math help

What is 97/75 + 4/6?

What is 97/75 + 4/6?

Here's how to add

97
75
 +
4
6

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 97 by 6, and get 582, then we multiply 75 by 6 and get 450.

97/75 times 6

Do the same for the second term. We multiply 4 by 75, and get 300, then multiply 75 by 6 and get 450.

4/6 times 75

The problem now has new fractions to add:

582
450
 +
300
450

Step 2

Since our denominators match, we can add the numerators.

582 + 300 = 882

The sum we get is

882
450

Step 3

The last step is to reduce the fraction if we can.

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:

882
450
 ÷ 2 =
441
225

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...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

441
225
 ÷ 3 =
147
75

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

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

147
75
 ÷ 3 =
49
25

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 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. 29 is larger than 25. So we're done reducing.

And we're done! Here's the final answer to 97/75 + 4/6

97
75
 +
4
6
 =
49
25
© 2014 Randy Tayler

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