math help

What is 97/75 + 2/12?

What is 97/75 + 2/12?

Here's how we add

97
75
 +
2
12

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 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 2 by 75, and get 150, then multiply 75 by 12 and get 900.

2/12 times 75

The problem now has new fractions to add:

1164
900
 +
150
900

Step 2

Since our denominators match, we can add the numerators.

1164 + 150 = 1314

This yields the answer

1314
900

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:

1314
900
 ÷ 2 =
657
450

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:

657
450
 ÷ 3 =
219
150

Let's try dividing by that again...

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

219
150
 ÷ 3 =
73
50

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...

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

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

No good. 53 is larger than 50. So we're done reducing.

There you have it! Here's the final answer to 97/75 + 2/12

97
75
 +
2
12
 =
73
50
© 2014 Randy Tayler

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