6th Grade Math Quiz: Convert Units Using Ratio Reasoning

20 questions · exam conditions

0:00

Convert Units Using Ratio ReasoningQuestion 1 of 20

A swimming pool holds 12,000 gallons of water. If the pool is being filled at a rate of 25 gallons per minute, how many hours will it take to fill an empty pool?

300 hours

20 hours

480 hours

8 hours

← Back to quizzes

6th Grade Math Quiz

6th Grade Math Quiz: Convert Units Using Ratio Reasoning

Practice Convert Units Using Ratio Reasoning in 6th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Convert Units Using Ratio Reasoning, giving you a quick way to practice the rules, question types, and explanations that matter most for 6th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A swimming pool holds 12,000 gallons of water. If the pool is being filled at a rate of 25 gallons per minute, how many hours will it take to fill an empty pool?

300 hours
20 hours
480 hours
8 hours (correct answer)

Explanation: This problem is all about rate — how fast something happens over time. Here, water flows in at 25 gallons every minute, and we want to know how long it takes to fill 12,000 gallons. First, find the total minutes. Divide the gallons by the rate:

12{,}000 \div 25 = 480 \text{ minutes}

Next, change minutes into hours. Since there are 60 minutes in an hour:

480 \div 60 = 8 \text{ hours}

So it takes 8 hours to fill the pool. Think of it like filling cups with a slow faucet. If you know how fast the water pours, you can predict exactly when it'll be full — no guessing needed! Try this at home: time how long it takes to fill a water bottle, then figure out how many you could fill in one hour at that same speed.

Question 2

A car is traveling at $60$ miles per hour. Convert $60\text{ mi/hr}$ to feet per second using $1\text{ mi}=5280\text{ ft}$ and $1\text{ hr}=3600\text{ s}$ . Use dimensional analysis so units cancel.

$88\text{ ft/s}$ because $60\dfrac{\text{mi}}{\text{hr}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}\times\dfrac{1\text{ hr}}{3600\text{ s}}=88\dfrac{\text{ft}}{\text{s}}$ (correct answer)
$105.6\text{ ft/s}$ because $60\times\dfrac{5280}{3600}=105.6\text{ ft/s}$
$31,680\text{ ft/s}$ because $60\times 5280=31,680\text{ ft/s}$
$1.14\text{ ft/s}$ because $60\times\dfrac{3600}{5280}=1.14\text{ ft/s}$

1 \text{ mi}=5280 \text{ ft}

gives

5280 \text{ ft}/1 \text{ mi}

1 \text{ hr}=3600 \text{ s}

gives

1 \text{ hr}/3600 \text{ s}

), multiply:

60 \text{ mi/hr} \times (5280 \text{ ft}/1 \text{ mi}) \times (1 \text{ hr}/3600 \text{ s})=88 \text{ ft/s}

(mi and hr cancel leaving ft/s). Direction: for compound units like speed, chain conversions to cancel step-by-step. Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example:

60 \text{ mph}

to ft/sec uses

60 \text{ mi/hr} \times (5280 \text{ ft}/1 \text{ mi}) \times (1 \text{ hr}/3600 \text{ sec})

, mi cancels, hr cancels, result:

(60\times5280/3600) \text{ ft/sec}=88 \text{ ft/sec}

; or

3 \text{ feet}

to inches:

3 \text{ ft} \times (12 \text{ in}/1 \text{ ft})=36 \text{ inches}

; or area

5 \text{ ft} \times 3 \text{ ft}=15 \text{ ft}^2

(units multiply: ft×ft=ft² square feet). The correct conversion is

60 \text{ mi/hr} \times (5280 \text{ ft} / 1 \text{ mi}) \times (1 \text{ hr} / 3600 \text{ s}) = 88 \text{ ft/s}

, with miles and hours canceling out. A common error is wrong direction (dividing when should multiply for certain factors), conversion factor wrong (using

5000 \text{ ft/mi}

), units not canceled (leaving mi/ft or similar), arithmetic error (

60\times5280/3600=

wrong calc), or omitting a factor (forgetting time conversion). Process: (1) identify units (start: mi/hr, target: ft/s), (2) find conversions (

1 \text{ mi}=5280 \text{ ft}

1 \text{ hr}=3600 \text{ s}

), (3) set up with cancellation (

60 \text{ mi/hr} \times (5280 \text{ ft}/1 \text{ mi}) \times (1 \text{ hr}/3600 \text{ s}

)), (4) calculate (

60\times5280/3600=88 \text{ ft/s}

), (5) verify units (answer should be in ft/s✓). Dimensional analysis: write conversion factors as fractions with units, multiply so units cancel leaving desired unit.

