Middle School Math Quiz: Understand Unit Rate Concept
20 questions · exam conditions
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Understand Unit Rate ConceptQuestion 1 of 20

A movie theater sells 15 tickets for $120 for a group. What is the unit rate in dollars per ticket?

$120 per 15 tickets
$105 per ticket
$7 per ticket
$8 per ticket
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Middle School Math Quiz

Middle School Math Quiz: Understand Unit Rate Concept

Practice Understand Unit Rate Concept in Middle School 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 Understand Unit Rate Concept, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School 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 movie theater sells 15 tickets for $120 for a group. What is the unit rate in dollars per ticket?

  1. $120 per 15 tickets
  2. $105 per ticket
  3. $7 per ticket
  4. $8 per ticket (correct answer)
Explanation: This question tests understanding of unit rate as the amount of dollars per one ticket, using rate language like 'per' in the context of group pricing. The ratio of $120 to 15 tickets becomes a unit rate by dividing 120 by 15, resulting in $8 per ticket, meaning 8foreachoneticket.Ratelanguageincludes′per′or′foreach,′suchas′8 for each one ticket. Rate language includes 'per' or 'for each,' such as '8 per ticket' or 'for each ticket, it costs $8.' Units are essential: 8perticket(8 per ticket (/ticket). Calculation: divide dollars by tickets (120 ÷ 15 = 8). For example, $120 for 15 tickets calculates to 120÷15=8, so the unit rate is $8 per ticket (each ticket costs $8). The correct unit rate is $8 per ticket with proper language and units. A common error is dividing incorrectly like 15/120=0.125 tickets per dollar, or stating the ratio $120:15, or miscalculating as 120÷15=7. To find the unit rate: (1) identify the ratio (120:15 dollars to tickets), (2) divide first by second (120÷15=8), (3) express with units (8 dollars per ticket), (4) use rate language ('costs $8 per ticket'). Interpretation: this unit rate tells that each ticket costs $8. Ratio vs unit rate: ratio compares (120:15), unit rate simplifies to per-unit (8 per).

Question 2

A music playlist has 45 minutes of songs spread across 9 songs. What is the unit rate in minutes per song?

  1. 54 minutes per song
  2. 9 minutes per 45 songs
  3. 5 minutes per song (correct answer)
  4. 4 minutes per song
Explanation: This question tests understanding of unit rate as the amount of minutes per one song, using rate language like 'per' in the context of playlists. The ratio of 45 minutes to 9 songs becomes a unit rate by dividing 45 by 9, resulting in 5 minutes per song, meaning 5 minutes for each one song. Rate language includes 'per' or 'for each,' such as '5 minutes per song' or 'for each song, it takes 5 minutes.' Units are essential: 5 minutes per song (min/song). Calculation: divide minutes by songs (45 ÷ 9 = 5). For example, 45 minutes across 9 songs calculates to 45÷9=5, so the unit rate is 5 minutes per song (each song is 5 minutes long). The correct unit rate is 5 minutes per song with proper language and units. A common error is reversing to 9/45=0.2 songs per minute, or stating the ratio 45:9, or adding like 45+9=54. To find the unit rate: (1) identify the ratio (45:9 minutes to songs), (2) divide first by second (45÷9=5), (3) express with units (5 minutes per song), (4) use rate language ('5 minutes per song'). Interpretation: this unit rate tells that each song lasts 5 minutes. Ratio vs unit rate: ratio compares (45:9), unit rate simplifies to per-unit (5 per).

Question 3

A coach buys 14 water bottles for $49. What is the unit rate in dollars per bottle?

  1. $35 per bottle
  2. $49 per bottle
  3. $3.50 per bottle (correct answer)
  4. $2.80 per bottle
Explanation: This question tests understanding of unit rate as the amount of dollars per one bottle, using rate language like 'per' in the context of bulk purchases. The ratio of $49 to 14 bottles becomes a unit rate by dividing 49 by 14, resulting in $3.50 per bottle, meaning 3.50foreachonebottle.Ratelanguageincludes′per′or′foreach,′suchas′3.50 for each one bottle. Rate language includes 'per' or 'for each,' such as '3.50 per bottle' or 'for each bottle, it costs $3.50.' Units are essential: 3.50perbottle(3.50 per bottle (/bottle). Calculation: divide dollars by bottles (49 ÷ 14 = 3.5). For example, $49 for 14 bottles calculates to 49÷14=3.5, so the unit rate is $3.50 per bottle (each bottle costs $3.50). The correct unit rate is $3.50 per bottle with proper language and units. A common error is dividing incorrectly like 14/49≈0.286 bottles per dollar, or rounding wrong like $3, or stating the ratio $49:14. To find the unit rate: (1) identify the ratio (49:14 dollars to bottles), (2) divide first by second (49÷14=3.5), (3) express with units (3.50 dollars per bottle), (4) use rate language ('costs $3.50 per bottle'). Interpretation: this unit rate tells that each bottle costs $3.50. Ratio vs unit rate: ratio compares (49:14), unit rate simplifies to per-unit (3.5 per).

