math help

What is 5/10 + 10/11?

What is 5/10 + 10/11?

Let's add

5
10
+
10
11

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 5 by 11, and get 55, then we multiply 10 by 11 and get 110.

5/10 times 11

Do the same for the second term. We multiply 10 by 10, and get 100, then multiply 10 by 11 and get 110.

10/11 times 10

So now our fractions look like this:

55
110
+
100
110

Step 2

Since our denominators match, we can add the numerators.

55 + 100 = 155

Now we have an answer.

155
110

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...

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

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

155
110
÷ 5 =
31
22

Let's try dividing by that again...

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...

No good. 23 is larger than 22. So we're done reducing.

There you have it! Here's the final answer to 5/10 + 10/11

5
10
+
10
11
=
31
22
© 2014 Randy Tayler

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