math help

What is 31/12 + 7/10?

What is 31/12 + 7/10?

Here's how we add

31
12
 +
7
10

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 31 by 10, and get 310, then we multiply 12 by 10 and get 120.

31/12 times 10

Do the same for the second term. We multiply 7 by 12, and get 84, then multiply 12 by 10 and get 120.

7/10 times 12

So now our fractions look like this:

310
120
 +
84
120

Step 2

Since our denominators match, we can add the numerators.

310 + 84 = 394

Now we have an answer.

394
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:

394
120
 ÷ 2 =
197
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 31/12 + 7/10

31
12
 +
7
10
 =
197
60
© 2014 Randy Tayler

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