Question 4

A bottle holds 1212 ounces of juice and costs $3. What is the unit rate in dollars per ounce?

  1. $0.25 per ounce (correct answer)
  2. $4 per ounce
  3. \3:12$ (not a unit rate)
  4. $0.36 per ounce
Explanation: This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in pricing contexts. A ratio like 3:12 dollars to ounces becomes a unit rate by dividing 3 by 12, giving 0.25 dollars per ounce or 0.25foreachounce.Ratelanguageshouldinclude′per′or′foreach,′suchas′0.25 for each ounce. Rate language should include 'per' or 'for each,' such as '0.25 per ounce,' and units are essential, like dollars per ounce ($/oz). The calculation involves dividing the first quantity by the second: 3 ÷ 12 = 0.25. For example, with $3 for 12 ounces, calculate 3 ÷ 12 = 0.25, so the unit rate is $0.25 per ounce, meaning each ounce costs $0.25. The correct unit rate is 0.25perounce.Acommonerrorisreversingtoouncesperdollarlike12/3=4,statingtheratio3:12,omittingunitslikejust′0.25,′orwrongmathlike3/8.333≈0.36.Tofindtheunitrate:(1)identifytheratio(3:12dollarstoounces),(2)dividefirstbysecond(3÷12=0.25),(3)expresswithunits(0.25 per ounce. A common error is reversing to ounces per dollar like 12/3=4, stating the ratio 3:12, omitting units like just '0.25,' or wrong math like 3/8.333≈0.36. To find the unit rate: (1) identify the ratio (3:12 dollars to ounces), (2) divide first by second (3 ÷ 12 = 0.25), (3) express with units (0.25 per ounce), (4) use rate language ('$0.25 per ounce'). Interpretation: the unit rate tells that for each 1 ounce, the cost is $0.25. Ratio compares totals (3:12), while unit rate simplifies to per unit (0.25 per). Common contexts include cost per unit, like dollars per ounce in products.

Question 5

A video game downloads 500500 megabytes in 44 minutes. What is the unit rate in megabytes per minute?

  1. 125125 megabytes per minute (correct answer)
  2. 20002000 megabytes per minute
  3. 44 megabytes per minute
  4. 4500\frac{4}{500} megabytes per minute
Explanation: This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in download speed contexts. A ratio like 500:4 megabytes to minutes becomes a unit rate by dividing 500 by 4, giving 125 megabytes per minute or 125 MB for each minute. Rate language should include 'per' or 'for each,' such as '125 megabytes per minute,' and units are essential, like megabytes per minute (MB/min). The calculation involves dividing the first quantity by the second: 500 ÷ 4 = 125. For example, with 500 megabytes in 4 minutes, calculate 500 ÷ 4 = 125, so the unit rate is 125 megabytes per minute, meaning 125 MB downloaded each minute. The correct unit rate is 125 megabytes per minute. A common error is reversing to minutes per megabyte like 4/500, multiplying 500*4=2000, omitting units like just '125,' or dividing wrong like 500/125=4. To find the unit rate: (1) identify the ratio (500:4 megabytes to minutes), (2) divide first by second (500 ÷ 4 = 125), (3) express with units (125 megabytes per minute), (4) use rate language ('125 megabytes per minute'). Interpretation: the unit rate tells that in each 1 minute, 125 megabytes are downloaded. Ratio compares totals (500:4), while unit rate simplifies to per unit (125 per). Common contexts include download rates, like data per time.

Question 6

A movie theater sells 15 tickets for $120. Which statement correctly gives the unit rate using rate language?

