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:

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

$$
LATEXBLOCK0
$$

Subtract the feet and inches separately

Using the Mixed Numbers Subtraction knowledge point

$$
LATEXBLOCK1
$$

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.

Answer:

• (A) 3' 8-1/4"
• (B) 2' 9-3/4" (Correct answer)
• (C) 2' 8-1/4"
• (D) 3' 9-3/4"