math help

What is 48/30 + 6/11?

What is 48/30 + 6/11?

Here's how we add

48
30
+
6
11

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 48 by 11, and get 528, then we multiply 30 by 11 and get 330.

48/30 times 11

Now for the second term. You multiply 6 by 30, and get 180, then multiply 30 by 11 and get 330.

6/11 times 30

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

528
330
+
180
330

Step 2

Since our denominators match, we can add the numerators.

528 + 180 = 708

That gives us the sum, which is

708
330

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:

708
330
÷ 2 =
354
165

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:

354
165
÷ 3 =
118
55

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. So next you try the next prime number, which is 53...

No good. So next you try the next prime number, which is 59...

No good. 59 is larger than 55. So we're done reducing.

And we're done! Here's the final answer to 48/30 + 6/11

48
30
+
6
11
=
118
55
© 2014 Randy Tayler