## anonymous 3 years ago Perform the indicated operation. 9/32-1/16 I did the math: 9*16/32*16 - 1*32/32*16 = 144/512 - 32/512 = 112/512 How would I simplify this?

1. theEric

I would recommend that you start like so: $\frac{9}{32}-\frac{1}{16}=$$\frac{9}{32}-\frac{1*2}{16*2}=$ $\frac{9}{32}-\frac{2}{32}= \frac{7}{32}$

2. theEric

However, $\frac{112}{512}$is also correct, and we can simplify it so you know how for another time!

3. anonymous

Oh ok, that would be great if you could help with that. Im lost with that big of a number

4. theEric

Okay! The quickest way is to divide by the "greatest common factor". But then you have to know the greatest common factor. So instead, I divide top and bottom by prime numbers to get whole numbers on top and bottom until I can't anymore!

5. theEric

I divide top and bottom by two until I get a decimal from one.

6. anonymous

So divide them by 2 until the smallest number can't divide down?

7. theEric

$\frac{112}{512}=\frac{112\div2}{512\div2}=\frac{56}{256}$

8. theEric

Yep! Keep on dividing down.

9. anonymous

Oh, I kept dividing till I got 1/2

10. anonymous

But the answers are: 1/4. 5/16. and 7/32

11. theEric

$\frac{56\div2}{256\div2}=\frac{28}{128}$

12. theEric

$\frac{28\div2}{128\div2}=\frac{14}{64}$

13. anonymous

oh so just divide by 2 one more time?

14. theEric

$\frac{14\div2}{64\div2}=\frac{7}{32}$

15. theEric

7 is a prime number, so it can't be divided by anything but itself to get a whole number. So you could divide top and bottom by 7, but 7 doesn't go evenly into 32, so you're left with $\frac{7}{32}$

16. theEric

The trick is dividing by prime numbers as long as you can.

17. theEric

Once you hit a prime number, you know it can be divided only by itself. Once a prime number is on the bottom, you're done (unless you divide the bottom by itself, and then you don't have a fraction). For the top, just keep trying to divide by prime numbers until there are no prime numbers left that are smaller than the number on top.

18. theEric

Thanks! Take care! Ask any follow-up questions here and I'll look for them later! Lists of prime numbers are on the internet!