math help

What is 9/48 + 6/9?

What is 9/48 + 6/9?

This is how you add

9
48
 +
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 48 by 9 and get 432.

9/48 times 9

Do the same for the second term. We multiply 6 by 48, and get 288, then multiply 48 by 9 and get 432.

6/9 times 48

So now our fractions look like this:

81
432
 +
288
432

Step 2

Since our denominators match, we can add the numerators.

81 + 288 = 369

So the answer is:

369
432

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:

369
432
 ÷ 3 =
123
144

Let's try dividing by that again...

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

123
144
 ÷ 3 =
41
48

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...

No good. 43 is larger than 41. So we're done reducing.

There you have it! Here's the final answer to 9/48 + 6/9

9
48
 +
6
9
 =
41
48
© 2014 Randy Tayler

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