math help

What is 100/24 + 6/10?

What is 100/24 + 6/10?

Here's how to add

100
24
 +
6
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 100 by 10, and get 1000, then we multiply 24 by 10 and get 240.

100/24 times 10

Do the same for the second term. We multiply 6 by 24, and get 144, then multiply 24 by 10 and get 240.

6/10 times 24

So now our fractions look like this:

1000
240
 +
144
240

Step 2

Since our denominators match, we can add the numerators.

1000 + 144 = 1144

Now we have an answer.

1144
240

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:

1144
240
 ÷ 2 =
572
120

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:

572
120
 ÷ 2 =
286
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:

286
60
 ÷ 2 =
143
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 + 6/10

100
24
 +
6
10
 =
143
30
© 2014 Randy Tayler

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