Question 3

A video is $2.25$ minutes long. Convert $2.25$ minutes to seconds using $1\text{ min}=60\text{ s}$ . Show the setup with unit cancellation.

$135\text{ s}$ because $2.25\text{ min}\times\dfrac{60\text{ s}}{1\text{ min}}=135\text{ s}$ (min cancels) (correct answer)
$37.5\text{ s}$ because $2.25\div 60=37.5\text{ s}$
$122.25\text{ s}$ because $2.25+120=122.25\text{ s}$
$225\text{ s}$ because $2.25\times 100=225\text{ s}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 min=60 s gives ratio 60 s per 1 min), multiply: 2.25 min×(60 s/1 min)=135 s (min cancels: min in numerator and denominator divide out leaving s). Direction: larger unit→smaller unit multiply (min→s: ×60), smaller→larger divide (s→min: ÷60, or ×(1/60)). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 2.25 minutes to seconds using 1 min=60 s, multiply: 2.25 min×(60 s/1 min)=2.25×60 s=135 seconds (minutes cancel); or 3 feet to inches: 3 ft×(12 in/1 ft)=36 inches; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 2.25 min × (60 s / 1 min) = 135 s, with minute units canceling out. A common error is wrong direction (dividing when should multiply: 2.25÷60=0.0375 min instead of s), conversion factor wrong (using 100 s/min), units not canceled (answer 135 min·s instead of 135 s), arithmetic error (2.25×60=120), or adds instead of multiplies (2.25+120=122.25 nonsense). Process: (1) identify units (start: min, target: s), (2) find conversion (1 min=60 s), (3) set up with cancellation (2.25 min×(60 s/1 min), min cancels), (4) calculate (2.25×60=135 s), (5) verify units (answer should be in seconds✓). Dimensional analysis: write conversion factors as fractions with units (60 s/1 min), multiply so units cancel leaving desired unit.

Question 4

During practice, Maya runs for 2.5 hours. Convert 2.5 hours to minutes using $1\text{ hr}=60\text{ min}$ and show unit cancellation.

$62.5\text{ minutes}$ because $2.5+60=62.5$
$0.0417\text{ minutes}$ because $2.5\div 60\approx0.0417$
$120\text{ minutes}$ because $2\text{ hr}\times 60=120$
$150\text{ minutes}$ because $2.5\text{ hr}\times\frac{60\text{ min}}{1\text{ hr}}=150\text{ min}$ (hr cancels) (correct answer)

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 hr=60 min gives ratio 60 min per 1 hr), multiply: 2.5 hr×(60 min/1 hr)=150 min (hr cancels: hr in numerator and denominator divide out leaving min). Direction: larger unit→smaller unit multiply (hr→min: ×60), smaller→larger divide (min→hr: ÷60, or ×(1/60)). For example, convert 2.5 hours to minutes using 1 hr=60 min, multiply: 2.5 hr×(60 min/1 hr)=2.5×60 min=150 minutes (hours cancel). The correct conversion is 2.5 hr × (60 min/1 hr) = 150 min, with hour units canceling out. A common error is reversing the direction, like dividing 2.5 by 60 to get about 0.0417 hr instead of multiplying, or ignoring the decimal and using only 2 hr to get 120 min, or adding instead of multiplying like 2.5+60=62.5. The process is: (1) identify units (start: hr, target: min), (2) find conversion (1 hr=60 min), (3) set up with cancellation (2.5 hr×(60 min/1 hr), hr cancels), (4) calculate (2.5×60=150 min), (5) verify units (answer in minutes✓). Dimensional analysis ensures units cancel properly, and common mistakes include arithmetic errors or not handling decimal values correctly.

Question 5

A bag of trail mix weighs $3$ pounds. Use $1\text{ lb}=16\text{ oz}$ to convert $3$ pounds to ounces, showing unit cancellation.

