math help

What is 100/24 + 3/5?

What is 100/24 + 3/5?

This is how to add

100
24
+
3
5

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

100/24 times 5

Do the same for the second term. We multiply 3 by 24, and get 72, then multiply 24 by 5 and get 120.

3/5 times 24

So now our fractions look like this:

500
120
+
72
120

Step 2

Since our denominators match, we can add the numerators.

500 + 72 = 572

Now we have an answer.

572
120

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:

572
120
÷ 2 =
286
60

Let's try dividing by that again...

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

286
60
÷ 2 =
143
30

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

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

There you have it! Here's the final answer to 100/24 + 3/5

100
24
+
3
5
=
143
30
© 2014 Randy Tayler