math help

What is 3/10 + 11/12?

What is 3/10 + 11/12?

Let's add

3
10
 +
11
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 3 by 12, and get 36, then we multiply 10 by 12 and get 120.

3/10 times 12

Do the same for the second term. We multiply 11 by 10, and get 110, then multiply 10 by 12 and get 120.

11/12 times 10

So now our fractions look like this:

36
120
 +
110
120

Step 2

Since our denominators match, we can add the numerators.

36 + 110 = 146

Now we have an answer.

146
120

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:

146
120
 ÷ 2 =
73
60

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...

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...

Nope! So now we try the next greatest prime number, 47...

Nope! So now we try the next greatest prime number, 53...

Nope! So now we try the next greatest prime number, 59...

Nope! So now we try the next greatest prime number, 61...

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

There you have it! Here's the final answer to 3/10 + 11/12

3
10
 +
11
12
 =
73
60
© 2014 Randy Tayler

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