math help

What is 25/9 + 6/12?

What is 25/9 + 6/12?

This is how we add

25
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 25 by 12, and get 300, then we multiply 9 by 12 and get 108.

25/9 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:

300
108
 +
54
108

Step 2

Since our denominators match, we can add the numerators.

300 + 54 = 354

Now we have an answer.

354
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:

354
108
 ÷ 2 =
177
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:

177
54
 ÷ 3 =
59
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 25/9 + 6/12

25
9
 +
6
12
 =
59
18
© 2014 Randy Tayler

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