📝 Make Unit Conversions in the U.S. System (21 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 21 questions available

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What is Make Unit Conversions in the U.S. System?

Definition:
Making unit conversions in the U.S. system involves changing a measurement from one U.S. customary unit to another (e.g., feet to yards, ounces to pounds) using defined conversion factors, which are exact ratios that relate different units within this system.

Working:
Identify the conversion factor between the given unit and the desired unit (e.g., $1 \text{ yd} = 3 \text{ ft}$ ), then multiply the given measurement by the conversion factor, arranging it so that the undesired unit cancels, leaving the desired unit.

Example:
Convert 48 ounces to pounds.
Solution: $1 \text{ lb} = 16 \text{ oz}$ ; so $48 \text{ oz} \times \frac{1 \text{ lb}}{16 \text{ oz}} = 3 \text{ lb}$ .

Reason:
U.S. system conversions are common in everyday life (cooking, construction, travel), and they reinforce the algebraic skill of dimensional analysis, which is also used in science and engineering.

Easy

Medium

Hard

📝 All Make Unit Conversions in the U.S. System MCQs

Q1. A delivery truck travels $2.5$ miles. If $1$ mile equals $5,280$ feet, which expression correctly represents the distance in feet before calculating the final value?

2.5 \times 5,280

✅

2.5 \div 5,280

5,280 \div 2.5

2.5 + 5,280

💡 Difficulty: easy | ✅ Correct: A

📖 Explanation: Because each mile contains $5,280$ feet, multiplying $2.5$ miles by $5,280$ feet per mile cancels the mile unit and leaves feet. The other operations do not correctly apply the conversion relationship.

Q2. A recipe requires $3$ cups of flour. A baker wants to measure the flour using tablespoons, knowing that $1$ cup equals $16$ tablespoons. Which amount should the baker measure, and why?

19

tablespoons, because

3+16=19

48

tablespoons, because

3\times16=48

✅

5\frac{1}{3}

tablespoons, because

16\div3

13

tablespoons, because

16-3=13

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The conversion factor is $16$ tablespoons for every cup. Since the recipe has $3$ cups, multiplying $3\times16$ gives $48$ tablespoons. Addition or subtraction would not preserve the proportional relationship between the units.

Q3. A runner completes $2$ miles and $440$ yards. Since $1$ mile equals $1,760$ yards, what is the total distance in yards?

3,200

yards

3,960

yards ✅

4,000

yards

4,080

yards

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: First convert the $2$ miles into yards: $2\times1,760=3,520$ yards. Then add the additional $440$ yards, giving $3,960$ yards. This requires converting before combining quantities expressed in the same unit.

Q4. A student converts $5$ feet to inches by calculating $5\div12=0.4167$ inches. What is the most important error in the student's reasoning?

A.The student should subtract

12

from

5

B.The student used a conversion factor that changes inches into feet rather than feet into inches. ✅

C.The student should multiply by

5

twice.

D.The student should convert feet into yards first.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Since $1$ foot contains $12$ inches, converting a larger unit to a smaller unit requires multiplication by $12$ . The student's division reverses the needed conversion direction, producing a value smaller than the original numerical amount.

Q5. A graph shows four bars representing distances converted to feet: $1$ mile is at $5,280$ , $0.5$ mile is at $2,640$ , $0.25$ mile is at $1,320$ , and $2$ miles is at $10,560$ . Which conclusion best explains the pattern?

A.Doubling miles doubles the number of feet. ✅

B.Adding miles always adds exactly

1,320

feet.

C.The number of feet decreases as miles increase.

D.The graph shows that

1

mile equals

2,640

feet.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The graph demonstrates a proportional relationship between miles and feet. When the number of miles doubles from $1$ to $2$ , the number of feet also doubles from $5,280$ to $10,560$ , confirming the conversion factor.

Q6. A carpenter has a board $7$ feet $6$ inches long. He needs pieces that are $30$ inches long. Ignoring waste, how many complete pieces can he cut?

A.2 pieces

B.3 pieces ✅

C.4 pieces

D.5 pieces

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Convert the board length completely into inches: $7\times12+6=90$ inches. Dividing $90$ by $30$ gives $3$ , so exactly three complete pieces can be cut. Keeping mixed units would make the comparison easier to misinterpret.

Q7. A rectangular garden is $4$ yards long and $6$ feet wide. A student converts $4$ yards to $12$ feet and then calculates $12\times6=72$ . What does $72$ represent, and why is the conversion valid?