  1. 120÷15=60120 \div 15 = 60 dollars per ticket
  2. $120 per 15 tickets
  3. $8 per ticket (correct answer)
  4. $105 per ticket
Explanation: This question tests understanding of unit rate as the amount of dollars per one ticket, using rate language like 'per' in the context of ticket pricing. The ratio of $120 to 15 tickets becomes a unit rate by dividing 120 by 15, resulting in 8, which means $8 per ticket or 8foreachoneticket;ratelanguageincludes′per′or′foreach,′andunitsareessential,suchasdollarsperticket(8 for each one ticket; rate language includes 'per' or 'for each,' and units are essential, such as dollars per ticket (/ticket). For example, with $120 for 15 tickets, calculate 120 ÷ 15 = 8, so the unit rate is $8 per ticket (each ticket costs $8). The correct statement is $8 per ticket, which properly uses rate language and units. A common error is leaving it as the ratio 120per15ticketswithoutdividing,ormiscalculatinglike120÷15=60,oromitting′per′makingitunclear.Tofindtheunitrate:(1)identifytheratio(120:15dollarstotickets),(2)dividedollarsbytickets(120÷15=8),(3)expresswithunits(120 per 15 tickets without dividing, or miscalculating like 120 ÷ 15 = 60, or omitting 'per' making it unclear. To find the unit rate: (1) identify the ratio (120:15 dollars to tickets), (2) divide dollars by tickets (120 ÷ 15 = 8), (3) express with units (8 per ticket), (4) use rate language ('$8 per ticket'). This unit rate tells the cost per one ticket, distinguishing it from the bulk price ratio.

Question 7

A school store sells 12 notebooks for $18. What is the unit rate, in dollars per notebook?

  1. $18 per notebook
  2. $1.50 per notebook (correct answer)
  3. $6 per notebook
  4. 12:18 dollars per notebook
Explanation: This question tests understanding of unit rate as the amount of dollars per one notebook, using rate language like 'per' in the context of pricing. The ratio of $18 to 12 notebooks becomes a unit rate by dividing 18 by 12, resulting in 1.5, which means $1.50 per notebook or 1.50foreachonenotebook;ratelanguageincludes′per′or′foreach,′andunitsareessential,suchasdollarspernotebook(1.50 for each one notebook; rate language includes 'per' or 'for each,' and units are essential, such as dollars per notebook (/notebook). For example, with $18 for 12 notebooks, calculate 18 ÷ 12 = 1.5, so the unit rate is $1.50 per notebook (each notebook costs $1.50). The correct unit rate is 1.50pernotebook.Acommonerrorisstatingtheratioas12:18insteadoftheunitrate,orreversingtofindnotebooksperdollar,oromittingunitslikejustsaying′1.50′withoutspecifyingdollarspernotebook.Tofindtheunitrate:(1)identifytheratio(18:12dollarstonotebooks),(2)dividedollarsbynotebooks(18÷12=1.5),(3)expresswithunits(1.50 per notebook. A common error is stating the ratio as 12:18 instead of the unit rate, or reversing to find notebooks per dollar, or omitting units like just saying '1.50' without specifying dollars per notebook. To find the unit rate: (1) identify the ratio (18:12 dollars to notebooks), (2) divide dollars by notebooks (18 ÷ 12 = 1.5), (3) express with units (1.50 per notebook), (4) use rate language ('costs $1.50 per notebook'). This unit rate tells the cost per one notebook, simplifying the comparison from the total ratio.

Question 8

A video game downloads 600 megabytes in 5 minutes. What is the unit rate in megabytes per minute?

  1. 3000 megabytes per minute
  2. 5 megabytes per 600 minutes
  3. 60 megabytes per minute
  4. 120 megabytes per minute (correct answer)
Explanation: This question tests understanding of unit rate as the amount of megabytes per one minute, using rate language like 'per' in the context of download speeds. The ratio of 600 megabytes to 5 minutes becomes a unit rate by dividing 600 by 5, resulting in 120 megabytes per minute, meaning 120 megabytes for each one minute. Rate language includes 'per' or 'for each,' such as '120 megabytes per minute' or 'for each minute, downloads 120 megabytes.' Units are essential: 120 megabytes per minute (MB/min). Calculation: divide megabytes by minutes (600 ÷ 5 = 120). For example, 600 megabytes in 5 minutes calculates to 600÷5=120, so the unit rate is 120 megabytes per minute (downloads 120 MB each minute). The correct unit rate is 120 megabytes per minute with proper language and units. A common error is stating the ratio like 600:5, or reversing to 5/600 minutes per megabyte, or miscalculating as 600×5=3000. To find the unit rate: (1) identify the ratio (600:5 megabytes to minutes), (2) divide first by second (600÷5=120), (3) express with units (120 megabytes per minute), (4) use rate language ('120 megabytes per minute'). Interpretation: this unit rate tells that in each minute, 120 megabytes are downloaded. Ratio vs unit rate: ratio compares (600:5), unit rate simplifies to per-unit (120 per).

