Middle School Math Quiz: Solve Problems With Rational Numbers
15 questions · exam conditions
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Solve Problems With Rational NumbersQuestion 1 of 15

A student has $18.00 and buys a notebook for $4.80 (subtract). They earn $7.50 for helping after school (add). Then they decide to donate 13\frac{1}{3} of the money they have at that moment (multiply and subtract). How much money do they have left?​

$6.90
$20.70
$13.80
$9.20
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Middle School Math Quiz

Middle School Math Quiz: Solve Problems With Rational Numbers

Practice Solve Problems With Rational Numbers 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 Solve Problems With Rational Numbers, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

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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.

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Question 1

A student has $18.00 and buys a notebook for $4.80 (subtract). They earn $7.50 for helping after school (add). Then they decide to donate 13\frac{1}{3} of the money they have at that moment (multiply and subtract). How much money do they have left?​

  1. $6.90
  2. $20.70
  3. $13.80 (correct answer)
  4. $9.20
Explanation: This question tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start $50, subtract 18.50→18.50→31.50, add 30→30→61.50, divide by 3→20.50each).Context:negativenumbersfordebt/loss/belowzero/descent(meaningfulnegatives).Forexample,profit/lossaverage:Monday+20.50 each). Context: negative numbers for debt/loss/below zero/descent (meaningful negatives). For example, profit/loss average: Monday +120, Tuesday -45,Wednesday+45, Wednesday +80, calculate (120+(-45)+80)÷3=(120-45+80)÷3=155÷3≈$51.67 average daily profit; or temperature: start -12°C, rise 8° (add): -12+8=-4°C, then drop half the rise: -4-4=-8°C; or recipe: 2/3 cup for 4 servings, make 6 (multiply by 6/4=1.5): (2/3)×(3/2)=1 cup. To solve, $18.00 - $4.80 = $13.20, then $13.20 + $7.50 = 20.70,thendonate(1/3)×20.70, then donate (1/3)×20.70 = $6.90, so $20.70 - $6.90 = 13.80.Acommonerroriscalculatingthedonationonthewrongbalance,likeafterbuyingbutbeforeearning:(1/3)×13.80. A common error is calculating the donation on the wrong balance, like after buying but before earning: (1/3)×13.20 ≈ $4.40, $13.20 - $4.40 = 8.80(notanoption),ordecimalarithmeticerrorlike20.70−6.90as14.70.Solving:(1)identifyalloperationsneeded(readproblem:add,subtract,multiply,divide?),(2)sequenceoperations(ordermatters:(a+b)÷c≠a+(b÷c)),(3)applyoperationrules(signrulesforallfour:same→positivequotient/product,different→negative),(4)convertformsifneeded(2/3and1.5tocommonform),(5)trackthroughsteps(runningvalueaftereachoperation),(6)interpret(resultincontext:−8.80 (not an option), or decimal arithmetic error like 20.70 - 6.90 as 14.70. Solving: (1) identify all operations needed (read problem: add, subtract, multiply, divide?), (2) sequence operations (order matters: (a+b)÷c≠a+(b÷c)), (3) apply operation rules (sign rules for all four: same→positive quotient/product, different→negative), (4) convert forms if needed (2/3 and 1.5 to common form), (5) track through steps (running value after each operation), (6) interpret (result in context: -5 means owes $5, -8°C means below zero). Operation priority: handle within parentheses or natural groups first, then multiply/divide, then add/subtract (or left-to-right if equal precedence). Context clues: "share" suggests divide, "total" suggests add/multiply, "difference" suggests subtract, "of" with fraction suggests multiply. Mistakes: operation order, sign errors (most common across all four operations), arithmetic with decimals/fractions, context interpretation (negative meaning).

Question 2

A student has $18.00 and buys a notebook for $4.80 (subtract). They earn $7.50 for helping after school (add). Then they decide to donate 13\frac{1}{3} of the money they have at that moment (multiply and subtract). How much money do they have left?

