Question

a recipe requires \\(\frac{3}{4}\\) cup of butter. if you make half the recipe, how much butter do you need?\
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problem 21\
calculate the area of a rectangle with length \\(3\frac{1}{2}\\) feet and width \\(2\frac{1}{4}\\) feet.\
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problem 22\
a storage box has dimensions 2 feet by 3 feet by 4 feet. what is its volume?\
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problem 23\
if 12 cookies are shared equally among 4 people, how many cookies does each person get?\
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problem 24\
calculate: \\(\frac{5}{6} \div 2\\)

Explanation:

First Problem (Butter in Recipe)

Step1: Identify the operation

We need to find half of $\frac{3}{4}$ cup, so we multiply $\frac{3}{4}$ by $\frac{1}{2}$.
$$\frac{3}{4} \times \frac{1}{2}$$

Step2: Multiply the fractions

Multiply the numerators and denominators: $3\times1 = 3$ and $4\times2 = 8$.
$$\frac{3\times1}{4\times2}=\frac{3}{8}$$

Step1: Convert mixed numbers to improper fractions

Length: $3\frac{1}{2}=\frac{3\times2 + 1}{2}=\frac{7}{2}$ feet.
Width: $2\frac{1}{4}=\frac{2\times4+1}{4}=\frac{9}{4}$ feet.

Step2: Use the area formula for rectangle ($A = l\times w$)

Multiply the two improper fractions: $\frac{7}{2}\times\frac{9}{4}$.
$$\frac{7\times9}{2\times4}=\frac{63}{8}$$

Step3: Convert back to mixed number (optional)

$\frac{63}{8}=7\frac{7}{8}$ square feet.

Step1: Recall the volume formula for a rectangular prism

The volume $V$ of a rectangular prism is $V = l\times w\times h$, where $l = 2$ ft, $w = 3$ ft, $h = 4$ ft.

Step2: Multiply the dimensions

$$2\times3\times4 = 24$$

Answer:

$\frac{3}{8}$ cup

Problem 21 (Area of Rectangle)