Question 9

The graph shows the relationship between time and distance for a jogger running at a constant speed. What is the jogger's unit rate, and what does it represent?

  1. 6 miles per hour, representing the distance traveled in one hour of jogging (correct answer)
  2. 10 minutes per mile, representing the time needed to jog each mile
  3. 0.1 hours per mile, representing the fraction of an hour needed per mile
  4. 3 miles per 30 minutes, representing the distance covered in half an hour
Explanation: From the graph, the jogger travels 3 miles in 30 minutes (0.5 hours). The unit rate for speed is 3 miles ÷ 0.5 hours = 6 miles per hour, which represents distance per unit time. Choice B gives time per distance (the reciprocal) rather than the standard speed unit rate. Choice C also gives time per distance, just in decimal form. Choice D gives a rate but not a unit rate since it uses 30 minutes rather than 1 hour as the time unit.

Question 10

A bakery sells cookies in packages. The table shows the number of packages and their total cost. Based on this information, which statement correctly describes the unit rate and its meaning?

  1. The unit rate is $3.50 per package, meaning each package costs $3.50
  2. The unit rate is $7.00 per package, meaning the cost doubles for each additional package
  3. The unit rate is $2.50 per package, meaning each package costs $2.50 (correct answer)
  4. The unit rate is $1.75 per package, meaning half a package costs $1.75
Explanation: Looking at the table, 2 packages cost $5.00, so the unit rate is $5.00 ÷ 2 = $2.50 per package. This can be verified with other rows: 4 packages for $10.00 gives $10.00 ÷ 4 = $2.50 per package. Choice A uses an incorrect calculation. Choice B incorrectly calculates the unit rate as $14.00 ÷ 2. Choice D incorrectly divides by 4 instead of finding the rate per single package.

Question 11

A recipe uses 3 cups of flour for every 4 cups of sugar. What is the unit rate of flour per 1 cup of sugar?

  1. 0.34 cup flour per cup sugar
  2. 3:4 cups flour per cup sugar
  3. 34\frac{3}{4} cup flour per cup sugar (correct answer)
  4. 43\frac{4}{3} cup flour per cup sugar
Explanation: This question tests understanding of unit rate as the amount of flour per one cup of sugar, using rate language like 'per' in the context of recipes. The ratio of 3 cups flour to 4 cups sugar becomes a unit rate by dividing 3 by 4, resulting in 3/4, which means 3/4 cup flour per cup sugar or 3/4 cup flour for each one cup sugar; rate language includes 'per' or 'for each,' and units are essential, such as cups flour per cup sugar. For example, with 3 cups flour for 4 cups sugar, calculate 3 ÷ 4 = 3/4, so the unit rate is 3/4 cup flour per cup sugar (for each cup of sugar, use 3/4 cup flour). The correct unit rate is 3/4 cup flour per cup sugar. A common error is stating the reciprocal as 4/3 instead of 3/4, or leaving it as the ratio 3:4 without dividing, or reversing the direction to sugar per flour. To find the unit rate: (1) identify the ratio (3:4 flour to sugar), (2) divide flour by sugar (3 ÷ 4 = 3/4), (3) express with units (3/4 cup flour per cup sugar), (4) use rate language ('3/4 cup flour per cup sugar'). This unit rate tells the amount of flour needed per one cup of sugar, distinguishing it from the overall ratio.

Question 12

At a fruit stand, apples cost $4.50 for 3 pounds and oranges cost $6.40 for 4 pounds. Sarah wants to buy 5 pounds of the cheaper fruit. How much will she spend?

