math help

What is 4/10 + 10/11?

What is 4/10 + 10/11?

Here's how to add

4
10
+
10
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 4 by 11, and get 44, then we multiply 10 by 11 and get 110.

4/10 times 11

Now for the second term. You multiply 10 by 10, and get 100, then multiply 10 by 11 and get 110.

10/11 times 10

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

44
110
+
100
110

Step 2

Since our denominators match, we can add the numerators.

44 + 100 = 144

Answer:

144
110

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:

144
110
÷ 2 =
72
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 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. 59 is larger than 55. So we're done reducing.

And we're done! Here's the final answer to 4/10 + 10/11

4
10
+
10
11
=
72
55
© 2014 Randy Tayler

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