72

square feet; both dimensions are now measured in feet. ✅

72

feet; multiplication always produces feet.

72

square yards; the width was already in feet.

72

cubic feet; two dimensions create volume.

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: Because $1$ yard equals $3$ feet, $4$ yards becomes $12$ feet. Multiplying $12$ feet by $6$ feet produces $72$ square feet. Converting both dimensions to the same unit is essential before finding area.

Q8. A student needs to measure the length of a classroom, the amount of water in a tank, and the duration of a lesson. Which combination of U.S. units is most appropriate for these three measurements?

A.Inches, ounces, seconds

B.Feet, gallons, minutes ✅

C.Pounds, quarts, hours

D.Yards, pounds, seconds

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Feet are practical for measuring classroom length, gallons are appropriate for measuring a substantial amount of liquid, and minutes are suitable for measuring a lesson. Choosing units should depend on the quantity being measured and its scale.

Q9. A shipping box weighs $8$ pounds and contains $3$ quarts of liquid. Which statement correctly distinguishes the two measurements?

A.Both measurements describe length.

B.Pounds measure weight while quarts measure capacity. ✅

C.Quarts measure weight while pounds measure capacity.

D.Both measurements describe time.

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: Pounds describe how heavy an object is, while quarts describe the amount of liquid a container can hold. Although both are numerical measurements, they represent different physical quantities and cannot be directly compared.

Q10. A school orders $4$ gallons of juice for an event. Each gallon contains $4$ quarts, and each serving requires $2$ cups. If $1$ quart contains $4$ cups, how many servings can be prepared?

A.16 servings

B.32 servings ✅

C.64 servings

D.128 servings

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: First convert gallons to quarts: $4\times4=16$ quarts. Then convert to cups: $16\times4=64$ cups. Since each serving requires $2$ cups, $64\div2=32$ servings can be prepared.

Q11. A student says, 'Since $1$ pound is larger than $1$ ounce, $6$ ounces must be heavier than $2$ pounds.' What is the best analysis of this reasoning?

A.It is correct because

6>2

B.It is incorrect because the units must be converted before comparing the quantities. ✅

C.It is correct because ounces are normally used for heavy objects.

D.It is incorrect because pounds and ounces measure length.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The numerical values cannot be compared directly because the units differ. Since $1$ pound equals $16$ ounces, $2$ pounds equals $32$ ounces, which is much greater than $6$ ounces.

Q12. A graph records water used during four activities: cooking $2$ quarts, cleaning $6$ quarts, gardening $10$ quarts, and washing $8$ quarts. Which conclusion is supported by the graph?

A.Cooking used twice as much as gardening.

B.Gardening used

4

quarts more than cleaning. ✅

C.Washing used

8

times as much as cooking.

D.Cleaning and washing together used

12

quarts less than gardening.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The graph shows gardening at $10$ quarts and cleaning at $6$ quarts. Their difference is $10-6=4$ quarts. The other statements either reverse the relationship or incorrectly interpret multiplication from the displayed values.

Q13. A delivery schedule takes $1$ hour $45$ minutes for loading and $2$ hours $30$ minutes for transportation. The driver also spends $35$ minutes at a checkpoint. What is the total elapsed time?

A.4 hours 10 minutes

B.4 hours 40 minutes ✅

C.5 hours 10 minutes

D.5 hours 50 minutes

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Add the minutes first: $45+30+35=110$ minutes, which equals $1$ hour $50$ minutes. Add the original hours: $1+2+1=4$ hours, giving a total of $4$ hours $40$ minutes.

Q14. Two methods are proposed for describing a $2$ -hour trip. Method A records $120$ minutes, while Method B records $7,200$ seconds. Which statement best evaluates the methods?

A.Method A is correct, but Method B is too large to represent the same time.

B.Both are correct because

2

hours equals

120

minutes and

7,200

seconds. ✅

C.Only Method B is correct because seconds are more precise.

D.Neither is correct because hours cannot be converted into smaller units.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Both methods represent the same duration using different units. Since $1$ hour equals $60$ minutes and $3,600$ seconds, $2$ hours equals $120$ minutes and $7,200$ seconds. Different units can describe the same quantity.

Q15. A student wants to convert $7$ feet to inches using a factor that does not change the measured quantity. Which expression correctly represents the conversion?

