math help

What is 53/9 + 6/12?

What is 53/9 + 6/12?

This is how we add

53
9
 +
6
12

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 53 by 12, and get 636, then we multiply 9 by 12 and get 108.

53/9 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

So now our fractions look like this:

636
108
 +
54
108

Step 2

Since our denominators match, we can add the numerators.

636 + 54 = 690

So the answer is:

690
108

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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:

690
108
 ÷ 2 =
345
54

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

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

345
54
 ÷ 3 =
115
18

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

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

And we're done! Here's the final answer to 53/9 + 6/12

53
9
 +
6
12
 =
115
18
© 2014 Randy Tayler

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