$0.1875\text{ oz}$ because $3\div 16=0.1875\text{ oz}$
$48\text{ oz}$ because $3\text{ lb}\times\dfrac{16\text{ oz}}{1\text{ lb}}=48\text{ oz}$ (lb cancels) (correct answer)
$64\text{ oz}$ because $3\times 16+16=64\text{ oz}$
$19\text{ oz}$ because $3+16=19\text{ oz}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 lb=16 oz gives ratio 16 oz per 1 lb), multiply: 3 lb×(16 oz/1 lb)=48 oz (lb cancels: lb in numerator and denominator divide out leaving oz). Direction: larger unit→smaller unit multiply (lb→oz: ×16), smaller→larger divide (oz→lb: ÷16, or ×(1/16)). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 3 pounds to ounces using 1 lb=16 oz, multiply: 3 lb×(16 oz/1 lb)=3×16 oz=48 ounces (pounds cancel); or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 3 lb × (16 oz / 1 lb) = 48 oz, with pound units canceling out. A common error is wrong direction (dividing when should multiply: 3÷16=0.1875 lb instead of oz), conversion factor wrong (using 10 oz/lb), units not canceled (answer 48 lb·oz instead of 48 oz), arithmetic error (3×16=42), or adds instead of multiplies (3+16=19 nonsense). Process: (1) identify units (start: lb, target: oz), (2) find conversion (1 lb=16 oz), (3) set up with cancellation (3 lb×(16 oz/1 lb), lb cancels), (4) calculate (3×16=48 oz), (5) verify units (answer should be in ounces✓). Dimensional analysis: write conversion factors as fractions with units (16 oz/1 lb), multiply so units cancel leaving desired unit.

Question 6

A student walks 1.5 miles to a park. About how many feet is that? Use $1\text{ mi}=5280\text{ ft}$ and show unit cancellation.

$0.000284\text{ ft}$ because $1.5\div 5280\approx0.000284$
$3520\text{ ft}$ because $5280-1760=3520$
$8800\text{ ft}$ because $1.5\times 6000=9000$ then subtract 200
$7920\text{ ft}$ because $1.5\text{ mi}\times\frac{5280\text{ ft}}{1\text{ mi}}=7920\text{ ft}$ (mi cancels) (correct answer)

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 mi=5280 ft gives ratio 5280 ft per 1 mi), multiply: 1.5 mi×(5280 ft/1 mi)=7920 ft (mi cancels: mi in numerator and denominator divide out leaving ft). Direction: larger unit→smaller unit multiply (mi→ft: ×5280). For example, convert 1.5 miles to feet using 1 mi=5280 ft, multiply: 1.5 mi×(5280 ft/1 mi)=1.5×5280 ft=7920 feet (miles cancel). The correct conversion is 1.5 mi × (5280 ft/1 mi) = 7920 ft, with mile units canceling out. A common error is reversing the direction, like dividing 1.5 by 5280 to get about 0.000284 mi, or using approximations like 1.5×6000=9000 then subtracting arbitrarily, or subtracting like 5280-1760=3520. The process is: (1) identify units (start: mi, target: ft), (2) find conversion (1 mi=5280 ft), (3) set up with cancellation (1.5 mi×(5280 ft/1 mi), mi cancels), (4) calculate (1.5×5280=7920 ft), (5) verify units (answer in feet✓). Common conversions to memorize include 1 mi=5280 ft, and mistakes include arithmetic errors with decimals.

Question 7

A student walks $450$ centimeters in a hallway. Use $1\text{ m}=100\text{ cm}$ to convert $450\text{ cm}$ to meters. Show the setup with units canceling.

$4.5\text{ m}$ because $450\text{ cm}\times\dfrac{1\text{ m}}{100\text{ cm}}=4.5\text{ m}$ (cm cancels) (correct answer)
$45\text{ m}$ because $450\times\dfrac{1}{10}=45\text{ m}$
$0.45\text{ m}$ because $450\div 1000=0.45\text{ m}$
$45,000\text{ m}$ because $450\times 100=45,000\text{ m}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 m=100 cm gives ratio 1 m per 100 cm), multiply: 450 cm×(1 m/100 cm)=4.5 m (cm cancels: cm in numerator and denominator divide out leaving m). Direction: smaller unit→larger unit divide (cm→m: ÷100, or ×(1/100)), larger→smaller multiply (m→cm: ×100). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 450 centimeters to meters using 1 m=100 cm, multiply: 450 cm×(1 m/100 cm)=450/100 m=4.5 meters (centimeters cancel); or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 450 cm × (1 m / 100 cm) = 4.5 m, with centimeter units canceling out. A common error is wrong direction (multiplying when should divide: 450×100=45,000 cm instead of m), conversion factor wrong (using 1 m=10 cm), units not canceled (answer 4.5 cm·m instead of 4.5 m), arithmetic error (450/100=4), or adds instead of multiplies (450+100=550 nonsense). Process: (1) identify units (start: cm, target: m), (2) find conversion (1 m=100 cm), (3) set up with cancellation (450 cm×(1 m/100 cm), cm cancels), (4) calculate (450/100=4.5 m), (5) verify units (answer should be in meters✓). Dimensional analysis: write conversion factors as fractions with units (1 m/100 cm), multiply so units cancel leaving desired unit.

