math help

What is 3/64 + 6/12?

What is 3/64 + 6/12?

Let's add

3
64
 +
6
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 3 by 12, and get 36, then we multiply 64 by 12 and get 768.

3/64 times 12

Now for the second term. You multiply 6 by 64, and get 384, then multiply 64 by 12 and get 768.

6/12 times 64

This gives us a new problem that looks like so:

36
768
 +
384
768

Step 2

Since our denominators match, we can add the numerators.

36 + 384 = 420

So what's the answer so far?

420
768

Step 3

Can this fraction be reduced?

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

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

420
768
 ÷ 2 =
210
384

Now, try the same number again.

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

210
384
 ÷ 2 =
105
192

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:

105
192
 ÷ 3 =
35
64

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...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

No good. 37 is larger than 35. So we're done reducing.

Congratulations! Here's your final answer to 3/64 + 6/12

3
64
 +
6
12
 =
35
64
© 2014 Randy Tayler

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