math help

What is 6/19 + 6/8?

What is 6/19 + 6/8?

Here's how we add

6
19
 +
6
8

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 6 by 8, and get 48, then we multiply 19 by 8 and get 152.

6/19 times 8

Now for the second term. You multiply 6 by 19, and get 114, then multiply 19 by 8 and get 152.

6/8 times 19

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

48
152
 +
114
152

Step 2

Since our denominators match, we can add the numerators.

48 + 114 = 162

That gives us the sum, which is

162
152

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:

162
152
 ÷ 2 =
81
76

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 76. So we're done reducing.

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

6
19
 +
6
8
 =
81
76
© 2014 Randy Tayler

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