math help

What is 48/30 + 6/12?

What is 48/30 + 6/12?

Here's how you add

48
30
 +
6
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 48 by 12, and get 576, then we multiply 30 by 12 and get 360.

48/30 times 12

Do the same for the second term. We multiply 6 by 30, and get 180, then multiply 30 by 12 and get 360.

6/12 times 30

So now our fractions look like this:

576
360
 +
180
360

Step 2

Since our denominators match, we can add the numerators.

576 + 180 = 756

So the answer is:

756
360

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:

756
360
 ÷ 2 =
378
180

Let's try dividing by that again...

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

378
180
 ÷ 2 =
189
90

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:

189
90
 ÷ 3 =
63
30

Let's try dividing by that again...

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

63
30
 ÷ 3 =
21
10

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...

No good. 11 is larger than 10. So we're done reducing.

There you have it! Here's the final answer to 48/30 + 6/12

48
30
 +
6
12
 =
21
10
© 2014 Randy Tayler

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