Problem One
There is nothing wrong with the answer you got.
Gives and required.
1 batch of cookies requires 1/3 cup of sugar
x batches of cookies will need 5 cups of sugar.
Proportion
1 / x = 1/3 / 5
Solve
You could change 1/3 into 0.33333333
1/x= 0.33333333/5 Cross multiply
5 * 1 = 0.333333x
5 = 0.33333333x Divide by 0.3333333
x = 5/0.33333333
x = 15 <<<<< Answer
Problem 2
Givens
9 cups of sugar
Proportion
1 batch requires 1/3 cup of sugar
x batches will require 9 cups of sugar.
1/x = 1/3 //9
1/x = 0.3333333 / 9 Cross multiply
9*1 = 0.3333333 x
9 = 0.33333333x Divide by 0.33333333
9/0.33333333 = x
x = 27 batches of cookies. <<< Answer
Ignore the very small decimal you get. It does not matter. It is a rounding error.
Problem 3
Let the whole shift = x
Let the shift Fred signed up for = x/2
Now x/2 has to be split 3 ways. How do we do that?
Well we can represent it.
[tex] \dfrac{ \frac{x}{2} }{3} [/tex]
The best way to proceed is to put a 1 under the three.
[tex]\dfrac{\dfrac{x}{2}}{\dfrac{3}{1} }[/tex]
Now you get to invert the bottom fraction (3/1) so that it becomes (1/3) and multiply the two fractions together.
[tex] \dfrac{x}{2} * \dfrac{1}{3}=\dfrac{x*1}{2*3}= \dfrac{x}{6} [/tex]
Answer: Each friend will work 1/6 of a whole shift.
