Here's the question you clicked on:
careless850
Simplify!
\[\frac {12x^{5}}{20x^{2}}\]
can you simplify just the numbers? the 12/20 part?
divide them by 4..3/5 is the answer..
I want to know how to do this.
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
but the thing is. how would i know how to do that?
the x's are actually not too hard, if you remember this rule: if dividing x's to different powers, subtract the powers.
\[(12/20) \div4=3/5\]
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
but what aout the powers?
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
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)
So, on my problem, we'd subtract?
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
notice that the rule is just a fast way to get to the answer 5-2= 3
so my answer would ACTUALLY be \[\frac {3}{5}x^{3}\]
Could you help with another?