- During a winter morning, the temperatures were −5∘C at 7 a.m. and 3∘C at noon. Which inequality correctly compares the temperatures (from colder to warmer)?
Answer: −5<3
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct inequality is -5<3, meaning the temperature at 7 a.m. (-5°C) is colder than at noon (3°C). A common error is confusing magnitude for negatives, like thinking -5>3 because 5 is larger than 3, or reversing context by writing 3<-5 to indicate warmer to colder. Writing: (1) identify values in context (temperatures -5 and 3), (2) determine relationship (which colder? -5 farther below zero, colder), (3) write inequality (-5<3 mathematically), (4) explain in context (-5°C is colder than 3°C because below zero). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - A timer shows minutes relative to now: −10 means 10 minutes ago, 0 means now, and 5 means 5 minutes from now. Put these times in order from earliest to latest.
Answer: −10<0<5
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct order is -10<0<5, meaning 10 minutes ago is earliest, then now, then 5 minutes from now as latest. A common error is treating positives as earlier, like 5<0<-10, or misinterpreting negatives as future times. Writing: (1) identify values in context (times -10, 0, 5), (2) determine relationship (which earlier? -10 is past, earliest), (3) write inequality (-10<0<5 mathematically), (4) explain in context (10 minutes ago is earlier than now, which is earlier than 5 minutes from now). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - Four temperatures were recorded during a science lab: −2∘C, 3∘C, 0∘C, and −5∘C. Arrange them from coldest to warmest using an inequality chain.
Answer: −5<−2<0<3
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct order is -5<-2<0<3, meaning -5°C is the coldest, followed by -2°C, then 0°C, and 3°C as the warmest. A common error is ordering by magnitude without sign, like -2<-5<0<3, or treating 0 as the coldest. Writing: (1) identify values in context (temperatures -5, -2, 0, 3), (2) determine relationship (which colder? -5 most negative), (3) write inequality (-5<-2<0<3 mathematically), (4) explain in context (-5°C coldest to 3°C warmest). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - A hiker's elevation relative to sea level is shown for three points on a trail: Point A is −30 m, Point B is 0 m, and Point C is 40 m. Arrange the elevations from lowest to highest.
Answer: −30<0<40
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct order is -30<0<40, meaning Point A (-30 m) is the lowest elevation, followed by Point B (0 m), then Point C (40 m) as the highest. A common error is reversing the order, like thinking 40<0<-30 because positives seem smaller in elevation context, or misplacing zero as the lowest. Writing: (1) identify values in context (elevations -30, 0, 40), (2) determine relationship (which lower? -30 farthest below zero), (3) write inequality (-30<0<40 mathematically), (4) explain in context (-30 m is lower than 0 m, which is lower than 40 m). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - In a football drill, a player is at −15 yards (15 yards behind the line of scrimmage) and another is at 8 yards (8 yards ahead). Which inequality correctly compares their positions on the field?
Answer: −15<8
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct inequality is -15<8, meaning the player at -15 yards is behind (less advanced) compared to the one at 8 yards ahead. A common error is reversing the inequality, like -15>8, thinking larger magnitude negative is greater, or confusing field positions. Writing: (1) identify values in context (positions -15 and 8), (2) determine relationship (which behind? -15 is negative, behind), (3) write inequality (-15<8 mathematically), (4) explain in context (-15 yards is behind 8 yards). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - A bank app shows three balances: −$50 (debt), −$20 (debt), and $0 (no money owed). Which inequality chain correctly orders the balances from most debt to least debt?
Answer: −50<−20<0
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct order is -50<-20<0, meaning -$50 is most debt, then -$20, and $0 as least debt (no debt). A common error is ordering by magnitude, like -20<-50<0, thinking smaller debt number is more debt, or placing 0 as most debt. Writing: (1) identify values in context (balances -50, -20, 0), (2) determine relationship (which more debt? -50 larger negative), (3) write inequality (-50<-20<0 mathematically), (4) explain in context (most debt to least debt). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - A student's lunch account shows a balance of −$12 (they owe money). Another student has $5 (money available). Which statement best interprets the inequality −12<5 in this context?
Answer: The student who owes $12 has less money than the student with $5.
This problem is all about comparing positive and negative numbers using a number line. The key idea is simple: the number farther to the left is always smaller.
