Answer:
We know that for every (3/4) cups of sugar, she uses (1/2) cups of flour.
Now let's find how much flour she needs to use for each case:
If she uses (1/8) cups of sugar, how much flour she uses?
First, we need to count how many times we have (3/4) cups of sugar in (1/8) cups of sugar, which is the quotient:
(1/8)/(3/4) = 4/(3*8) = 4/24 = 1/6
This means that we need to use (1/6) times (1/2) cups of flour.
this is:
(1/6)*(1/2) cups of flour = (1/12) cups of flour.
If she uses (4/3) cups of sugar, we need to count how many times we have (3/4) cups of flour in that amount, this is:
(4/3)/(3/4) = (4*4)/(3*3) = 16/9
Then we need to se (16/9) times (1/2) cups of flour, this is:
(16/9)*(1/2) cups of flour = (16/18) cups of flour = (8/9) cups of flour
If she uses (1/2) cups of sugar, we need to count how many times we have (3/4) cups of sugar in that amount, this is:
(1/2)/(3/4) = 4/(2*3) = 4/6
Then she needs to use (4/6) times (1/2) cups of flour
this is:
(4/6)*(1/2) cups of flour = 4/(6*2) cups of flour = (1/3) cups of flour.
If she uses (1/4) cups of sugar, we need to count how many times we have (3/4) cups of sugar in that amount, this is:
(1/4)/(3/4) = 4/(4*3) = 4/12
Then she needs to use (4/12) times (1/2) cups of flour
this is:
(4/12)*(1/2) cups of flour = 4/(12*2) cups of flour = (1/6) cups of flour.
If she uses (1/5) cups of sugar, we need to count how many times we have (3/4) cups of sugar in that amount, this is:
(1/5)/(3/4) = 4/(5*3) = 4/15
Then she needs to use (4/15) times (1/2) cups of flour
this is:
(4/15)*(1/2) cups of flour = 4/(15*2) cups of flour = (2/15) cups of flour.
