math help

What is 31/12 + 4/10?

What is 31/12 + 4/10?

Let's add

31
12
 +
4
10

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

31/12 times 10

Now for the second term. You multiply 4 by 12, and get 48, then multiply 12 by 10 and get 120.

4/10 times 12

This gives us a new problem that looks like so:

310
120
 +
48
120

Step 2

Since our denominators match, we can add the numerators.

310 + 48 = 358

That gives us an answer of

358
120

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:

358
120
 ÷ 2 =
179
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 + 4/10

31
12
 +
4
10
 =
179
60
© 2014 Randy Tayler

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