math help

What is 4/52 + 9/12?

What is 4/52 + 9/12?

Here's how to add

4
52
 +
9
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 4 by 12, and get 48, then we multiply 52 by 12 and get 624.

4/52 times 12

Now for the second term. You multiply 9 by 52, and get 468, then multiply 52 by 12 and get 624.

9/12 times 52

This gives us a new problem that looks like so:

48
624
 +
468
624

Step 2

Since our denominators match, we can add the numerators.

48 + 468 = 516

So what's the answer so far?

516
624

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:

516
624
 ÷ 2 =
258
312

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:

258
312
 ÷ 2 =
129
156

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...

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

129
156
 ÷ 3 =
43
52

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 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. 47 is larger than 43. So we're done reducing.

And we're done! Here's the final answer to 4/52 + 9/12

4
52
 +
9
12
 =
43
52
© 2014 Randy Tayler

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