math help

What is 9/34 + 1/6?

What is 9/34 + 1/6?

Let's add

9
34
 +
1
6

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 9 by 6, and get 54, then we multiply 34 by 6 and get 204.

9/34 times 6

Do the same for the second term. We multiply 1 by 34, and get 34, then multiply 34 by 6 and get 204.

1/6 times 34

The problem now has new fractions to add:

54
204
 +
34
204

Step 2

Since our denominators match, we can add the numerators.

54 + 34 = 88

This yields the answer

88
204

Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

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

88
204
 ÷ 2 =
44
102

So far so good... let's try to divide by that number again.

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

44
102
 ÷ 2 =
22
51

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. 23 is larger than 22. So we're done reducing.

And we're done! Here's the final answer to 9/34 + 1/6

9
34
 +
1
6
 =
22
51
© 2014 Randy Tayler

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