Question

hurrah for the pumpkin pie
complete the table below to help grandma double her recipe.
ingredient | original amount | visual fraction | improper fraction | simplest form | doubled
pie crust | 2 6/8 cups | | | |
pumpkin | 2 2/4 cups | | | |
cream | 1 3/4 cup | | | |
flour | 1 7/8 cup | | | |
cinnamon | 3 3/6 tbsp | | | |
nutmeg | 2 2/3 tbsp | | | |
sugar | 1 2/6 cup | | | |
brown sugar | ½ cup | | | |
a mouthful of math
use the information above to answer the following questions
for the original recipe, how much more sugar is required than brown sugar?
in the double recipe, how much more pie crust is there than pumpkin?
you buy sugar by the pound. one pound of sugar has 4 cups of sugar in it. how many pounds of sugar would you need to buy to be sure you have enough for the doubled recipe? explain.
in the doubled recipe, how much sugar (brown included) is in the pie total?
how much more flour do you need than cream (in the doubled recipe)?
how much cinnamon and nutmeg do you need for the original recipe?

Explanation:

Step1: Simplify Sugar and Brown Sugar Amounts

Sugar original: \(1\frac{2}{6}=\frac{8}{6}=\frac{4}{3}\) cup. Brown Sugar: \(\frac{1}{2}\) cup. Difference: \(\frac{4}{3}-\frac{1}{2}=\frac{8 - 3}{6}=\frac{5}{6}\) cup.

Step2: Double Pie Crust and Pumpkin

Pie Crust doubled: \(2\frac{6}{8}\times2=\frac{22}{8}\times2=\frac{22}{4}=\frac{11}{2}=5\frac{1}{2}\) cups. Pumpkin doubled: \(2\frac{2}{4}\times2=\frac{10}{4}\times2 = 5\) cups. Difference: \(5\frac{1}{2}-5=\frac{1}{2}\) cup.

Step3: Total Sugar (Brown Included) Doubled

Sugar doubled: \(\frac{4}{3}\times2=\frac{8}{3}\) cups. Brown Sugar doubled: \(\frac{1}{2}\times2 = 1\) cup. Total: \(\frac{8}{3}+1=\frac{11}{3}=3\frac{2}{3}\) cups.

Step4: Double Flour and Cream

Flour doubled: \(1\frac{7}{8}\times2=\frac{15}{8}\times2=\frac{15}{4}=3\frac{3}{4}\) cups. Cream doubled: \(1\frac{3}{4}\times2=\frac{7}{4}\times2=\frac{7}{2}=3\frac{1}{2}\) cups. Difference: \(3\frac{3}{4}-3\frac{1}{2}=\frac{1}{4}\) cup.

Step5: Add Cinnamon and Nutmeg

Cinnamon: \(3\frac{3}{6}=3\frac{1}{2}=\frac{7}{2}\) TBSP. Nutmeg: \(2\frac{2}{3}=\frac{8}{3}\) TBSP. Total: \(\frac{7}{2}+\frac{8}{3}=\frac{21 + 16}{6}=\frac{37}{6}=6\frac{1}{6}\) TBSP.

Step6: Sugar Pounds for Doubled Recipe

Doubled sugar: \(\frac{8}{3}\) cups. 1 pound = \(1\frac{1}{4}=\frac{5}{4}\) cups. Pounds needed: \(\frac{8}{3}\div\frac{5}{4}=\frac{32}{15}\approx2.13\), so 3 pounds (to be sure).

Answer:

1. \(\frac{5}{6}\) cup
2. \(\frac{1}{2}\) cup
3. \(3\frac{2}{3}\) cups
4. \(\frac{1}{4}\) cup
5. \(6\frac{1}{6}\) TBSP
6. 3 pounds (explanation: \(\frac{8}{3}\div\frac{5}{4}=\frac{32}{15}\approx2.13\), round up to 3)