Question 8

A science lab uses 750 milliliters of solution. Convert 750 mL to liters using $1 \text{ L} = 1000 \text{ mL}$ . How many liters is that?

75 L
0.75 L (correct answer)
7.5 L
0.075 L

1 \text{ L} = 1000 \text{ mL}

gives

1 \text{ L}/1000 \text{ mL}

), multiply:

750 \text{ mL} \times (1 \text{ L}/1000 \text{ mL}) = 0.75 \text{ L}

(

\text{mL}

cancels leaving

\text{L}

). Direction: smaller unit→larger unit divide (

\text{mL}

→

\text{L}

: ÷1000, or ×(1/1000)). Units multiply/divide: length×length=area (

\text{ft} \times \text{ft} = \text{ft}^2

), distance÷time=speed (

\text{mi} \div \text{hr} = \text{mi/hr}

or mph), units treated algebraically. Example: convert 3 feet to inches using

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

, multiply:

3 \text{ ft} \times (12 \text{ in}/1 \text{ ft}) = 3 \times 12 \text{ in} = 36 \text{ inches}

(feet cancel); or 2.5 hours to minutes:

2.5 \text{ hr} \times (60 \text{ min}/1 \text{ hr}) = 150 \text{ minutes}

; or area

5 \text{ ft} \times 3 \text{ ft} = 15 \text{ ft}^2

(units multiply:

\text{ft} \times \text{ft} = \text{ft}^2

square feet). The correct conversion is

750 \text{ mL} / 1000 = 0.75 \text{ L}

. A common error is multiplying instead of dividing, like

750 \times 1000 = 750,000

(way too large), or misplaced decimal (7.5 instead of 0.75). Process: (1) identify units (start: mL, target: L), (2) find conversion (

1 \text{ L} = 1000 \text{ mL}

), (3) set up with cancellation (

750 \text{ mL} \times (1 \text{ L}/1000 \text{ mL}

, mL cancels), (4) calculate (

750/1000 = 0.75 \text{ L}

), (5) verify units (answer should be in liters✓). Dimensional analysis: write conversion factors as fractions with units (

1 \text{ L}/1000 \text{ mL}

), multiply so units cancel leaving desired unit.

Question 9

A rectangular poster is $8$ inches wide and $2$ feet tall. Convert the height to inches using $1\text{ ft}=12\text{ in}$ , then find the area in square inches. (Remember: when you multiply lengths, units multiply.)

$192\text{ in}$ because $8\text{ in}\times 24\text{ in}=192\text{ in}$
$32\text{ in}^2$ because $8\times 2\times 2=32\text{ in}^2$
$192\text{ in}^2$ because $2\text{ ft}\times\dfrac{12\text{ in}}{1\text{ ft}}=24\text{ in}$ , then $8\text{ in}\times 24\text{ in}=192\text{ in}^2$ (correct answer)
$96\text{ in}$ because $8\times 12=96\text{ in}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 ft=12 in gives ratio 12 in per 1 ft), multiply for area: first 2 ft×(12 in/1 ft)=24 in, then 8 in×24 in=192 in² (units multiply: in×in=in²). Direction: larger unit→smaller unit multiply (ft→in: ×12), and remember area units square when multiplying lengths. Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 2 feet to inches using 1 ft=12 in, multiply: 2 ft×(12 in/1 ft)=24 inches (feet cancel), then area 8 in×24 in=192 in² (units multiply: in×in=in² square inches); or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes; or area 5 ft×3 ft=15 ft². The correct conversion is 2 ft × (12 in / 1 ft) = 24 in, then 8 in × 24 in = 192 in², with feet canceling and units squaring properly. A common error is wrong direction (dividing height), conversion factor wrong, units not squared (answer 192 in instead of in²), arithmetic error (8×24=180), area units wrong (192 ft² not in²), or adds instead of multiplies. Process: (1) identify units (height: ft to in, then area in in²), (2) find conversion (1 ft=12 in), (3) set up conversion (2 ft×(12 in/1 ft)), (4) calculate area (8×24=192 in²), (5) verify units (answer in square inches✓). Dimensional analysis: write conversion factors as fractions with units, ensure multiplied units result in squared form for area.

