math help

What is 9/16 + 6/12?

What is 9/16 + 6/12?

Let's add

9
16
 +
6
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 6 by 16, and get 96, then multiply 16 by 12 and get 192.

6/12 times 16

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

108
192
 +
96
192

Step 2

Since our denominators match, we can add the numerators.

108 + 96 = 204

Answer:

204
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:

204
192
 ÷ 2 =
102
96

Now, try the same number again.

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

102
96
 ÷ 2 =
51
48

Now, try the same number again.

Nope. Try the next prime number, 3...

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

51
48
 ÷ 3 =
17
16

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

No good. 17 is larger than 16. So we're done reducing.

Congratulations! Here's your final answer to 9/16 + 6/12

9
16
 +
6
12
 =
17
16
© 2014 Randy Tayler

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