math help

What is 10/12 + 3/10?

What is 10/12 + 3/10?

Here's how to add

10
12
+
3
10

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 10, and get 100, then we multiply 12 by 10 and get 120.

10/12 times 10

Now for the second term. You multiply 3 by 12, and get 36, then multiply 12 by 10 and get 120.

3/10 times 12

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

100
120
+
36
120

Step 2

Since our denominators match, we can add the numerators.

100 + 36 = 136

Answer:

136
120

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:

136
120
÷ 2 =
68
60

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:

68
60
÷ 2 =
34
30

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:

34
30
÷ 2 =
17
15

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. 17 is larger than 15. So we're done reducing.

And we're done! Here's the final answer to 10/12 + 3/10

10
12
+
3
10
=
17
15
© 2014 Randy Tayler