  1. $7.50 because oranges cost $1.50 per pound and 5 × $1.50 = $7.50
  2. $8.00 because oranges cost $1.60 per pound and 5 × $1.60 = $8.00
  3. $8.00 because apples cost $1.60 per pound and 5 × $1.60 = $8.00
  4. $7.50 because apples cost $1.50 per pound and 5 × $1.50 = $7.50 (correct answer)
Explanation: When you encounter word problems involving rates and unit prices, you need to find the cost per unit first, then compare to determine which option is cheaper. Let's calculate the cost per pound for each fruit. For apples: $4.503 pounds=$1.50 per pound\frac{\$4.50}{3 \text{ pounds}} = \$1.50 \text{ per pound}. For oranges: $6.404 pounds=$1.60 per pound\frac{\$6.40}{4 \text{ pounds}} = \$1.60 \text{ per pound}. Since apples cost $1.50 per pound and oranges cost $1.60 per pound, apples are the cheaper fruit. Sarah wants 5 pounds of the cheaper fruit (apples), so her total cost is: $5 \times \1.50 = $7.50 Now let's examine why the other answers are wrong. Choice A incorrectly states that oranges cost $1.50 per pound—this is actually the price of apples. The calculation is right, but it's applied to the wrong fruit. Choice B correctly calculates that oranges cost $1.60 per pound, but oranges aren't the cheaper option, so Sarah wouldn't buy them. Choice C makes a calculation error by claiming apples cost $1.60 per pound, which is actually the price of oranges. Choice D correctly identifies that apples cost $1.50 per pound, recognizes that apples are cheaper than oranges, and properly calculates the total cost as $7.50. Study tip: In multi-step word problems, work systematically: calculate all unit rates first, compare them to find what you're looking for, then do your final calculation. Double-check that you're using the right numbers for the right items—mixing up which price belongs to which option is a common mistake.

Question 13

Marcus reads at a rate of 180 words in 4 minutes. His sister Emma reads 270 words in 5 minutes. How many more words per minute does the faster reader read compared to the slower reader?

  1. 54 words per minute more than the slower reader
  2. 9 words per minute more than the slower reader (correct answer)
  3. 45 words per minute more than the slower reader
  4. 90 words per minute more than the slower reader
Explanation: First, calculate each reader's unit rate. Marcus: 180 words ÷ 4 minutes = 45 words per minute. Emma: 270 words ÷ 5 minutes = 54 words per minute. Emma is faster. The difference is 54 - 45 = 9 words per minute. Choice A gives Emma's rate instead of the difference. Choice C gives Marcus's rate instead of the difference. Choice D incorrectly adds the rates instead of finding the difference.

Question 14

A cyclist rides 180 miles in 3 hours. What is the unit rate, in miles per hour?

  1. 60 miles per hour (correct answer)
  2. 183 miles per hour
  3. 180:3 miles per hour
  4. 90 miles per hour
Explanation: This question tests understanding of unit rate as the amount of miles per one hour, using rate language like 'per' in the context of cycling speed. The ratio of 180 miles to 3 hours becomes a unit rate by dividing 180 by 3, resulting in 60, which means 60 miles per hour or 60 miles for each one hour; rate language includes 'per' or 'for each,' and units are essential, such as miles per hour (mph). For example, with 180 miles in 3 hours, calculate 180 ÷ 3 = 60, so the unit rate is 60 miles per hour (travel 60 miles in each hour). The correct unit rate is 60 miles per hour. A common error is stating the ratio as 180:3 without dividing, or adding like 180 + 3 = 183, or inverting to hours per mile. To find the unit rate: (1) identify the ratio (180:3 miles to hours), (2) divide miles by hours (180 ÷ 3 = 60), (3) express with units (60 miles per hour), (4) use rate language ('60 miles per hour'). This unit rate tells the speed per one hour, simplifying the total journey into a per-unit measure.

Question 15

A school store sells 6 notebooks for $18. What is the unit rate in dollars per notebook?

