math help

What is 7/11 + 4/12?

What is 7/11 + 4/12?

This is how to add

7
11
 +
4
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 11 by 12 and get 132.

7/11 times 12

Do the same for the second term. We multiply 4 by 11, and get 44, then multiply 11 by 12 and get 132.

4/12 times 11

The problem now has new fractions to add:

84
132
 +
44
132

Step 2

Since our denominators match, we can add the numerators.

84 + 44 = 128

This yields the answer

128
132

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:

128
132
 ÷ 2 =
64
66

Now, try the same number again.

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

64
66
 ÷ 2 =
32
33

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...

No good. 37 is larger than 32. So we're done reducing.

Congratulations! Here's your final answer to 7/11 + 4/12

7
11
 +
4
12
 =
32
33
© 2014 Randy Tayler

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