math help

What is 12/13 + 2/12?

What is 12/13 + 2/12?

Here's how we add

12
13
 +
2
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 12 by 12, and get 144, then we multiply 13 by 12 and get 156.

12/13 times 12

Now for the second term. You multiply 2 by 13, and get 26, then multiply 13 by 12 and get 156.

2/12 times 13

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

144
156
 +
26
156

Step 2

Since our denominators match, we can add the numerators.

144 + 26 = 170

That gives us the sum, which is

170
156

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:

170
156
 ÷ 2 =
85
78

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

No good. 79 is larger than 78. So we're done reducing.

There you have it! Here's the final answer to 12/13 + 2/12

12
13
 +
2
12
 =
85
78
© 2014 Randy Tayler

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