📝 Mixed Units of Measurement in the U.S. System (17 MCQs)

📖 Explanation: First convert the length to one unit: $5$ feet $8$ inches equals $68$ inches. Dividing $68$ by $14$ gives $4$ complete pieces with $12$ inches remaining, but the available board must be reconsidered if cuts require kerf. Without kerf, the correct result is 4 pieces and 12 inches remaining; therefore none of the listed choices is correct. This question exposes why unit consistency must be checked before selecting an answer.

📖 Explanation: Convert everything to yards before comparing. The first distance is $3(1{,}760)+1{,}760=7{,}040$ yards, or $4$ miles. The second is $7{,}040-880=6{,}160$ yards, or $3.5$ miles. Thus the first driver travels $0.5$ mile farther. The distractors reflect common errors such as subtracting unlike units or assuming the numerical values can be compared directly.

📖 Explanation: Since $4$ tablespoons is $4/16=0.25$ cup, $2$ cups $4$ tablespoons equals $2.25$ cups. The student's conversion is therefore correct. This requires recognizing the relationship between mixed units and fractional units rather than treating the numbers $2$ and $4$ as decimal parts without conversion.

📖 Explanation: Use a common unit to interpret the graph accurately. Since $1$ mile equals $1{,}760$ yards, A covers $2{,}080$ yards, B covers $2{,}200$ yards, C covers $2{,}080$ yards, and D covers $2{,}360$ yards. Therefore D is greatest. The problem tests graph interpretation together with mixed-unit conversion.

📖 Explanation: There are $12$ inches in a foot, so $3$ inches represents $3/12=0.25$ foot. Therefore $6$ feet $3$ inches equals $6.25$ feet, not $6.3$ feet. The error comes from treating inches as tenths of a foot instead of converting according to the actual unit relationship.

📖 Explanation: The student's method is invalid because $6$ inches is $0.5$ foot, while $9$ inches is $0.75$ foot. Thus the dimensions are $4.5$ feet and $3.75$ feet, giving an area of $16.875$ square feet. Consistent units are essential before multiplying measurements to obtain area.

📖 Explanation: The increase from the first to second marker is $440$ yards, which equals $1/4$ mile because $1$ mile is $1{,}760$ yards. The second to third marker increases by $880$ yards, so the displayed pattern is not a constant mixed-unit increase. Therefore the information does not uniquely determine a fourth marker; choosing A assumes an unsupported pattern. The correct reasoning is to identify insufficient information rather than force a calculation.

📖 Explanation: Add the feet and inches separately: $4+3=7$ feet and $9+7=16$ inches. Since $12$ inches make $1$ foot, convert $16$ inches to $1$ foot $4$ inches. Therefore the total is $8$ feet $4$ inches.

📖 Explanation: Because $1$ inch cannot be reduced by $2$ inches, regroup $1$ foot as $12$ inches. Then $8$ feet $1$ inch becomes $7$ feet $13$ inches. Subtracting gives $2$ feet $11$ inches, showing why regrouping is necessary.

📖 Explanation: Convert both dimensions to inches before multiplying. The length is $2(12)+8=32$ inches and the width is $1(12)+9=21$ inches. Therefore the area is $32\times21=672$ square inches, so option C is actually correct. The listed alternatives reveal why unit conversion and careful multiplication must both be checked; therefore the correct answer is C.

📖 Explanation: Add the mile portions to obtain $4$ miles and the yard portions to obtain $1{,}500$ yards. Since $1$ mile equals $1{,}760$ yards, $1{,}500$ yards is less than one mile. Thus the total is $4$ miles $1{,}500$ yards, making option A correct. This requires recognizing that conversion is unnecessary when the remaining yards stay below one mile.

📖 Explanation: Convert the ribbon to $76$ inches and each gift length to $19$ inches. Since $76\div19=4$, exactly four complete gifts can be made with no ribbon remaining. Therefore option C is correct. The key is to convert both measurements before dividing rather than separately dividing feet and inches.

📖 Explanation: Multiplying gives $12$ feet and $32$ inches. Since $32$ inches equals $2$ feet $8$ inches, the total becomes $14$ feet $8$ inches. Thus the student's numerical result is correct, although the reasoning should explicitly regroup the $32$ inches. Option C is therefore correct.

📖 Explanation: Add the feet to obtain $5$ feet and the inches to obtain $18$ inches. Convert $18$ inches to $1$ foot $6$ inches. Therefore the complete length is $6$ feet $6$ inches. This graph-based problem requires combining adjacent segments and normalizing the resulting mixed-unit measurement.

📖 Explanation: Convert the dimensions first: $5$ feet $6$ inches equals $5.5$ feet, and $3$ feet $4$ inches equals $3+\frac{4}{12}=\frac{10}{3}$ feet. Doubling the length gives $11$ feet. The new area is $11\times\frac{10}{3}=\frac{110}{3}=36\frac{2}{3}$ square feet.

📖 Explanation: Method A gives $9$ feet $15$ inches, which becomes $10$ feet $3$ inches. Method B converts the measurements to $94$ inches and $29$ inches, totaling $123$ inches, which is also $10$ feet $3$ inches. Both approaches are valid when unit relationships are handled correctly.

📖 Explanation: Each piece is $2(12)+9=33$ inches, so eight pieces require $264$ inches, or $22$ feet exactly. The roll contains $22(12)+6=270$ inches. Subtracting $264$ from $270$ leaves $6$ inches, so the material is sufficient and $0$ feet $6$ inches remains. This multi-step model requires multiplication, conversion, and subtraction.