math help

What is 25/9 + 6/10?

What is 25/9 + 6/10?

Let's add

25
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 25 by 10, and get 250, then we multiply 9 by 10 and get 90.

25/9 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:

250
90
 +
54
90

Step 2

Since our denominators match, we can add the numerators.

250 + 54 = 304

This yields the answer

304
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:

304
90
 ÷ 2 =
152
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 25/9 + 6/10

25
9
 +
6
10
 =
152
45
© 2014 Randy Tayler

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