math help

What is 97/75 + 2/6?

What is 97/75 + 2/6?

Here's how you add

97
75
 +
2
6

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 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 2 by 75, and get 150, then multiply 75 by 6 and get 450.

2/6 times 75

So now our fractions look like this:

582
450
 +
150
450

Step 2

Since our denominators match, we can add the numerators.

582 + 150 = 732

Now we have an answer.

732
450

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:

732
450
 ÷ 2 =
366
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:

366
225
 ÷ 3 =
122
75

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...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

Nope! So now we try the next greatest prime number, 67...

Nope! So now we try the next greatest prime number, 71...

Nope! So now we try the next greatest prime number, 73...

Nope! So now we try the next greatest prime number, 79...

No good. 79 is larger than 75. So we're done reducing.

There you have it! Here's the final answer to 97/75 + 2/6

97
75
 +
2
6
 =
122
75
© 2014 Randy Tayler

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