math help

What is 31/12 + 2/10?

What is 31/12 + 2/10?

This is how to add

31
12
+
2
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 31 by 10, and get 310, then we multiply 12 by 10 and get 120.

31/12 times 10

Now for the second term. You multiply 2 by 12, and get 24, then multiply 12 by 10 and get 120.

2/10 times 12

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

310
120
+
24
120

Step 2

Since our denominators match, we can add the numerators.

310 + 24 = 334

That gives us the sum, which is

334
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:

334
120
÷ 2 =
167
60

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

No good. 61 is larger than 60. So we're done reducing.

Congratulations! Here's your final answer to 31/12 + 2/10

31
12
+
2
10
=
167
60
© 2014 Randy Tayler