math help

What is 97/75 + 8/12?

What is 97/75 + 8/12?

This is how we add

97
75
 +
8
12

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 97 by 12, and get 1164, then we multiply 75 by 12 and get 900.

97/75 times 12

Do the same for the second term. We multiply 8 by 75, and get 600, then multiply 75 by 12 and get 900.

8/12 times 75

So now our fractions look like this:

1164
900
 +
600
900

Step 2

Since our denominators match, we can add the numerators.

1164 + 600 = 1764

So the answer is:

1764
900

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:

1764
900
 ÷ 2 =
882
450

Let's try dividing by that again...

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

882
450
 ÷ 2 =
441
225

Let's try dividing by that again...

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

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

441
225
 ÷ 3 =
147
75

Let's try dividing by that again...

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

147
75
 ÷ 3 =
49
25

Let's try dividing by that again...

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...

No good. 29 is larger than 25. So we're done reducing.

There you have it! Here's the final answer to 97/75 + 8/12

97
75
 +
8
12
 =
49
25
© 2014 Randy Tayler

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