math help

What is 49/9 + 6/10?

What is 49/9 + 6/10?

Here's how we add

49
9
+
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 49 by 10, and get 490, then we multiply 9 by 10 and get 90.

49/9 times 10

Do the same for the second term. We multiply 6 by 9, and get 54, then multiply 9 by 10 and get 90.

6/10 times 9

The problem now has new fractions to add:

490
90
+
54
90

Step 2

Since our denominators match, we can add the numerators.

490 + 54 = 544

This yields the answer

544
90

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:

544
90
÷ 2 =
272
45

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 3...

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. 47 is larger than 45. So we're done reducing.

And we're done! Here's the final answer to 49/9 + 6/10

49
9
+
6
10
=
272
45
© 2014 Randy Tayler