math help

What is 10/11 + 4/6?

What is 10/11 + 4/6?

This is how we add

10
11
 +
4
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 10 by 6, and get 60, then we multiply 11 by 6 and get 66.

10/11 times 6

Now for the second term. You multiply 4 by 11, and get 44, then multiply 11 by 6 and get 66.

4/6 times 11

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

60
66
 +
44
66

Step 2

Since our denominators match, we can add the numerators.

60 + 44 = 104

That gives us the sum, which is

104
66

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:

104
66
 ÷ 2 =
52
33

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

No good. 37 is larger than 33. So we're done reducing.

Congratulations! Here's your final answer to 10/11 + 4/6

10
11
 +
4
6
 =
52
33
© 2014 Randy Tayler

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