math help

What is 5/8 + 10/12?

What is 5/8 + 10/12?

Here's how to add

5
8
+
10
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 5 by 12, and get 60, then we multiply 8 by 12 and get 96.

5/8 times 12

Now for the second term. You multiply 10 by 8, and get 80, then multiply 8 by 12 and get 96.

10/12 times 8

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

60
96
+
80
96

Step 2

Since our denominators match, we can add the numerators.

60 + 80 = 140

Answer:

140
96

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:

140
96
÷ 2 =
70
48

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:

70
48
÷ 2 =
35
24

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. 29 is larger than 24. So we're done reducing.

And we're done! Here's the final answer to 5/8 + 10/12

5
8
+
10
12
=
35
24
© 2014 Randy Tayler