math help

What is 31/12 + 9/10?

What is 31/12 + 9/10?

This is how to add

31
12
 +
9
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 31 by 10, and get 310, then we multiply 12 by 10 and get 120.

31/12 times 10

Do the same for the second term. We multiply 9 by 12, and get 108, then multiply 12 by 10 and get 120.

9/10 times 12

The problem now has new fractions to add:

310
120
 +
108
120

Step 2

Since our denominators match, we can add the numerators.

310 + 108 = 418

The sum we get is

418
120

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:

418
120
 ÷ 2 =
209
60

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. 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 31/12 + 9/10

31
12
 +
9
10
 =
209
60
© 2014 Randy Tayler

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