math help

What is 36/4 + 5/11?

What is 36/4 + 5/11?

Here's how to add

36
4
+
5
11

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 36 by 11, and get 396, then we multiply 4 by 11 and get 44.

36/4 times 11

Do the same for the second term. We multiply 5 by 4, and get 20, then multiply 4 by 11 and get 44.

5/11 times 4

So now our fractions look like this:

396
44
+
20
44

Step 2

Since our denominators match, we can add the numerators.

396 + 20 = 416

So the answer is:

416
44

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

416
44
÷ 2 =
208
22

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:

208
22
÷ 2 =
104
11

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. 13 is larger than 11. So we're done reducing.

And we're done! Here's the final answer to 36/4 + 5/11

36
4
+
5
11
=
104
11
© 2014 Randy Tayler