math help

What is 9/16 + 10/12?

What is 9/16 + 10/12?

Here's how you add

9
16
 +
10
12

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 9 by 12, and get 108, then we multiply 16 by 12 and get 192.

9/16 times 12

Now for the second term. You multiply 10 by 16, and get 160, then multiply 16 by 12 and get 192.

10/12 times 16

We now have a new problem, that looks like this:

108
192
 +
160
192

Step 2

Since our denominators match, we can add the numerators.

108 + 160 = 268

That gives us the sum, which is

268
192

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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

268
192
 ÷ 2 =
134
96

So far so good... let's try to divide by that number again.

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

134
96
 ÷ 2 =
67
48

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. So next you try the next prime number, which is 53...

No good. 53 is larger than 48. So we're done reducing.

And we're done! Here's the final answer to 9/16 + 10/12

9
16
 +
10
12
 =
67
48
© 2014 Randy Tayler

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