math help

What is 9/34 + 6/8?

What is 9/34 + 6/8?

Let's add

9
34
 +
6
8

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 9 by 8, and get 72, then we multiply 34 by 8 and get 272.

9/34 times 8

Now for the second term. You multiply 6 by 34, and get 204, then multiply 34 by 8 and get 272.

6/8 times 34

This gives us a new problem that looks like so:

72
272
 +
204
272

Step 2

Since our denominators match, we can add the numerators.

72 + 204 = 276

That gives us an answer of

276
272

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:

276
272
 ÷ 2 =
138
136

Let's try dividing by that again...

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

138
136
 ÷ 2 =
69
68

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...

No good. 71 is larger than 69. So we're done reducing.

There you have it! Here's the final answer to 9/34 + 6/8

9
34
 +
6
8
 =
69
68
© 2014 Randy Tayler

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