  1. $18 per notebook
  2. $3 per notebook (correct answer)
  3. $12 per notebook
  4. $18:6 per notebook
Explanation: This question tests understanding of unit rate as the amount of dollars per one notebook, using rate language like 'per' in the context of pricing. The ratio of $18 to 6 notebooks becomes a unit rate by dividing 18 by 6, resulting in $3 per notebook, meaning 3foreachonenotebook.Ratelanguageincludes′per′or′foreach,′suchas′3 for each one notebook. Rate language includes 'per' or 'for each,' such as '3 per notebook' or 'for each notebook, it costs $3.' Units are essential: 3pernotebook(3 per notebook (/notebook). Calculation: divide dollars by notebooks (18 ÷ 6 = 3). For example, $18 for 6 notebooks calculates to 18÷6=3, so the unit rate is $3 per notebook (each notebook costs $3). The correct unit rate is $3 per notebook with proper language and units. A common error is stating the ratio like 18:6insteadoftheunitrate,orreversingto6/18=18:6 instead of the unit rate, or reversing to 6/18=0.33 notebooks per dollar, or omitting units like just '3.' To find the unit rate: (1) identify the ratio (18:6 dollars to notebooks), (2) divide first by second (18÷6=3), (3) express with units (3 dollars per notebook), (4) use rate language ('costs $3 per notebook'). Interpretation: this unit rate tells that each notebook costs $3. Ratio vs unit rate: ratio compares (18:6), unit rate simplifies to per-unit (3 per).

Question 16

A pack of markers costs $14 for 7 markers. What is the unit rate in dollars per marker?

  1. $7 per marker
  2. $2 per marker (correct answer)
  3. $0.50 per marker
  4. 14:7 dollars per marker
Explanation: This question tests understanding of unit rate as the amount of dollars per one marker, using rate language like 'per' in the context of unit pricing. The ratio of $14 to 7 markers becomes a unit rate by dividing 14 by 7, resulting in 2, which means $2 per marker or 2foreachonemarker;ratelanguageincludes′per′or′foreach,′andunitsareessential,suchasdollarspermarker(2 for each one marker; rate language includes 'per' or 'for each,' and units are essential, such as dollars per marker (/marker). For example, with $14 for 7 markers, calculate 14 ÷ 7 = 2, so the unit rate is $2 per marker (each marker costs $2). The correct unit rate is 2permarker.Acommonerrorisstatingtheratioas14:7withoutdividing,orreversingtomarkersperdollarlike7/14=0.50,oraddinginsteadofdividing.Tofindtheunitrate:(1)identifytheratio(14:7dollarstomarkers),(2)dividedollarsbymarkers(14÷7=2),(3)expresswithunits(2 per marker. A common error is stating the ratio as 14:7 without dividing, or reversing to markers per dollar like 7/14 = 0.50, or adding instead of dividing. To find the unit rate: (1) identify the ratio (14:7 dollars to markers), (2) divide dollars by markers (14 ÷ 7 = 2), (3) express with units (2 per marker), (4) use rate language ('$2 per marker'). This unit rate tells the cost per one marker, making it distinct from the pack ratio for individual pricing.

Question 17

A bus travels 9696 miles in 22 hours. What is the unit rate in miles per hour?

  1. 4848 miles per hour (correct answer)
  2. 192192 miles per hour
  3. 9494 miles per hour
  4. 296\frac{2}{96} miles per hour
Explanation: This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in speed contexts. A ratio like 96:2 miles to hours becomes a unit rate by dividing 96 by 2, giving 48 miles per hour or 48 mph for each hour. Rate language should include 'per' or 'for each,' such as '48 miles per hour,' and units are essential, like miles per hour (mph). The calculation involves dividing the first quantity by the second: 96 ÷ 2 = 48. For example, with 96 miles in 2 hours, calculate 96 ÷ 2 = 48, so the unit rate is 48 miles per hour, meaning 48 miles traveled each hour. The correct unit rate is 48 miles per hour. A common error is adding like 96-2=94 or 96*2=192, reducing wrong like 2/96, omitting units like just '48,' or reversing direction. To find the unit rate: (1) identify the ratio (96:2 miles to hours), (2) divide first by second (96 ÷ 2 = 48), (3) express with units (48 miles per hour), (4) use rate language ('48 miles per hour'). Interpretation: the unit rate tells that in each 1 hour, 48 miles are traveled. Ratio compares totals (96:2), while unit rate simplifies to per unit (48 per). Common contexts include transportation speed, like miles per hour.

Question 18

A runner travels 12 miles in 3 hours. What is the unit rate in miles per hour?

