math help

What is 7/20 + 10/12?

What is 7/20 + 10/12?

Here's how to add

7
20
 +
10
12

Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 7 by 12, and get 84, then we multiply 20 by 12 and get 240.

7/20 times 12

Now for the second term. You multiply 10 by 20, and get 200, then multiply 20 by 12 and get 240.

10/12 times 20

This gives us a new problem that looks like so:

84
240
 +
200
240

Step 2

Since our denominators match, we can add the numerators.

84 + 200 = 284

That gives us an answer of

284
240

Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

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

284
240
 ÷ 2 =
142
120

Now, try the same number again.

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

142
120
 ÷ 2 =
71
60

Now, try the same number again.

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

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

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...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

Nope. Try the next prime number, 53...

Nope. Try the next prime number, 59...

Nope. Try the next prime number, 61...

No good. 61 is larger than 60. So we're done reducing.

Congratulations! Here's your final answer to 7/20 + 10/12

7
20
 +
10
12
 =
71
60
© 2014 Randy Tayler

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