math help

What is 9/60 + 6/9?

What is 9/60 + 6/9?

Here's how to add

9
60
 +
6
9

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 9 by 9, and get 81, then we multiply 60 by 9 and get 540.

9/60 times 9

Do the same for the second term. We multiply 6 by 60, and get 360, then multiply 60 by 9 and get 540.

6/9 times 60

So now our fractions look like this:

81
540
 +
360
540

Step 2

Since our denominators match, we can add the numerators.

81 + 360 = 441

Now we have an answer.

441
540

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...

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
540
 ÷ 3 =
147
180

Let's try dividing by that again...

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

147
180
 ÷ 3 =
49
60

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 49. So we're done reducing.

There you have it! Here's the final answer to 9/60 + 6/9

9
60
 +
6
9
 =
49
60
© 2014 Randy Tayler

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