math help

What is 9/34 + 10/12?

What is 9/34 + 10/12?

This is how you add

9
34
 +
10
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 9 by 12, and get 108, then we multiply 34 by 12 and get 408.

9/34 times 12

Now for the second term. You multiply 10 by 34, and get 340, then multiply 34 by 12 and get 408.

10/12 times 34

This gives us a new problem that looks like so:

108
408
 +
340
408

Step 2

Since our denominators match, we can add the numerators.

108 + 340 = 448

That gives us an answer of

448
408

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:

448
408
 ÷ 2 =
224
204

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:

224
204
 ÷ 2 =
112
102

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:

112
102
 ÷ 2 =
56
51

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 51. So we're done reducing.

And we're done! Here's the final answer to 9/34 + 10/12

9
34
 +
10
12
 =
56
51
© 2014 Randy Tayler

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