math help

What is 20/64 + 5/6?

What is 20/64 + 5/6?

Here's how we add

20
64
 +
5
6

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 20 by 6, and get 120, then we multiply 64 by 6 and get 384.

20/64 times 6

Now for the second term. You multiply 5 by 64, and get 320, then multiply 64 by 6 and get 384.

5/6 times 64

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

120
384
 +
320
384

Step 2

Since our denominators match, we can add the numerators.

120 + 320 = 440

That gives us the sum, which is

440
384

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:

440
384
 ÷ 2 =
220
192

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:

220
192
 ÷ 2 =
110
96

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:

110
96
 ÷ 2 =
55
48

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 48. So we're done reducing.

And we're done! Here's the final answer to 20/64 + 5/6

20
64
 +
5
6
 =
55
48
© 2014 Randy Tayler

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