Let's place our two numbers on a number line. We have −12 (owing money) and 5 (having money). Zero sits in the middle. Since −12 is to the left of 5, we know −12<5. In words, −12 is less than 5.
Now connect that back to the lunch accounts. Owing $12 means you're below zero, while having $5 means you're above zero. So the student who owes $12 truly has less money than the student with $5. That matches choice A!
Think of it like temperature: −12 degrees is much colder (lower) than 5 degrees.
Try this at home: Draw a number line and compare −3 and 2. Which is farther left? - A maintenance worker needs to visit all floors that the elevator stopped at that are higher than basement level 5 but lower than the 8th floor. Which floors meet this requirement?
Answer: Basement level 2 and the 3rd floor both meet these elevation requirements
Floors that are higher than basement level 5 (-5) but lower than the 8th floor (8): basement level 2 (-2) and 3rd floor (3) both satisfy -5 < floor < 8. The 8th floor and basement level 5 are the boundary values and don't meet the 'between' requirement.
- A football team's net yardage for five plays were: gained 12 yards, lost 8 yards, gained 3 yards, lost 15 yards, and gained 6 yards. The coach wants to identify which plays resulted in field position that was better than the position after the fourth play but not as good as the position after the second play.
Answer: Only the fifth play meets these specific field position criteria for this comparison
Cumulative positions: Play 1: +12, Play 2: +4, Play 3: +7, Play 4: -8, Play 5: -2. After play 4: -8 yards. After play 2: +4 yards. Only play 5 position (-2) is between -8 and +4. Play 3 position (+7) is better than both benchmarks.
- A weather app shows these temperatures: −4∘C, −1∘C, 0∘C, and 6∘C. Which order statement correctly arranges them from coldest to warmest?
Answer: −4<−1<0<6
This question tests writing and interpreting order statements for rational numbers in contexts like temperature, where a < b means a is to the left of b on the number line and contextually a is colder than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); ordering: arrange least to greatest using number line (left-to-right: -4 < -1 < 0 < 6 for coldest to warmest). For example, compare temperatures -4°C, -1°C, 0°C, 6°C; number line shows -4 left of -1 left of 0 left of 6, order -4 < -1 < 0 < 6 (coldest to warmest). The correct order statement is -4 < -1 < 0 < 6, arranging from coldest (-4°C) to warmest (6°C). A common error is magnitude for negatives like -4 > -1 thinking 4 larger, or wrong order like -1 < -4 < 0 < 6. Ordering: from smallest to largest (coldest to warmest); comparing negatives: less negative is warmer (-1 > -4). Mistakes include context reversed, zero as coldest, or not following left-to-right. - Two towns report temperatures of −4∘C and −9∘C. Which town is warmer, and what inequality matches that comparison?
Answer: −4∘C is warmer, so −4>−9.
This question tests writing and interpreting order statements for rational numbers in contexts like temperature, where a < b means a is to the left of b on the number line and contextually a is colder than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in temperature context, -5°C < 3°C means -5 is colder (farther below zero, more negative, lower value) than 3. For example, compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5 < 3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above). The correct statement is -4°C is warmer, so -4 > -9, since -4 is less negative and to the right on the number line. A common error is magnitude for negatives like -9 > -4 thinking larger magnitude is greater, or context reversed (-4 warmer but written -4 < -9). To write: (1) identify values (-4 and -9), (2) determine relationship (which warmer? -4 closer to zero), (3) write -4 > -9, (4) explain (-4°C warmer than -9°C). Comparing negatives: less negative is greater (-2 > -5 because -2 closer to zero, farther right); mistakes: context language reversed (warmer as less not greater), or interpretation not contextual. - A diver is at an elevation of −12 m (below sea level) and a hiker is at 25 m (above sea level). Which statement best interprets the inequality −12<25 in this context?
Answer: The diver is lower than the hiker.
This question tests writing and interpreting order statements for rational numbers in contexts like elevation, where a < b means a is to the left of b on the number line and contextually a is lower than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in elevation context, -30 m < 40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive). For example, elevations -20 m, 0 m, 30 m order: -20 < 0 < 30 (lowest altitude to highest, below sea level < sea level < above). The inequality -12 < 25 interprets as the diver at -12 m is lower than the hiker at 25 m. A common error is context reversed, like saying the diver is higher despite -12 < 25, or interpretation not contextual (says -12 < 25 mathematically but doesn't explain lower elevation). Interpreting: inequality a < b in context means a is less in contextual terms (lower elevation); ordering: arrange from smallest to largest (left-to-right), interpret in context (lowest-to-highest). Comparing negatives: less negative is greater (-2 > -5 because -2 closer to zero, farther right); mistakes: zero as extreme, order wrong, or context language reversed (lower as greater not less).
