math help

What is 30/50 + 2/6?

What is 30/50 + 2/6?

Here's how we add

30
50
 +
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 30 by 6, and get 180, then we multiply 50 by 6 and get 300.

30/50 times 6

Do the same for the second term. We multiply 2 by 50, and get 100, then multiply 50 by 6 and get 300.

2/6 times 50

So now our fractions look like this:

180
300
 +
100
300

Step 2

Since our denominators match, we can add the numerators.

180 + 100 = 280

So the answer is:

280
300

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:

280
300
 ÷ 2 =
140
150

Now, try the same number again.

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

140
150
 ÷ 2 =
70
75

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

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

70
75
 ÷ 5 =
14
15

Now, try the same number again.

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

No good. 17 is larger than 14. So we're done reducing.

Congratulations! Here's your final answer to 30/50 + 2/6

30
50
 +
2
6
 =
14
15
© 2014 Randy Tayler

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