Question 10

A rectangle on graph paper is $5$ feet long and $3$ feet wide. What is its area, and what units should the area have?

$8\text{ ft}$
$15\text{ ft}^3$
$15\text{ ft}^2$ because $5\text{ ft}\times 3\text{ ft}=15\text{ ft}^2$ (correct answer)
$15\text{ ft}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically; here, no conversion needed, but area requires squaring units. Direction: for area, multiply lengths and square the units (ft × ft = ft²). Example: area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet); or convert 3 feet to inches: 3 ft×(12 in/1 ft)=36 inches; or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes. The correct area is 5 ft × 3 ft = 15 ft², with units properly squared for area. A common error is area units wrong (15 ft not 15 ft²), or confusing with volume (ft³), arithmetic error (5×3=10), or adds instead of multiplies (5+3=8 nonsense). Process: (1) identify task (area of rectangle), (2) no conversion, but use lengths (5 ft and 3 ft), (3) set up multiplication (5 ft × 3 ft), (4) calculate (5×3=15), (5) verify units (ft × ft = ft² ✓). Dimensional analysis for area: treat units algebraically, ensuring exponents for square units (ft²). Mistakes: area/volume unit exponents missed (ft not ft²).

Question 11

A student cuts a ribbon that is 7 feet long. Convert 7 ft to inches using $1\text{ ft}=12\text{ in}$ . Which setup correctly shows unit cancellation and the final answer?

$7\text{ ft}\div 12=0.583\text{ in}$
$7\text{ ft}\times 12\text{ in}=84\text{ ft}\cdot\text{in}$
$7\text{ ft}\times\dfrac{1\text{ ft}}{12\text{ in}}=\dfrac{7}{12}\text{ in}$
$7\text{ ft}\times\dfrac{12\text{ in}}{1\text{ ft}}=84\text{ in}$ (correct answer)

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

gives ratio

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

), multiply:

7 \text{ ft} \times (12 \text{ in}/1 \text{ ft})=84 \text{ in}

(ft cancels: ft in numerator and denominator divide out leaving in). Direction: larger unit→smaller unit multiply (ft→in: ×12), smaller→larger divide (in→ft: ÷12, or ×(1/12)). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 3 feet to inches using

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

, multiply:

3 \text{ ft} \times (12 \text{ in}/1 \text{ ft})=3\times12 \text{ in}=36 \text{ inches}

(feet cancel); or 2.5 hours to minutes:

2.5 \text{ hr} \times (60 \text{ min}/1 \text{ hr})=150 \text{ minutes}

; or area

5 \text{ ft} \times 3 \text{ ft}=15 \text{ ft}^2

(units multiply: ft×ft=ft² square feet). The correct setup is

7 \text{ ft} \times (12 \text{ in} / 1 \text{ ft}) = 84 \text{ in}

, as the units cancel properly leaving inches. A common error is reversing the fraction like in choice A, leading to dividing instead of multiplying, or forgetting to cancel units as in D, resulting in mixed units like ft·in. Process: (1) identify units (start: ft, target: in), (2) find conversion (

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

), (3) set up with cancellation (

7 \text{ ft} \times (12 \text{ in}/1 \text{ ft}

, ft cancels), (4) calculate (

7\times12=84 \text{ in}

), (5) verify units (answer should be in inches✓). Dimensional analysis: write conversion factors as fractions with units (

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

), multiply so units cancel leaving desired unit.

Question 12

A water bottle holds $2$ liters. Use $1\text{ L}=1000\text{ mL}$ to convert $2$ liters to milliliters, showing unit cancellation.

