Question

(3m^4)/(2m^2n) divided by (15m^3n^2)/(16m)

Answer 1

do you know how to solve this much simpler problem ?

3/2 divided by 15/16

Answer 2

yeah 8/5

Answer 3

how did you do it ?

Answer 4

show all steps

Answer 5

3/2 divided by 15/16; 3/2 16/15; cross out 3 and get one then cross out 15 and get 5; cross out to and get one then cross out 16 and get 8. 8/5

Answer 6

do you know this rule ?
\[\frac{(\frac{a}{b})}{(\frac{c}{d})}=\frac{a}{b}*\frac{d}{c}\]

Answer 7

no

Answer 8

wait, maybe

Answer 9

it's just a way to make a big division problem look less scary

Answer 10

ok does it mean turn the division into mutipication?

Answer 11

on the left side we have something very scary (4 levels high), and on the right side we have the same thing, but it looks like a normal fraction.

Answer 12

yeah

Answer 13

yes you turn a division into multiplication. instead of dividing, you multiply by the reciprocal. so you know this method ?

Answer 14

yeah

Answer 15

now, do you know how to solve this:

\[\frac{5^5}{5^2}\]

Answer 16

1\[^{3}\]

Answer 17

1^3

Answer 18

\[\frac{5^5}{5^2}=\frac{5^3}{5^0}=5^3=5*5*5=125\]

Answer 19

see what happened there ?

Answer 20

nope

Answer 21

Look carefully at what happens to the powers of 5

Answer 22

oh, I get it

Answer 23

when we divide

Answer 24

try this one:
\[\frac{5^3}{5^5}=?\]

Answer 25

1/^2

Answer 26

?

Answer 27

The number 5 should appear in your answer.

Answer 28

5^0/5^2?

Answer 29

yep

Answer 30

how about this:
5^3 * 5^2 = ?

Answer 31

25^5

Answer 32

5^3 * 5^2 = 5^(3+2) = 5^5

Answer 33

but 5*5 is 25

Answer 34

5*5=5^2=25

In multiplcation we add the powers of 5:

5*5=5^1 * 5^1 = 5^(1+1) = 5^2


In division we substract the powers of 5:

5^3 / 5^5 = 5^(3-5) = 5^(-2) = 1/5^2

Answer 35

If any of the above doesnt make sense let me know :)

Answer 36

ok

Answer 37

now try these:

m^2 * m^3 = ?

m^3/m^4 =?

m^5/m^3=?

Answer 38

so whats the answer to the problem (3m^4)/(2m^2n) divided by (15m^3n^2)/(16m)

Answer 39

do you just want the answer, or to be able to answer the question yourself easily ?

Answer 40

If you just want the answer - you can use wolfram.

e.g.: copy/paste the link below into your browser

http://www.wolframalpha.com/input/?i=%28%283*m^4%29%2F%282*m^2*n%29%29+++%2F+%28%2815*m^3*n^2%29%2F%2816*m%29%29&a=*MC.m^4-_*Variable-&a=UnitClash_*m.*Meters.dflt--&a=UnitClash_*m^4.*MetersToTheFourth.dflt--&a=UnitClash_*n.*Newtons.dflt--

Answer 41

I wanna know how to do it to

Answer 42

You already solved for the number in the beginning remember ?
you got the 8/5 part of the answer.

Answer 43

now we need to focus on the m's and the n's .

Answer 44

ok

Answer 45

for example the m's

what is:

m^4/m^2 = ?

Answer 46

m^2

Answer 47

good.
now what is

m^3/m=?

Answer 48

m^2

Answer 49

so what is:

( m^4/m^2) / (m^3/m) =?

Answer 50

m/m

Answer 51

its:
(m^2)/(m^2) = 1

Answer 52

which means all the m's cancel out, and your final answer will have no m in it!

Answer 53

oh

Answer 54

does that make sense ?

Answer 55

yes :)

Answer 56

so lastly we need to look at the n's

Answer 57

n^3

Answer 58

we have:

(1/n) / (n^2/1) = (1/n) * (1/n^2) = 1/n^3

Answer 59

ok thanks :)

Answer 60

so now we need to get the final answer, which is a product
of the numeric part of the answer times the m's part of the answer times the n's part of the answer.

that's how we get to:
\[\frac{8}{5n^3}\]

Answer 61

to summarize:

\[\frac{(\frac{3m^4}{2m^2n})}{(\frac{15m^3n^2}{16m})}\]

Answer 62

ok cool

Answer 63

\[=\frac{3m^4}{2m^2n}*\frac{16m}{15m^3n^2}=\frac{3*16*m ^{4+1}}{2*15*m^{2+3}n^{1+2}}=\frac{8m^5}{5m^5n^3}=\frac{8m^0}{5n^3}=\frac{8}{5n^3}\]

Answer 64

so we only did two things.
First we converted a big division problem into a smaller multiplication problem.
Then, we just did some addition and subtraction on the powers of m and powers of n.