math help

What is 25/36 + 5/10?

What is 25/36 + 5/10?

This is how to add

25
36
+
5
10

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 10, and get 250, then we multiply 36 by 10 and get 360.

25/36 times 10

Do the same for the second term. We multiply 5 by 36, and get 180, then multiply 36 by 10 and get 360.

5/10 times 36

So now our fractions look like this:

250
360
+
180
360

Step 2

Since our denominators match, we can add the numerators.

250 + 180 = 430

Now we have an answer.

430
360

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:

430
360
÷ 2 =
215
180

Now, try the same number again.

Nope. Try the next prime number, 3...

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

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

215
180
÷ 5 =
43
36

Now, try the same number again.

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 36. So we're done reducing.

Congratulations! Here's your final answer to 25/36 + 5/10

25
36
+
5
10
=
43
36
© 2014 Randy Tayler