$200\text{ mL}$ because $2\text{ L}\times\dfrac{100\text{ mL}}{1\text{ L}}=200\text{ mL}$
$2000\text{ mL}$ because $2\text{ L}\times\dfrac{1000\text{ mL}}{1\text{ L}}=2000\text{ mL}$ (L cancels) (correct answer)
$2\text{ mL}$ because $2\text{ L}\div 1000=2\text{ mL}$
$1002\text{ mL}$ because $1000+2=1002\text{ mL}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 L=1000 mL gives ratio 1000 mL per 1 L), multiply: 2 L×(1000 mL/1 L)=2000 mL (L cancels: L in numerator and denominator divide out leaving mL). Direction: larger unit→smaller unit multiply (L→mL: ×1000), smaller→larger divide (mL→L: ÷1000, or ×(1/1000)). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 2 liters to milliliters using 1 L=1000 mL, multiply: 2 L×(1000 mL/1 L)=2×1000 mL=2000 milliliters (liters cancel); or 3 feet to inches: 3 ft×(12 in/1 ft)=36 inches; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 2 L × (1000 mL / 1 L) = 2000 mL, with liter units canceling out. A common error is wrong direction (dividing when should multiply: 2÷1000=0.002 L instead of mL), conversion factor wrong (using 100 mL/L), units not canceled (answer 2000 L·mL instead of 2000 mL), arithmetic error (2×1000=1000), or adds instead of multiplies (2+1000=1002 nonsense). Process: (1) identify units (start: L, target: mL), (2) find conversion (1 L=1000 mL), (3) set up with cancellation (2 L×(1000 mL/1 L), L cancels), (4) calculate (2×1000=2000 mL), (5) verify units (answer should be in milliliters✓). Dimensional analysis: write conversion factors as fractions with units (1000 mL/1 L), multiply so units cancel leaving desired unit.

Question 13

A rectangular poster is 5 ft wide and 3 ft tall. What is its area, including correct units?

$8\text{ ft}$
$15\text{ ft}$
$15\text{ ft}^2$ because $5\text{ ft}\times 3\text{ ft}=15\text{ ft}^2$ (correct answer)
$15\text{ ft}^3$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Units multiply/divide: length×length=area (ft×ft=ft²), units treated algebraically. For example, area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct calculation is 5 ft × 3 ft = 15 ft², with units multiplying to square feet for area. A common error is forgetting the squared unit, like just saying 15 ft instead of 15 ft², or adding dimensions like 5+3=8 ft, or mistakenly using cubic feet for 2D area. The process is: (1) identify operation (area: length × width), (2) multiply numbers (5×3=15), (3) multiply units (ft × ft = ft²), (4) verify (answer in square feet for area✓). Multiplying lengths: ft×ft=ft² (area in square feet), and mistakes include missing unit exponents (ft not ft²).

Question 14

A runner completes a 400-meter lap in 80 seconds. Convert this rate to meters per minute. (Use $1\text{ min}=60\text{ s}$ .) What is the runner's speed in m/min?

3.33 m/min
320 m/min
240 m/min
300 m/min (correct answer)

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting speed from m/s to m/min: first find speed as 400 m / 80 s = 5 m/s, then use ratio (1 min=60 s gives 60 s/1 min, but to convert: 5 m/s × (60 s/1 min) = 300 m/min (s cancels leaving m/min). Direction: smaller time unit to larger (s→min: multiply by 60). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: 60 mph to ft/sec uses 60 mi/hr×(5280 ft/1 mi)×(1 hr/3600 sec), mi cancels, hr cancels, result: (60×5280/3600) ft/sec=88 ft/sec. The correct speed is 400 m / 80 s × 60 = 300 m/min. A common error is dividing by 60 instead (5 / 60 ≈0.083, not matching), or wrong setup like 400 / (80 / 60) leading to 300 but confusing steps. Process: (1) identify units (start: m/s, target: m/min), (2) find conversion (1 min=60 s), (3) calculate speed (400/80=5 m/s), set up (5 m/s × 60 s/min), s cancels, (4) calculate (5×60=300 m/min), (5) verify units (answer should be in m/min✓). Speed conversions: mi/hr to ft/sec multiply by (5280 ft/mi)×(1 hr/3600 sec).

Question 15

A cooler holds 12 quarts of water. Convert 12 qt to gallons using $1\text{ gal}=4\text{ qt}$ . Which expression correctly converts quarts to gallons and gives the correct result?

$12\text{ qt}\times\dfrac{4\text{ qt}}{1\text{ gal}}=48\text{ gal}$
$12\text{ qt}\times\dfrac{1\text{ gal}}{4\text{ qt}}=3\text{ gal}$ (correct answer)
$12\text{ qt}\div 4=8\text{ gal}$
$12\text{ qt}\times\dfrac{1\text{ qt}}{4\text{ gal}}=3\text{ qt}$

1\text{ gal}=4\text{ qt}

gives ratio

1\text{ gal}

per

4\text{ qt}

), multiply:

12\text{ qt} \times (1\text{ gal}/4\text{ qt}) = 3\text{ gal}

(

\text{qt}

cancels:

