math help

What is 21/11 + 4/6?

What is 21/11 + 4/6?

Here's how to add

21
11
 +
4
6

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 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 4 by 11, and get 44, then multiply 11 by 6 and get 66.

4/6 times 11

The problem now has new fractions to add:

126
66
 +
44
66

Step 2

Since our denominators match, we can add the numerators.

126 + 44 = 170

This yields the answer

170
66

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:

170
66
 ÷ 2 =
85
33

Let's try dividing by that again...

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...

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

There you have it! Here's the final answer to 21/11 + 4/6

21
11
 +
4
6
 =
85
33
© 2014 Randy Tayler

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