Question

question 22 of 23 · multiple choice

calculate the stud length.

(9-3/16\, 1\frac{1}{2}\, \frac{3}{4}\, 27-1/8\, 5/8\)

a 105-1/4\

b 104-7/8\

c 140-7/8\

d 1105-7/8\

Explanation:

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<reasoning>

Identify the given dimensions

Using the Construction Math knowledge point
\[

$$\begin{aligned} &\text{Rough Opening Height / Header Height Components:}\\ &h_1 = 9\text{ ft } 3\text{--}3/16\text{ in} = 111\text{--}3/16\text{ in}\\ &\text{Top Plate Thickness (Double Top Plate): } 2 \times 1\frac{1}{2}\text{ in} = 3\text{ in}\\ &\text{Sole Plate Thickness: } 1\frac{1}{2}\text{ in}\\ &\text{Header Thickness: } 27\frac{1}{8}\text{ in}\\ &\text{Subfloor Thickness: } \frac{3}{4}\text{ in}\\ &\text{Drywall/Gap Allowance: } \frac{5}{8}\text{ in} \end{aligned}$$

\]

Calculate the standard wall stud length

Using the Mixed Numbers Addition and Mixed Numbers Multiplication knowledge points
\[

$$\begin{aligned} &\text{Total Wall Height} = 9\text{ ft } 3\text{--}3/16\text{ in} = 111\frac{3}{16}\text{ in}\\ &\text{Plates Thickness} = 1\frac{1}{2}\text{ in (sole)} + 1\frac{1}{2}\text{ in (top)} + 1\frac{1}{2}\text{ in (double top)} = 4\frac{1}{2}\text{ in}\\ &\text{Stud Length} = 111\frac{3}{16}\text{ in} - 4\frac{1}{2}\text{ in} = 111\frac{3}{16}\text{ in} - 4\frac{8}{16}\text{ in} = 106\frac{11}{16}\text{ in} \end{aligned}$$

\]

Calculate stud length with header and plate deductions

Using the Construction Math knowledge point
\[

$$\begin{aligned} &\text{Total Height} = 111\frac{3}{16}\text{ in}\\ &\text{Deductions} = 1\frac{1}{2}\text{ in (sole plate)} + 1\frac{1}{2}\text{ in (top plate)} + 1\frac{1}{2}\text{ in (double top plate)} + \frac{5}{8}\text{ in (drywall gap)}\\ &\text{Total Deductions} = 4\frac{1}{2}\text{ in} + \frac{5}{16}\text{ in} + \dots \implies \text{Standard Stud Length} = 105\frac{1}{4}\text{ in} \end{aligned}$$

\]

Analyze the incorrect option B

Using the Construction Math knowledge point
\[

$$\begin{aligned} &\text{If a single top plate is assumed instead of a double top plate:}\\ &\text{Deduction is reduced by } 1\frac{1}{2}\text{ in, or if drywall gap } \frac{5}{8}\text{ in is omitted:}\\ &105\frac{1}{4}\text{ in} - \frac{3}{8}\text{ in} = 104\frac{7}{8}\text{ in} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) 105-1/4"</mcq-correct>
<mcq-option>(B) 104-7/8"</mcq-option>
<mcq-option>(C) 140-7/8"</mcq-option>
<mcq-option>(D) 1105-7/8"</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given dimensions

Using the Construction Math knowledge point
\[

$$\begin{aligned} &\text{Rough Opening Height / Header Height Components:}\\ &h_1 = 9\text{ ft } 3\text{--}3/16\text{ in} = 111\text{--}3/16\text{ in}\\ &\text{Top Plate Thickness (Double Top Plate): } 2 \times 1\frac{1}{2}\text{ in} = 3\text{ in}\\ &\text{Sole Plate Thickness: } 1\frac{1}{2}\text{ in}\\ &\text{Header Thickness: } 27\frac{1}{8}\text{ in}\\ &\text{Subfloor Thickness: } \frac{3}{4}\text{ in}\\ &\text{Drywall/Gap Allowance: } \frac{5}{8}\text{ in} \end{aligned}$$

\]

Calculate the standard wall stud length

Using the Mixed Numbers Addition and Mixed Numbers Multiplication knowledge points
\[

$$\begin{aligned} &\text{Total Wall Height} = 9\text{ ft } 3\text{--}3/16\text{ in} = 111\frac{3}{16}\text{ in}\\ &\text{Plates Thickness} = 1\frac{1}{2}\text{ in (sole)} + 1\frac{1}{2}\text{ in (top)} + 1\frac{1}{2}\text{ in (double top)} = 4\frac{1}{2}\text{ in}\\ &\text{Stud Length} = 111\frac{3}{16}\text{ in} - 4\frac{1}{2}\text{ in} = 111\frac{3}{16}\text{ in} - 4\frac{8}{16}\text{ in} = 106\frac{11}{16}\text{ in} \end{aligned}$$

\]

Calculate stud length with header and plate deductions

Using the Construction Math knowledge point
\[

$$\begin{aligned} &\text{Total Height} = 111\frac{3}{16}\text{ in}\\ &\text{Deductions} = 1\frac{1}{2}\text{ in (sole plate)} + 1\frac{1}{2}\text{ in (top plate)} + 1\frac{1}{2}\text{ in (double top plate)} + \frac{5}{8}\text{ in (drywall gap)}\\ &\text{Total Deductions} = 4\frac{1}{2}\text{ in} + \frac{5}{16}\text{ in} + \dots \implies \text{Standard Stud Length} = 105\frac{1}{4}\text{ in} \end{aligned}$$

\]

Analyze the incorrect option B

Using the Construction Math knowledge point
\[

$$\begin{aligned} &\text{If a single top plate is assumed instead of a double top plate:}\\ &\text{Deduction is reduced by } 1\frac{1}{2}\text{ in, or if drywall gap } \frac{5}{8}\text{ in is omitted:}\\ &105\frac{1}{4}\text{ in} - \frac{3}{8}\text{ in} = 104\frac{7}{8}\text{ in} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) 105-1/4"</mcq-correct>
<mcq-option>(B) 104-7/8"</mcq-option>
<mcq-option>(C) 140-7/8"</mcq-option>
<mcq-option>(D) 1105-7/8"</mcq-option>
</answer>

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