  1. 9 miles per hour
  2. 36 miles per hour
  3. 12:3 miles per hour
  4. 4 miles per hour (correct answer)
Explanation: This question tests understanding of unit rate as the amount of miles per one hour, using rate language like 'per' in the context of speed. The ratio of 12 miles to 3 hours becomes a unit rate by dividing 12 by 3, resulting in 4 miles per hour, meaning 4 miles for each one hour. Rate language includes 'per' or 'for each,' such as '4 miles per hour' or 'for each hour, travels 4 miles.' Units are essential: 4 miles per hour (mph). Calculation: divide miles by hours (12 ÷ 3 = 4). For example, 12 miles in 3 hours calculates to 12÷3=4, so the unit rate is 4 miles per hour (travels 4 miles each hour). The correct unit rate is 4 miles per hour with proper language and units. A common error is multiplying instead of dividing like 12×3=36, or stating the ratio 12:3, or reversing to 3/12=0.25 hours per mile. To find the unit rate: (1) identify the ratio (12:3 miles to hours), (2) divide first by second (12÷3=4), (3) express with units (4 miles per hour), (4) use rate language ('4 miles per hour'). Interpretation: this unit rate tells that in each hour, the runner travels 4 miles. Ratio vs unit rate: ratio compares (12:3), unit rate simplifies to per-unit (4 per).

Question 19

A school store sells 99 notebooks for $27. What is the unit rate in dollars per notebook?

  1. $18 per notebook
  2. $3 per notebook (correct answer)
  3. $27 per notebook
  4. \27:9$ (not a unit rate)
Explanation: This question tests understanding of unit rate as the amount of the first quantity per one unit of the second, using rate language like 'per' or 'for each' in pricing contexts. A ratio like 27:927:9 dollars to notebooks becomes a unit rate by dividing 2727 by 99, giving 33 dollars per notebook or 33 for each notebook. Rate language should include 'per' or 'for each,' such as '33 per notebook,' and units are essential, like dollars per notebook ($/notebook). The calculation involves dividing the first quantity by the second: 27÷9=327 ÷ 9 = 3. For example, with 2727 for 99 notebooks, calculate 27÷9=327 ÷ 9 = 3, so the unit rate is 33 per notebook, meaning each notebook costs 33. The correct unit rate is 33 per notebook. A common error is reversing to notebooks per dollar like 9/27=1/39/27=1/3, stating the ratio 27:927:9, omitting units like just '3,' or multiplying 27/1.5=1827/1.5=18 or adding to 27+9/27+9/ something=something.Tofindtheunitrate:(1)identifytheratio(= something. To find the unit rate: (1) identify the ratio (27:9dollarstonotebooks),(2)dividefirstbysecond( dollars to notebooks), (2) divide first by second (27 ÷ 9 = 3),(3)expresswithunits(), (3) express with units (3pernotebook),(4)useratelanguage(′ per notebook), (4) use rate language ('3pernotebook′).Interpretation:theunitratetellsthatforeach1notebook,thecostisper notebook'). Interpretation: the unit rate tells that for each 1 notebook, the cost is3.Ratiocomparestotals(. Ratio compares totals (27:9),whileunitratesimplifiestoperunit(), while unit rate simplifies to per unit (3$ per). Common contexts include school supplies pricing, like cost per item.

Question 20

A class has 24 students and 3 teachers. What is the unit rate of students per teacher?

  1. 21 students per teacher
  2. 8 students per teacher (correct answer)
  3. 3 students per teacher
  4. 24:3 students per teacher
Explanation: This question tests understanding of unit rate as the amount of students per one teacher, using rate language like 'per' in the context of class ratios. The ratio of 24 students to 3 teachers becomes a unit rate by dividing 24 by 3, resulting in 8, which means 8 students per teacher or 8 students for each one teacher; rate language includes 'per' or 'for each,' and units are essential, such as students per teacher. For example, with 24 students and 3 teachers, calculate 24 ÷ 3 = 8, so the unit rate is 8 students per teacher (each teacher has 8 students). The correct unit rate is 8 students per teacher. A common error is reversing to teachers per student like 3/24, or stating the ratio as 24:3 without dividing, or subtracting like 24 - 3 = 21. To find the unit rate: (1) identify the ratio (24:3 students to teachers), (2) divide students by teachers (24 ÷ 3 = 8), (3) express with units (8 students per teacher), (4) use rate language ('8 students per teacher'). This unit rate tells the number of students per one teacher, making it easier to compare class sizes than the total ratio.