\text{qt}

in numerator and denominator divide out leaving

\text{gal}

). Direction: smaller unit→larger unit divide (

\text{qt} \to \text{gal}

: ÷4, or ×(1/4)). Units multiply/divide: length×length=area (

\text{ft} \times \text{ft} = \text{ft}^2

), distance÷time=speed (

\text{mi} \div \text{hr} = \text{mi/hr}

or mph), units treated algebraically. Example: convert 3 feet to inches using

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

, multiply:

3\text{ ft} \times (12\text{ in}/1\text{ ft}) = 3 \times 12\text{ in} = 36\text{ inches}

(feet cancel); or 2.5 hours to minutes:

2.5\text{ hr} \times (60\text{ min}/1\text{ hr}) = 150\text{ minutes}

; or area

5\text{ ft} \times 3\text{ ft} = 15\text{ ft}^2

(units multiply:

\text{ft} \times \text{ft} = \text{ft}^2

square feet). The correct expression is

12\text{ qt} \times (1\text{ gal} / 4\text{ qt}) = 3\text{ gal}

, with proper unit cancellation. A common error is inverting the ratio like in A, leading to multiplying by 4 instead of dividing (48 gal, too large), or arithmetic mistakes like B saying

12 \div 4 = 8

instead of 3. Process: (1) identify units (start: qt, target: gal), (2) find conversion (

1\text{ gal}=4\text{ qt}

), (3) set up with cancellation (

12\text{ qt} \times (1\text{ gal}/4\text{ qt}

, qt cancels), (4) calculate (

12/4=3\text{ gal}

), (5) verify units (answer should be in gallons✓). Dimensional analysis: write conversion factors as fractions with units (

1\text{ gal}/4\text{ qt}

), multiply so units cancel leaving desired unit.

Question 16

A video is 2.5 hours long. Convert 2.5 hours to minutes using $1\text{ hr}=60\text{ min}$ . What is the length of the video in minutes?

42 minutes
120 minutes
2.5 minutes
150 minutes (correct answer)

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting from hours to minutes: use the conversion factor as a ratio (1 hr=60 min gives ratio 60 min per 1 hr), multiply: 2.5 hr×(60 min/1 hr)=150 min (hr cancels: hr in numerator and denominator divide out leaving min). Direction: larger unit→smaller unit multiply (hr→min: ×60), smaller→larger divide (min→hr: ÷60, or ×(1/60)). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 3 feet to inches using 1 ft=12 in, multiply: 3 ft×(12 in/1 ft)=3×12 in=36 inches (feet cancel); or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 2.5 hr × 60 = 150 minutes. A common error is dividing instead of multiplying, like confusing the direction (2.5 ÷ 60 = 0.0417, not matching any choice) or using the wrong factor (e.g., ×24 for hours in a day). Process: (1) identify units (start: hr, target: min), (2) find conversion (1 hr=60 min), (3) set up with cancellation (2.5 hr×(60 min/1 hr), hr cancels), (4) calculate (2.5×60=150 min), (5) verify units (answer should be in minutes✓). Dimensional analysis: write conversion factors as fractions with units (60 min/1 hr), multiply so units cancel leaving desired unit.

Question 17

A student measures a ribbon that is $7$ feet long. Use $1\text{ ft}=12\text{ in}$ to convert the length to inches. Show the setup with unit cancellation (dimensional analysis).

$84\text{ in}$ because $7\text{ ft}\times\dfrac{12\text{ in}}{1\text{ ft}}=84\text{ in}$ (ft cancels) (correct answer)
$19\text{ in}$ because $7+12=19\text{ in}$
$84\text{ ft}\cdot\text{in}$ because $7\text{ ft}\times 12\text{ in}=84\text{ ft}\cdot\text{in}$
$0.58\text{ in}$ because $7\text{ ft}\div 12=0.58\text{ in}$

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting: use conversion factor as ratio (1 ft=12 in gives ratio 12 in per 1 ft), multiply: 7 ft×(12 in/1 ft)=84 in (ft cancels: ft in numerator and denominator divide out leaving in). Direction: larger unit→smaller unit multiply (ft→in: ×12), smaller→larger divide (in→ft: ÷12, or ×(1/12)). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 7 feet to inches using 1 ft=12 in, multiply: 7 ft×(12 in/1 ft)=7×12 in=84 inches (feet cancel); or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 7 ft × (12 in / 1 ft) = 84 in, with feet units canceling out. A common error is wrong direction (dividing when should multiply: 7÷12=0.583 ft instead of in), conversion factor wrong (using 10 in/ft), units not canceled (answer 84 ft·in instead of 84 in), arithmetic error (7×12=72), or adds instead of multiplies (7+12=19 nonsense). Process: (1) identify units (start: ft, target: in), (2) find conversion (1 ft=12 in), (3) set up with cancellation (7 ft×(12 in/1 ft), ft cancels), (4) calculate (7×12=84 in), (5) verify units (answer should be in inches✓). Dimensional analysis: write conversion factors as fractions with units (12 in/1 ft), multiply so units cancel leaving desired unit.

