math help

What is 5/9 + 10/12?

What is 5/9 + 10/12?

Let's add

5
9
+
10
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 5 by 12, and get 60, then we multiply 9 by 12 and get 108.

5/9 times 12

Do the same for the second term. We multiply 10 by 9, and get 90, then multiply 9 by 12 and get 108.

10/12 times 9

So now our fractions look like this:

60
108
+
90
108

Step 2

Since our denominators match, we can add the numerators.

60 + 90 = 150

Now we have an answer.

150
108

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:

150
108
÷ 2 =
75
54

Let's try dividing by that again...

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

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

75
54
÷ 3 =
25
18

Let's try dividing by that again...

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...

No good. 19 is larger than 18. So we're done reducing.

There you have it! Here's the final answer to 5/9 + 10/12

5
9
+
10
12
=
25
18
© 2014 Randy Tayler