math help

What is 21/33 + 6/10?

What is 21/33 + 6/10?

Here's how to add

21
33
 +
6
10

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 21 by 10, and get 210, then we multiply 33 by 10 and get 330.

21/33 times 10

Do the same for the second term. We multiply 6 by 33, and get 198, then multiply 33 by 10 and get 330.

6/10 times 33

The problem now has new fractions to add:

210
330
 +
198
330

Step 2

Since our denominators match, we can add the numerators.

210 + 198 = 408

The sum we get is

408
330

Step 3

The last step is to reduce the fraction if we can.

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:

408
330
 ÷ 2 =
204
165

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:

204
165
 ÷ 3 =
68
55

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...

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...

No good. 59 is larger than 55. So we're done reducing.

Congratulations! Here's your final answer to 21/33 + 6/10

21
33
 +
6
10
 =
68
55
© 2014 Randy Tayler

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