Please explain this before I go insane:?

Question

solve:

2n/3 divided by 4 1/7 = 3 1/2

Answer 1

When you divide by a mixed number you need to turn the divisor (the second number) into an improper fraction.
Then you flip it over and multiply....
Here you have 2n/3 divided by 4 1/7 = 3 1/2
First turn all mixed numbers into improper fractions.
here's how you do that....
http://www.visualfractions.com/MixtoFrCircle.html
http://www.purplemath.com/modules/fraction2.htm
So now you have
2n/3 divided by 29/7 = 7/2
Division by a fraction is the same as multiplying by its reciprocal. So flip the 29/7 over, to create its reciprocal, and now you have
(2n/3) times (7/29) = 7/2
You want to get the n by itself so again multiply -each- side by the reciprocal of 7/29. Anything times its reciprocal is 1, so this effectively cancels out the 7/29 from the left side. So you have...
(2n/3) times (7/29) times (29/7) = (7/2) times (29/7) =
(2n/3) times 1 = 29/2 (the sevens cancelled on the right side)
You're almost there. get the n by itself by multiplying each side by the reciprocal of 2/3, which is 3/2
(2n/3) times (3/2) = n = 29/2 times 3/2 = 87/4
Now turn that 87/4 back into a mixed number (see above link for how to do this)
n = 21 3/4
check:
2/3 times 87/4 divided by 4 1/7 =
2/3 times 87/4 divided by 29/7 =
2/3 times 87/4 times 7/29 =
(2x87x7)/(3x4x29) = 1218/348 = 7/2 = 3 1/2
There's lots of information online about how to do various kinds of math. To find something to help you better than anything we can write here (due to limitations of this online text editor, etc)
just put tutorial subject into your search window.
When I put tutorial solving equations fractions I get...
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut14_solve.htm
http://library.thinkquest.org/20991/alg2/eq.html
Check out these links and try some more, you'll understand it and then you can do it without going insane. Good luck!

Answer 2

Think about what the question is asking you:
First, the equation means what?
(2N/3) / (4 1/7) = 3 1/2

A critical concept of the question is improper fractions, to make things easier make all the numbers into fractions. Like so:
4 1/7 = 29/7 because (4 * 7) + 1 = 29 but you are still working in sevenths so the result is 29/7
and
3 1/2 = 7/2 for the same reason, think about like this; if you have 3 1/2 pizzas how many half pizzas do you have?

Okay now that you have that parts all into fractions lets look at it again:

(2N/3) / (29/7) = 7/2

What do you do when you divide by a fraction? Switch the numbers to get the reciprocal and multiply. So:

(2N/3) / (29/7) becomes (2N/3) * (7/29) * (29/7) this is a form of one, make sure you do this to both sides of the equation!
(2N/3) = (7/2) * (29/7)
The sevens cancel leaving 29/2

2N/3 = 29/2
Solve for N by multiplying both sides by 3/2 (form of one again):
N = (29/2) *(3/2)
N = 87/4
N = 21 3/4

Check your answer by plugging it back in!

Answer 3

2n/3
------ = 3 1/2
4 1/7

first change all the mixed numbers to improper fractions:

2n/3
----- = 7/2
29/7

remember that you can't divide by a fraction, so invert the denominator and multiply (bring it into the numerator), and you get:

2n/3 x 7/29 = 7/2

now multiply the numerators on the LEFT side of the equal sign by each other, then do the same for the denominators and get:

14n/87 = 7/2, which is the same as (14/87)n = 7/2

now it is a regular fraction problem, just multiply both sides by the inverse of 14/87, which is 87/14 like so:

n(87/14) (14/87) = (7/2) (87/14)
now just do the multiplication and cancel out terms to get

n = 87/4, or n=21 3/4

check:

(2/3)(21 3/4)
---------------- =
4 1/7

(2/3)(87/4)
-------------- = now cross cancel the 2 and 4 to get
(29/7)

(1/3)(87/2)
-------------- =
(29/7)


(87/6)
-------- =
(29/7)

(87/6) (7/29) = (87x7) / (6x29) = 7/2 = 3 1/2

Answer 4

Solving for n:

To get the numeric terms on one side, first multiply both sides by 4 1/7. That cancels the complex denominator on the left of the =, giving:

2n/3 = 4 1/7 * 3 1/2; solve the right side = 14 1/2

Multiply both sides by 3/2: n = 14 1/2 * 3/2 = 21 3/4

Multiplying the fractions in my head was painful!

Answer 5

2n/3 divided by 4 1/7 = 3 1/2

2n/3 div 29/7 = 7/2

2n/3 times 7/29 = 7/2

14n/87 = 7/2

28n = 87 x 7 = 609

n = 609/28 = 21 21/28 = 21 3/4

Answer 6

4 1/7=29/7
3 1/2=7/2
2n/3/(29/7)=7/2
(2n/3)*(7/29)=7/2
2n*7/(3*29)=7/2
14n/87=7/2 multiply both sides by 87
14n=609/2 dibide both sides by t
2n=87/2 divide both sides by 2
n=87/4=21 3/4

Answer 7

n= 21 3/4

(2n/3)/(4 1/7)= 3 1/2
(2n/3) multiplied by (7/29)=7/2
by cross multiplication,
28n=609

609/28

21.75

Answer 8

( 2n / 3 ) / ( 4 1/7 ) = 13/12
( 2n / 3 ) / ( 29/7 ) = 13/12
(2n * 29) / ( 3 * 7) = (13/12)
58n / 21 = 13/12
n = (13 * 21 ) / ( 12 * 58)
n = 273 / 696
n = 91 / 232

Answer 9

You have to find n. Which means isolating n on one side and you'll end up with 3 1/2 on the other.

Answer 10

n = 35.1