math help

What is 21/33 + 1/7?

What is 21/33 + 1/7?

This is how to add

21
33
+
1
7

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 7, and get 147, then we multiply 33 by 7 and get 231.

21/33 times 7

Do the same for the second term. We multiply 1 by 33, and get 33, then multiply 33 by 7 and get 231.

1/7 times 33

The problem now has new fractions to add:

147
231
+
33
231

Step 2

Since our denominators match, we can add the numerators.

147 + 33 = 180

The sum we get is

180
231

Step 3

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

To find out, we try dividing it by 2...

No good. So next you try the next prime number, which is 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

180
231
÷ 3 =
60
77

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. So next you try the next prime number, which is 53...

No good. So next you try the next prime number, which is 59...

No good. So next you try the next prime number, which is 61...

No good. 61 is larger than 60. So we're done reducing.

And we're done! Here's the final answer to 21/33 + 1/7

21
33
+
1
7
=
60
77
© 2014 Randy Tayler