math help

What is 10/3 + 10/11?

What is 10/3 + 10/11?

This is how to add

10
3
+
10
11

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 10 by 11, and get 110, then we multiply 3 by 11 and get 33.

10/3 times 11

Do the same for the second term. We multiply 10 by 3, and get 30, then multiply 3 by 11 and get 33.

10/11 times 3

The problem now has new fractions to add:

110
33
+
30
33

Step 2

Since our denominators match, we can add the numerators.

110 + 30 = 140

This yields the answer

140
33

Step 3

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

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...

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

Congratulations! Here's your final answer to 10/3 + 10/11

10
3
+
10
11
=
140
33
© 2014 Randy Tayler

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