- In a science lab, a freezer is at −18∘C and a refrigerator is at 4∘C. Which is colder, and what inequality matches that comparison?
Answer: The freezer is colder; −18<4.
This question tests writing and interpreting order statements for rational numbers in contexts like temperature, where a < b means a is to the left of b on the number line and contextually a is colder than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in temperature context, -18°C < 4°C means -18 is colder (farther below zero, more negative, lower value) than 4. For example, compare temperatures -18°C and 4°C; the number line shows -18 left of 4, so inequality -18 < 4 (mathematically less), and interpret: -18°C is colder than 4°C (18 below zero is colder than 4 above). The correct statement is the freezer is colder with -18 < 4. A common error is thinking larger magnitude means greater, like -18 > 4, or reversing context by saying 4 < -18 implies refrigerator colder. When writing: (1) identify values (-18 and 4), (2) determine relationship (which colder? -18 farther below zero), (3) write inequality (-18 < 4), (4) explain in context (freezer colder). Comparing negatives: more negative is colder (-18 < -5); mistakes include context reversed (colder as greater) or zero misplaced. - A delivery truck's route involves elevation changes measured from sea level. The route elevations are: 125 feet above sea level, 45 feet below sea level, 200 feet above sea level, 80 feet below sea level, and finally 15 feet above sea level. The dispatcher needs to identify route points that are lower than the highest point but higher than the lowest point on the route.
Answer: The first, second, and fifth route points all satisfy these elevation conditions for the analysis
Elevations: 125, -45, 200, -80, 15 feet. Highest: 200 feet, Lowest: -80 feet. Points between -80 and 200: first point (125) and fifth point (15). The second point (-45) and fourth point (-80) are too low, third point (200) is the maximum.
- Jada has an account balance of −$18 (she owes money). Mateo has an account balance of $6. Which inequality correctly compares their balances?
Answer: −18<6
This question tests writing and interpreting order statements for rational numbers in contexts like money, where a < b means a is to the left of b on the number line and contextually a is less (more debt) than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in money context, -$25 < $18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). For example, money -$30 < -$10 < $0 < $25 (most debt to most credit). The correct inequality is -18 < 6, meaning Jada's balance (-$18, debt) is less than Mateo's ($6, credit). A common error is reversing like -18 > 6 thinking larger magnitude debt is greater, or context reversed (debt as greater not less). To write: (1) identify values (balances -18 and 6), (2) determine relationship (which less? -18 more debt), (3) write -18 < 6, (4) explain (-$18 is less than $6). Interpreting: a < b means a is less in context (more debt); comparing negatives: less negative is greater (-2 > -5); mistakes: magnitude comparison, context language reversed, or interpretation not contextual. - A classroom thermometer shows −4∘C outside and −9∘C inside a freezer. Which location is warmer, and what inequality matches that comparison?
Answer: Outside is warmer; −4>−9.
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct statement is that outside is warmer with -4>-9, meaning -4°C is warmer than -9°C in the freezer. A common error is reversing the inequality direction, like -4<-9, or thinking the freezer is warmer due to larger magnitude. Writing: (1) identify values in context (temperatures -4 and -9), (2) determine relationship (which warmer? -4 less negative), (3) write inequality (-4>-9 mathematically), (4) explain in context (outside warmer than freezer). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - A football team's position relative to the line of scrimmage is −7 yards (behind), 0 yards (at the line), and +12 yards (ahead). Which order statement lists the positions from farthest behind to farthest ahead?
Answer: −7<0<12
This question tests writing and interpreting order statements for rational numbers in contexts like football positions, where a < b means a is to the left of b on the number line and contextually a is farther behind than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in position context, -7 yards < 12 yards means -7 is farther behind (negative is behind, positive ahead). For example, compare positions -7, 0, 12 yards; number line shows -7 left of 0 left of 12, order -7 < 0 < 12 (farthest behind to farthest ahead). The correct order is -7 < 0 < 12, listing from farthest behind (-7) to farthest ahead (12). A common error is wrong order like 12 < 0 < -7, not least-to-greatest, or thinking -7 > 0 due to magnitude. Ordering: arrange smallest to largest (left-to-right: -7 < 0 < 12 for behind to ahead); interpreting: a < b means a is more behind than b. Mistakes include magnitude for negatives, context reversed (behind as greater), or zero as extreme. - A student's lunch account balance is −$25 (they owe money), then later it is $18 (they have money left). Which statement best interprets the inequality −25<18 in this context?
