math help

What is 4/9 + 10/12?

What is 4/9 + 10/12?

Here's how to add

4
9
+
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 4 by 12, and get 48, then we multiply 9 by 12 and get 108.

4/9 times 12

Now for the second term. You multiply 10 by 9, and get 90, then multiply 9 by 12 and get 108.

10/12 times 9

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

48
108
+
90
108

Step 2

Since our denominators match, we can add the numerators.

48 + 90 = 138

Answer:

138
108

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:

138
108
÷ 2 =
69
54

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...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

69
54
÷ 3 =
23
18

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 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. 19 is larger than 18. So we're done reducing.

And we're done! Here's the final answer to 4/9 + 10/12

4
9
+
10
12
=
23
18
© 2014 Randy Tayler