math help

What is 99/7 + 10/12?

What is 99/7 + 10/12?

This is how you add

99
7
 +
10
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 10 by 7, and get 70, then multiply 7 by 12 and get 84.

10/12 times 7

So now our fractions look like this:

1188
84
 +
70
84

Step 2

Since our denominators match, we can add the numerators.

1188 + 70 = 1258

So the answer is:

1258
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:

1258
84
 ÷ 2 =
629
42

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. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. 43 is larger than 42. So we're done reducing.

And we're done! Here's the final answer to 99/7 + 10/12

99
7
 +
10
12
 =
629
42
© 2014 Randy Tayler

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