math help

What is 10/11 + 9/10?

What is 10/11 + 9/10?

Here's how you add

10
11
 +
9
10

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 10 by 10, and get 100, then we multiply 11 by 10 and get 110.

10/11 times 10

Do the same for the second term. We multiply 9 by 11, and get 99, then multiply 11 by 10 and get 110.

9/10 times 11

So now our fractions look like this:

100
110
 +
99
110

Step 2

Since our denominators match, we can add the numerators.

100 + 99 = 199

So the answer is:

199
110

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...

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

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...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

Nope. Try the next prime number, 67...

Nope. Try the next prime number, 71...

Nope. Try the next prime number, 73...

Nope. Try the next prime number, 79...

Nope. Try the next prime number, 83...

Nope. Try the next prime number, 89...

Nope. Try the next prime number, 97...

Nope. Try the next prime number, 101...

Nope. Try the next prime number, 103...

Nope. Try the next prime number, 107...

Nope. Try the next prime number, 109...

Nope. Try the next prime number, 113...

No good. 113 is larger than 110. So we're done reducing.

Congratulations! Here's your final answer to 10/11 + 9/10

10
11
 +
9
10
 =
199
110
© 2014 Randy Tayler

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