math help

What is 7/9 + 6/12?

What is 7/9 + 6/12?

This is how to add

7
9
 +
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 7 by 12, and get 84, then we multiply 9 by 12 and get 108.

7/9 times 12

Do the same for the second term. We multiply 6 by 9, and get 54, then multiply 9 by 12 and get 108.

6/12 times 9

The problem now has new fractions to add:

84
108
 +
54
108

Step 2

Since our denominators match, we can add the numerators.

84 + 54 = 138

This yields the answer

138
108

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:

138
108
 ÷ 2 =
69
54

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:

69
54
 ÷ 3 =
23
18

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...

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

No good. 19 is larger than 18. So we're done reducing.

Congratulations! Here's your final answer to 7/9 + 6/12

7
9
 +
6
12
 =
23
18
© 2014 Randy Tayler

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