math help

What is 100/24 + 2/5?

What is 100/24 + 2/5?

Here's how you add

100
24
+
2
5

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 100 by 5, and get 500, then we multiply 24 by 5 and get 120.

100/24 times 5

Now for the second term. You multiply 2 by 24, and get 48, then multiply 24 by 5 and get 120.

2/5 times 24

We now have a new problem, that looks like this:

500
120
+
48
120

Step 2

Since our denominators match, we can add the numerators.

500 + 48 = 548

Answer:

548
120

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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

548
120
÷ 2 =
274
60

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

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

274
60
÷ 2 =
137
30

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...

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. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. 31 is larger than 30. So we're done reducing.

And we're done! Here's the final answer to 100/24 + 2/5

100
24
+
2
5
=
137
30
© 2014 Randy Tayler