math help

What is 6/19 + 8/12?

What is 6/19 + 8/12?

This is how we add

6
19
 +
8
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 6 by 12, and get 72, then we multiply 19 by 12 and get 228.

6/19 times 12

Now for the second term. You multiply 8 by 19, and get 152, then multiply 19 by 12 and get 228.

8/12 times 19

This gives us a new problem that looks like so:

72
228
 +
152
228

Step 2

Since our denominators match, we can add the numerators.

72 + 152 = 224

So what's the answer so far?

224
228

Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

224
228
 ÷ 2 =
112
114

Let's try dividing by that again...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

112
114
 ÷ 2 =
56
57

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...

No good. 59 is larger than 56. So we're done reducing.

There you have it! Here's the final answer to 6/19 + 8/12

6
19
 +
8
12
 =
56
57
© 2014 Randy Tayler

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