Answer: −$25 is a smaller balance than $18, so owing money is less than having $18.
Tests writing and interpreting order statements for rational numbers in contexts (temperature, elevation, money), understanding a<b means a left of b on number line and contextually a is colder/lower/less than b. Inequality as position: a<b means a is less than b (a left of b on number line), a>b means a greater than b (a right of b). Context interpretation: temperature -5°C<3°C means -5 is colder (farther below zero, more negative, lower value) than 3; elevation -30 m<40 m means -30 is lower altitude (below sea level negative is lower than above sea level positive); money -$25<$18 means -25 is less money (debt/owe vs credit/have, debt is negative value less than credit). Ordering: arrange least to greatest using number line (left-to-right: -10<-5<0<3 for coldest to warmest temperatures). For example: compare temperatures -5°C and 3°C, number line shows -5 left of 3, inequality -5<3 (mathematically less), interpret: -5°C is colder than 3°C (5 below zero is colder than 3 above); or elevations -20 m, 0 m, 30 m order: -20<0<30 (lowest altitude to highest, below sea level < sea level < above); or money -$30<-$10<$0<$25 (most debt to most credit). The correct interpretation is that -$25 is a smaller balance than $18, meaning owing $25 is less than having $18 in the account. A common error is thinking negative magnitude makes it greater, like -$25 > $18 because 25 is bigger than 18, ignoring the debt context. Writing: (1) identify values in context (balances -25 and 18), (2) determine relationship (which less? -25 is debt, smaller), (3) write inequality (-25<18 mathematically), (4) explain in context (owing $25 is less than having $18). Interpreting: inequality a<b in context means a is less in contextual terms (colder, lower, more debt, earlier time, etc. depending on scenario). Ordering: arrange from smallest value to largest (using number line: left-to-right), interpret in context (coldest-to-warmest, lowest-to-highest, most debt-to-most credit). Comparing negatives: less negative is greater (-2>-5 because -2 closer to zero, farther right on number line). Mistakes: magnitude comparison for negatives, context language reversed (colder as greater not less), zero misplaced, order not following left-to-right. - A student tracks their library fine balance (money owed) and gift card credit (money available). One day the balance is −$8, and another day it is $0. Which interpretation is correct?
Answer: −8<0 because owing money is less than having no balance due.
This question tests writing and interpreting order statements for rational numbers in contexts like money balances, where a < b means a is to the left of b on the number line and contextually a is less (more owed) than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in money, -$8 < $0 means owing $8 is less than no balance. For example, compare -$8 and $0; number line shows -8 left of 0, inequality -8 < 0, interpret: owing $8 is less than having no balance due. The correct interpretation is -8 < 0 because owing money is less than having no balance due. A common error is thinking -8 > 0 because owing feels more significant, or 0 < -8 saying 0 is smallest. Interpreting: a < b means a is less money than b; comparing negatives: less negative better (-4 > -8). Mistakes include reversed context (owing as greater) or zero as smallest. - A video shows timestamps relative to "now": −9 minutes (9 minutes ago), 0 minutes (now), and +3 minutes (3 minutes from now). Which list is in order from earliest time to latest time?
Answer: −9<0<3
This question tests writing and interpreting order statements for rational numbers in contexts like timestamps, where a < b means a is to the left of b on the number line and contextually a is earlier than b. Inequality as position: a < b means a is less than b (a left of b on number line), a > b means a greater than b (a right of b); in time context, -9 min < 3 min means -9 is earlier (past negative, future positive). For example, compare timestamps -9, 0, 3 min; number line shows -9 left of 0 left of 3, order -9 < 0 < 3 (earliest to latest). The correct order is -9 < 0 < 3, from earliest (-9 min ago) to latest (+3 min from now). A common error is reversing like 3 < 0 < -9, or thinking -9 > 3 because 9 larger than 3. Ordering: arrange smallest to largest (left-to-right for earliest to latest); interpreting: a < b means a is earlier than b. Mistakes include context reversed (earlier as greater), zero misplaced, or not contextual interpretation.
