Question

complete the following fraction. answer must be in lowest terms:

\\(21\\ 3-1/2\\\)
\\(- 18\\ 5-3/4\\\)

?

a \\(3\\ 8-1/4\\\)
b \\(2\\ 9-3/4\\\)
c \\(2\\ 8-1/4\\\)
d \\(3\\ 9-3/4\\\)

Explanation:

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<reasoning>

Convert fractional inches to a common denominator

Using the Mixed Numbers Subtraction knowledge point
\[
\frac{1}{2} = \frac{2}{4}
\]

Borrow from feet to subtract inches

Using the Construction Math and Mixed Numbers Subtraction knowledge points
\[

$$\begin{aligned} 21'\ 3\frac{2}{4}'' &= 20'\ + 1'\ + 3\frac{2}{4}'' \\ &= 20'\ 15\frac{2}{4}'' \end{aligned}$$

\]

Subtract the feet and inches separately

Using the Mixed Numbers Subtraction knowledge point
\[

$$\begin{aligned} \text{Inches: } & 15\frac{2}{4}'' - 5\frac{3}{4}'' = 9\frac{3}{4}'' \\ \text{Feet: } & 20' - 18' = 2' \\ \text{Result: } & 2'\ 9\frac{3}{4}'' \end{aligned}$$

\]

Analyze the common misconception for Option B

Using the Mixed Numbers Subtraction knowledge point
The correct subtraction yields \(2'\ 9\frac{3}{4}''\), which is Option B. A student might incorrectly choose Option D (\(3'\ 9\frac{3}{4}''\)) if they subtract the fractional inches correctly but forget to reduce the feet from \(21'\) to \(20'\) after borrowing \(1'\) (\(12''\)) to perform the fractional subtraction.
</reasoning>

<answer>
<mcq-option>(A) 3' 8-1/4"</mcq-option>
<mcq-correct>(B) 2' 9-3/4"</mcq-correct>
<mcq-option>(C) 2' 8-1/4"</mcq-option>
<mcq-option>(D) 3' 9-3/4"</mcq-option>
</answer>

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Answer:

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<reasoning>

Convert fractional inches to a common denominator

Using the Mixed Numbers Subtraction knowledge point
\[
\frac{1}{2} = \frac{2}{4}
\]

Borrow from feet to subtract inches

Using the Construction Math and Mixed Numbers Subtraction knowledge points
\[

$$\begin{aligned} 21'\ 3\frac{2}{4}'' &= 20'\ + 1'\ + 3\frac{2}{4}'' \\ &= 20'\ 15\frac{2}{4}'' \end{aligned}$$

\]

Subtract the feet and inches separately

Using the Mixed Numbers Subtraction knowledge point
\[

$$\begin{aligned} \text{Inches: } & 15\frac{2}{4}'' - 5\frac{3}{4}'' = 9\frac{3}{4}'' \\ \text{Feet: } & 20' - 18' = 2' \\ \text{Result: } & 2'\ 9\frac{3}{4}'' \end{aligned}$$

\]

Analyze the common misconception for Option B

Using the Mixed Numbers Subtraction knowledge point
The correct subtraction yields \(2'\ 9\frac{3}{4}''\), which is Option B. A student might incorrectly choose Option D (\(3'\ 9\frac{3}{4}''\)) if they subtract the fractional inches correctly but forget to reduce the feet from \(21'\) to \(20'\) after borrowing \(1'\) (\(12''\)) to perform the fractional subtraction.
</reasoning>

<answer>
<mcq-option>(A) 3' 8-1/4"</mcq-option>
<mcq-correct>(B) 2' 9-3/4"</mcq-correct>
<mcq-option>(C) 2' 8-1/4"</mcq-option>
<mcq-option>(D) 3' 9-3/4"</mcq-option>
</answer>

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