Table of Values
Luisa is baking a cake. For every \frac{3}{4}
4
3
​
cup of sugar she uses 1\frac{1}{2}
2
1
​
cups of flour. Complete the table shown below, which shows a proportional relationship for the number of cups of sugar to the number of cups of flour.

Cups of Sugar Cups of Flour
\frac{1}{8}
8
1
​
A
\frac{3}{4}
4
3
​
1\frac{1}{2}
2
1
​

5\frac{1}{4}
4
1
​
B
10\frac{1}{5}
5
1
​
C

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.

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