## anonymous 4 years ago Simplify!

1. anonymous

$\frac {12x^{5}}{20x^{2}}$

2. anonymous

..help?

3. phi

can you simplify just the numbers? the 12/20 part?

4. anonymous

I don't know how..

5. anonymous

3x^3/5

6. anonymous

divide them by 4..3/5 is the answer..

7. anonymous

I want to know how to do this.

8. phi

can you find the factors of 12? like 3*4 for example for 20, 4*5 so the numbers part is $\frac{3\cdot 4}{4\cdot 5}$ the 4's "cancel" (that means 4/4 =1) you get 3/5

9. anonymous

but the thing is. how would i know how to do that?

10. phi

the x's are actually not too hard, if you remember this rule: if dividing x's to different powers, subtract the powers.

11. anonymous

$(12/20) \div4=3/5$

12. phi

but the thing is. how would i know how to do that? for 12/20 notice that both are even. so you divide both by 2. 6/10 they are still even, divide by 2 again 3/5

13. anonymous

but what aout the powers?

14. phi

there a simple tricks to know if a number is divisible by another: a number is even 2 sum of digits divisible by 3 then the number is divisible by 3 both of the above, then divisible by 6 ends in 0 or 5, divisible by 5

15. phi

powers are easier. subtract when dividing. add when multiplying here is how to remember: x^2 means x*x x^3 means x*x*x multiply: x^2 * x^3 = x*x * x*x*x count the x's It is x^5 (the sum of 2 and 3)

16. anonymous

hm...

17. anonymous

So, on my problem, we'd subtract?

18. phi

for $\frac{x^5}{x^2} = \frac{x*x*x*x*x}{x*x}$ we can cancel 2 of the x's from the top and bottom to get $\frac{x^5}{x^2} = \frac{x*x*x*\cancel{x}*\cancel{x}}{\cancel{x}*\cancel{x}}= x*x*x$ and x*x*x is written as $$x^3$$ because people don't like writing out all those x's

19. phi

notice that the rule is just a fast way to get to the answer 5-2= 3

20. anonymous

so my answer would ACTUALLY be $\frac {3}{5}x^{3}$

21. phi

yes.

22. anonymous

Could you help with another?

23. phi

sure