math help

What is 21/11 + 6/7?

What is 21/11 + 6/7?

This is how we add

21
11
 +
6
7

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 21 by 7, and get 147, then we multiply 11 by 7 and get 77.

21/11 times 7

Now for the second term. You multiply 6 by 11, and get 66, then multiply 11 by 7 and get 77.

6/7 times 11

This gives us a new problem that looks like so:

147
77
 +
66
77

Step 2

Since our denominators match, we can add the numerators.

147 + 66 = 213

So what's the answer so far?

213
77

Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

No good. 79 is larger than 77. So we're done reducing.

There you have it! Here's the final answer to 21/11 + 6/7

21
11
 +
6
7
 =
213
77
© 2014 Randy Tayler

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