/16 - 7/8
64/16 + 1/9
64/16 - 1/9
64/16 + 2/9
64/16 - 2/9
64/16 + 3/9
64/16 - 3/9
64/16 + 4/9
64/16 - 4/9
64/16 + 5/9
64/16 - 5/9
64/16 + 6/9
64/16 - 6/9
64/16 + 7/9
64/16 - 7/9
64/16 + 8/9
64/16 - 8/9
64/16 + 1/10
64/16 - 1/10
64/16 + 2/10
64/16 - 2/10
64/16 + 3/10
64/16 - 3/10
64/16 + 4/10
64/16 - 4/10
64/16 + 5/10
64/16 - 5/10
64/16 + 6/10
64/16 - 6/10
64/16 + 7/10
64/16 - 7/10
64/16 + 8/10
64/16 - 8/10
64/16 + 9/10
64/16 - 9/10
64/16 + 1/11
64/16 - 1/11
64/16 + 2/11
64/16 - 2/11
64/16 + 3/11
64/16 - 3/11
64/16 + 4/11
64/16 - 4/11
64/16 + 5/11
64/16 - 5/11
64/16 + 6/11
64/16 - 6/11
64/16 + 7/11
64/16 - 7/11
64/16 + 8/11
64/16 - 8/11
64/16 + 9/11
64/16 - 9/11
64/16 + 10/11
64/16 - 10/11
64/16 + 1/12
64/16 - 1/12
64/16 + 2/12
64/16 - 2/12
64/16 + 3/12
64/16 - 3/12
64/16 + 4/12
64/16 - 4/12
64/16 + 5/12
64/16 - 5/12
64/16 + 6/12
64/16 - 6/12
64/16 + 7/12
64/16 - 7/12
64/16 + 8/12
64/16 - 8/12
64/16 + 9/12
64/16 - 9/12
64/16 + 10/12
64/16 - 10/12
64/16 + 11/12
64/16 - 11/12