math help

What is 9/32 + 3/6?

What is 9/32 + 3/6?

Let's add

9
32
 +
3
6

Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 9 by 6, and get 54, then we multiply 32 by 6 and get 192.

9/32 times 6

Do the same for the second term. We multiply 3 by 32, and get 96, then multiply 32 by 6 and get 192.

3/6 times 32

The problem now has new fractions to add:

54
192
 +
96
192

Step 2

Since our denominators match, we can add the numerators.

54 + 96 = 150

This yields the answer

150
192

Step 3

The last step is to reduce the fraction if we can.

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
192
 ÷ 2 =
75
96

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

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

75
96
 ÷ 3 =
25
32

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. 29 is larger than 25. So we're done reducing.

And we're done! Here's the final answer to 9/32 + 3/6

9
32
 +
3
6
 =
25
32
© 2014 Randy Tayler

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