math help

What is 21/11 + 2/6?

What is 21/11 + 2/6?

Here's how you add

21
11
 +
2
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 21 by 6, and get 126, then we multiply 11 by 6 and get 66.

21/11 times 6

Do the same for the second term. We multiply 2 by 11, and get 22, then multiply 11 by 6 and get 66.

2/6 times 11

So now our fractions look like this:

126
66
 +
22
66

Step 2

Since our denominators match, we can add the numerators.

126 + 22 = 148

So the answer is:

148
66

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:

148
66
 ÷ 2 =
74
33

Now, try the same number again.

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...

No good. 37 is larger than 33. So we're done reducing.

Congratulations! Here's your final answer to 21/11 + 2/6

21
11
 +
2
6
 =
74
33
© 2014 Randy Tayler

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