math help

What is 7/20 + 8/12?

What is 7/20 + 8/12?

Here's how you add

7
20
 +
8
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 7 by 12, and get 84, then we multiply 20 by 12 and get 240.

7/20 times 12

Now for the second term. You multiply 8 by 20, and get 160, then multiply 20 by 12 and get 240.

8/12 times 20

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

84
240
 +
160
240

Step 2

Since our denominators match, we can add the numerators.

84 + 160 = 244

That gives us the sum, which is

244
240

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:

244
240
 ÷ 2 =
122
120

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:

122
120
 ÷ 2 =
61
60

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. So next you try the next prime number, which is 59...

No good. So next you try the next prime number, which is 61...

No good. 61 is larger than 60. So we're done reducing.

And we're done! Here's the final answer to 7/20 + 8/12

7
20
 +
8
12
 =
61
60
© 2014 Randy Tayler

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