7\text{ ft}\times\frac{1\text{ ft}}{12\text{ in}}

7\text{ ft}\times\frac{12\text{ in}}{1\text{ ft}}

✅

7\text{ ft}\times12\text{ ft}

7\text{ ft}\div\frac{12\text{ in}}{1\text{ ft}}

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: The fraction $\frac{12\text{ in}}{1\text{ ft}}$ represents one because $12$ inches and $1$ foot describe the same length. Multiplying by this equivalent-to-one factor changes the unit from feet to inches without changing the actual distance.

Q16. Why can $\frac{3\text{ ft}}{36\text{ in}}$ be used as a conversion factor without changing the actual length of a measurement?

A.Because the fraction equals

3

B.Because the fraction equals

12

C.Because the numerator and denominator represent equivalent lengths, making the ratio equal to

1

. ✅

D.Because any fraction containing two length units equals

1

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The numerator and denominator represent the same physical length because $3$ feet equals $36$ inches. Therefore, their ratio is $1$ , so multiplying by the fraction preserves the quantity while allowing units to be converted.

Q17. A hiking trail is $2.5$ miles long. A student writes $2.5\text{ mi}\times\frac{5,280\text{ ft}}{1\text{ mi}}$ . Another student writes $2.5\text{ mi}\times\frac{1\text{ mi}}{5,280\text{ ft}}$ . Which method is correct and why?

A.The first, because miles cancel and feet remain. ✅

B.The second, because feet should cancel first.

C.Both, because either ratio has value

1

D.Neither, because conversion factors cannot be fractions.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The first conversion factor represents one because $5,280$ feet equals $1$ mile. Multiplying by it cancels the mile units and leaves feet. The second factor reverses the units and would not produce the desired unit.

Q18. A student converts $48$ inches to feet by writing $48\times\frac{1\text{ ft}}{12\text{ in}}$ and obtains $4$ feet. Another student says multiplying by a fraction should always make the number smaller and therefore the method is invalid. What is wrong with the second student's reasoning?

A.Every fraction is greater than

1

B.The numerical value may change while the physical quantity remains equivalent because the units are also changing. ✅

C.Unit conversions never involve multiplication.

D.The conversion factor must always make the numerical value larger.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: A conversion factor equivalent to $1$ does not change the physical quantity, even though it can change the numerical value. Here, $48$ inches becomes $4$ feet because a larger unit requires fewer numerical units to describe the same length.

Q19. A graph shows that $1$ foot corresponds to $12$ inches, $2$ feet to $24$ inches, $3$ feet to $36$ inches, and $4$ feet to $48$ inches. Which conversion factor is consistent with the graph and preserves the quantity?

\frac{1\text{ ft}}{12\text{ in}}

when converting feet to inches

\frac{12\text{ in}}{1\text{ ft}}

when converting feet to inches ✅

12\text{ ft}

when converting feet to inches

\frac{1\text{ in}}{12\text{ ft}}

when converting feet to inches

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The graph shows that every $1$ foot corresponds to $12$ inches. Therefore, $\frac{12\text{ in}}{1\text{ ft}}$ equals $1$ and correctly changes feet into inches when multiplied by a measurement expressed in feet.

Q20. A rectangular sign is $3$ feet wide and $18$ inches tall. A student converts the width to $36$ inches and calculates $36\times18=648$ . Another student calculates $3\times18=54$ . Which result correctly represents the area in square inches?

54\text{ in}^2

108\text{ in}^2

648\text{ in}^2

✅

972\text{ in}^2

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The width must first be converted to the same unit as the height. Using $3\text{ ft}\times\frac{12\text{ in}}{1\text{ ft}}=36\text{ in}$ , the area is $36\times18=648\text{ in}^2$ . The $54$ result mixes incompatible units.

Q21. A machine part measures $2$ feet. A technician converts it to inches using $\frac{12\text{ in}}{1\text{ ft}}$ , then converts the result back using $\frac{1\text{ ft}}{12\text{ in}}$ . Which conclusion best explains why the original measurement is recovered?

A.The two conversion factors multiply to an equivalent factor of

1

, so the original quantity is preserved. ✅

B.The two conversion factors always increase the measurement.

C.The first conversion permanently changes the physical length.

D.The second conversion works only because

12

is prime.

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The factors $\frac{12\text{ in}}{1\text{ ft}}$ and $\frac{1\text{ ft}}{12\text{ in}}$ are reciprocals, so their product is $1$ . Multiplying by both therefore preserves the original quantity while the units cancel successively.

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