math help

What is 9/34 + 3/6?

What is 9/34 + 3/6?

This is how we add

9
34
 +
3
6

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we 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 3 by 34, and get 102, then multiply 34 by 6 and get 204.

3/6 times 34

So now our fractions look like this:

54
204
 +
102
204

Step 2

Since our denominators match, we can add the numerators.

54 + 102 = 156

Now we have an answer.

156
204

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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:

156
204
 ÷ 2 =
78
102

Now, try the same number again.

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

78
102
 ÷ 2 =
39
51

Now, try the same number again.

Nope. Try the next prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

39
51
 ÷ 3 =
13
17

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

No good. 17 is larger than 13. So we're done reducing.

Congratulations! Here's your final answer to 9/34 + 3/6

9
34
 +
3
6
 =
13
17
© 2014 Randy Tayler

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