math help

What is 5/7 + 10/12?

What is 5/7 + 10/12?

This is how to add

5
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 5 by 12, and get 60, then we multiply 7 by 12 and get 84.

5/7 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:

60
84
 +
70
84

Step 2

Since our denominators match, we can add the numerators.

60 + 70 = 130

This yields the answer

130
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:

130
84
 ÷ 2 =
65
42

Now, try the same number again.

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

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...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

No good. 43 is larger than 42. So we're done reducing.

Congratulations! Here's your final answer to 5/7 + 10/12

5
7
 +
10
12
 =
65
42
© 2014 Randy Tayler

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