math help

What is 57/7 + 10/12?

What is 57/7 + 10/12?

This is how you add

57
7
 +
10
12

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 57 by 12, and get 684, then we multiply 7 by 12 and get 84.

57/7 times 12

Do the same for the second term. We multiply 10 by 7, and get 70, then multiply 7 by 12 and get 84.

10/12 times 7

The problem now has new fractions to add:

684
84
 +
70
84

Step 2

Since our denominators match, we can add the numerators.

684 + 70 = 754

The sum we get is

754
84

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:

754
84
 ÷ 2 =
377
42

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. 43 is larger than 42. So we're done reducing.

And we're done! Here's the final answer to 57/7 + 10/12

57
7
 +
10
12
 =
377
42
© 2014 Randy Tayler

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