Question 18

A rectangular garden has a length of 15 feet and width of 8 feet. If a landscaper wants to buy mulch to cover the garden with a 3-inch deep layer, how many cubic feet of mulch are needed?

30 cubic feet (correct answer)
120 cubic feet
360 cubic feet
1,440 cubic feet

Explanation: First convert depth to feet:

3 \text{ inches} \times \frac{1 \text{ foot}}{12 \text{ inches}} = 0.25 \text{ feet}

. Then find volume:

15 \text{ feet} \times 8 \text{ feet} \times 0.25 \text{ feet} = 30 \text{ cubic feet}

. Choice B uses 3 feet instead of 0.25 feet for depth. Choice C uses 3 inches directly as feet. Choice D multiplies the area by 12 instead of dividing depth by 12.

Question 19

A recipe needs 3 pints of milk. Convert 3 pt to cups using $1\text{ pt}=2\text{ cups}$ . How many cups are needed?

6 cups (correct answer)
5 cups
1.5 cups
12 cups

Explanation: This question tests converting measurement units using ratio reasoning (conversion factors as ratios), unit cancellation (dimensional analysis), and manipulating units in multiplication/division. Converting from pints to cups: use the conversion factor as a ratio (1 pt=2 cups gives 2 cups/1 pt), multiply: 3 pt×(2 cups/1 pt)=6 cups (pt cancels leaving cups). Direction: larger unit→smaller unit multiply (pt→cups: ×2). Units multiply/divide: length×length=area (ft×ft=ft²), distance÷time=speed (mi÷hr=mi/hr or mph), units treated algebraically. Example: convert 3 feet to inches using 1 ft=12 in, multiply: 3 ft×(12 in/1 ft)=3×12 in=36 inches (feet cancel); or 2.5 hours to minutes: 2.5 hr×(60 min/1 hr)=150 minutes; or area 5 ft×3 ft=15 ft² (units multiply: ft×ft=ft² square feet). The correct conversion is 3 pt × 2 = 6 cups. A common error is dividing instead of multiplying (3 ÷ 2 = 1.5, like choice A), or using a wrong factor (e.g., ×4 for quarts). Process: (1) identify units (start: pt, target: cups), (2) find conversion (1 pt=2 cups), (3) set up with cancellation (3 pt×(2 cups/1 pt), pt cancels), (4) calculate (3×2=6 cups), (5) verify units (answer should be in cups✓). Dimensional analysis: write conversion factors as fractions with units (2 cups/1 pt), multiply so units cancel leaving desired unit.

Question 20

A carpenter cuts a 12-foot board into pieces that are each 8 inches long. How many complete pieces can be cut from the board?

1.5 pieces
9 pieces
96 pieces
18 pieces (correct answer)

Explanation: When you encounter a problem involving different units of measurement, your first step is always to convert everything to the same unit before doing any calculations. Here you have a 12-foot board being cut into 8-inch pieces. Since the answer choices are asking for number of pieces, let's convert the board length to inches:

12 \text{ feet} \times 12 \text{ inches per foot} = 144 \text{ inches}

. Now you can divide the total length by the length of each piece:

144 \text{ inches} \div 8 \text{ inches per piece} = 18 \text{ pieces}

. Since 144 divides evenly by 8, you get exactly 18 complete pieces with no waste. Let's examine why the other answers are wrong. Choice A (1.5 pieces) likely comes from incorrectly dividing 12 by 8 without converting units first—this ignores that feet and inches are different measurements. Choice B (9 pieces) might result from converting incorrectly or making an arithmetic error in the division. Choice C (96 pieces) probably comes from multiplying 12 × 8 instead of dividing, which shows a fundamental misunderstanding of the operation needed. The key strategy for unit conversion problems is to always write out your units and make sure they match before calculating. When you see different units in a problem, immediately convert to make them the same. Also, think logically about your answer—96 pieces from a 12-foot board cut into 8-inch pieces should seem unreasonably high, while 1.5 pieces seems too low for such a long board.