math help

What is 30/50 + 10/12?

What is 30/50 + 10/12?

Here's how we add

30
50
 +
10
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 30 by 12, and get 360, then we multiply 50 by 12 and get 600.

30/50 times 12

Do the same for the second term. We multiply 10 by 50, and get 500, then multiply 50 by 12 and get 600.

10/12 times 50

The problem now has new fractions to add:

360
600
 +
500
600

Step 2

Since our denominators match, we can add the numerators.

360 + 500 = 860

The sum we get is

860
600

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:

860
600
 ÷ 2 =
430
300

Let's try dividing by that again...

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

430
300
 ÷ 2 =
215
150

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

215
150
 ÷ 5 =
43
30

Let's try dividing by that again...

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...

No good. 31 is larger than 30. So we're done reducing.

There you have it! Here's the final answer to 30/50 + 10/12

30
50
 +
10
12
 =
43
30
© 2014 Randy Tayler

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