math help

What is 99/7 + 6/12?

What is 99/7 + 6/12?

Here's how you add

99
7
 +
6
12

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 99 by 12, and get 1188, then we multiply 7 by 12 and get 84.

99/7 times 12

Do the same for the second term. We multiply 6 by 7, and get 42, then multiply 7 by 12 and get 84.

6/12 times 7

So now our fractions look like this:

1188
84
 +
42
84

Step 2

Since our denominators match, we can add the numerators.

1188 + 42 = 1230

Now we have an answer.

1230
84

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:

1230
84
 ÷ 2 =
615
42

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:

615
42
 ÷ 3 =
205
14

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 14. So we're done reducing.

Congratulations! Here's your final answer to 99/7 + 6/12

99
7
 +
6
12
 =
205
14
© 2014 Randy Tayler

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