math help

What is 57/7 + 6/12?

What is 57/7 + 6/12?

Here's how you add

57
7
 +
6
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 6 by 7, and get 42, then multiply 7 by 12 and get 84.

6/12 times 7

The problem now has new fractions to add:

684
84
 +
42
84

Step 2

Since our denominators match, we can add the numerators.

684 + 42 = 726

This yields the answer

726
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:

726
84
 ÷ 2 =
363
42

Now, try the same number again.

Nope. Try the next prime number, 3...

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

363
42
 ÷ 3 =
121
14

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

No good. 17 is larger than 14. So we're done reducing.

Congratulations! Here's your final answer to 57/7 + 6/12

57
7
 +
6
12
 =
121
14
© 2014 Randy Tayler

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