math help

What is 3/9 + 10/12?

What is 3/9 + 10/12?

This is how to add

3
9
+
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 3 by 12, and get 36, then we multiply 9 by 12 and get 108.

3/9 times 12

Do the same for the second term. We multiply 10 by 9, and get 90, then multiply 9 by 12 and get 108.

10/12 times 9

The problem now has new fractions to add:

36
108
+
90
108

Step 2

Since our denominators match, we can add the numerators.

36 + 90 = 126

This yields the answer

126
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:

126
108
÷ 2 =
63
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:

63
54
÷ 3 =
21
18

Now, try the same number again.

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

21
18
÷ 3 =
7
6

Now, try the same number again.

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

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

No good. 7 is larger than 6. So we're done reducing.

Congratulations! Here's your final answer to 3/9 + 10/12

3
9
+
10
12
=
7
6
© 2014 Randy Tayler