  1. $6.90
  2. $13.80 (correct answer)
  3. $9.20
  4. $20.70
Explanation: This question tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start $50, subtract 18.50→18.50→31.50, add 30→30→61.50, divide by 3→20.50each).Context:negativenumbersfordebt/loss/belowzero/descent(meaningfulnegatives).Forexample,profit/lossaverage:Monday+20.50 each). Context: negative numbers for debt/loss/below zero/descent (meaningful negatives). For example, profit/loss average: Monday +120, Tuesday -45,Wednesday+45, Wednesday +80, calculate (120+(-45)+80)÷3=(120-45+80)÷3=155÷3≈$51.67 average daily profit; or temperature: start -12°C, rise 8° (add): -12+8=-4°C, then drop half the rise: -4-4=-8°C; or recipe: 2/3 cup for 4 servings, make 6 (multiply by 6/4=1.5): (2/3)×(3/2)=1 cup. To solve, $18.00 - $4.80 = $13.20, then $13.20 + $7.50 = 20.70,thendonate(1/3)×20.70, then donate (1/3)×20.70 = $6.90, so $20.70 - $6.90 = 13.80.Acommonerroriscalculatingthedonationonthewrongbalance,likeafterbuyingbutbeforeearning:(1/3)×13.80. A common error is calculating the donation on the wrong balance, like after buying but before earning: (1/3)×13.20 ≈ $4.40, $13.20 - $4.40 = 8.80(notanoption),ordecimalarithmeticerrorlike20.70−6.90as14.70.Solving:(1)identifyalloperationsneeded(readproblem:add,subtract,multiply,divide?),(2)sequenceoperations(ordermatters:(a+b)÷c≠a+(b÷c)),(3)applyoperationrules(signrulesforallfour:same→positivequotient/product,different→negative),(4)convertformsifneeded(2/3and1.5tocommonform),(5)trackthroughsteps(runningvalueaftereachoperation),(6)interpret(resultincontext:−8.80 (not an option), or decimal arithmetic error like 20.70 - 6.90 as 14.70. Solving: (1) identify all operations needed (read problem: add, subtract, multiply, divide?), (2) sequence operations (order matters: (a+b)÷c≠a+(b÷c)), (3) apply operation rules (sign rules for all four: same→positive quotient/product, different→negative), (4) convert forms if needed (2/3 and 1.5 to common form), (5) track through steps (running value after each operation), (6) interpret (result in context: -5 means owes $5, -8°C means below zero). Operation priority: handle within parentheses or natural groups first, then multiply/divide, then add/subtract (or left-to-right if equal precedence). Context clues: "share" suggests divide, "total" suggests add/multiply, "difference" suggests subtract, "of" with fraction suggests multiply. Mistakes: operation order, sign errors (most common across all four operations), arithmetic with decimals/fractions, context interpretation (negative meaning).

Question 3

A fish tank is −0.6-0.6 m below the top of a stand (so its water surface is −0.6-0.6 m relative to the top). Water is added, raising the level by 0.350.35 m (add). Then 25\frac{2}{5} of that added amount is drained out (multiply and subtract). What is the final water level relative to the top of the stand?

  1. −0.74 m-0.74\text{ m}
  2. −0.11 m-0.11\text{ m}
  3. 0.39 m0.39\text{ m}
  4. −0.39 m-0.39\text{ m} (correct answer)
Explanation: This question tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start $50, subtract 18.50→18.50→31.50, add 30→30→61.50, divide by 3→20.50each).Context:negativenumbersfordebt/loss/belowzero/descent(meaningfulnegatives).Forexample,profit/lossaverage:Monday+20.50 each). Context: negative numbers for debt/loss/below zero/descent (meaningful negatives). For example, profit/loss average: Monday +120, Tuesday -45,Wednesday+45, Wednesday +80, calculate (120+(-45)+80)÷3=(120-45+80)÷3=155÷3≈51.67averagedailyprofit;ortemperature:start−12°C,rise8°(add):−12+8=−4°C,thendrophalftherise:−4−4=−8°C;orrecipe:2/3cupfor4servings,make6(multiplyby6/4=1.5):(2/3)×(3/2)=1cup.Tosolve,−0.6+0.35=−0.25,thendrain(2/5)×0.35=0.14,so−0.25−0.14=−0.39m.Acommonerrorissignerrorliketreatingadditionof0.35assubtractionto−0.6−0.35=−0.95,thensubtracting0.14to−1.09(notanoption),orwrongfractionlike2/5×0.35as0.7/5=0.14butmisapplying.Solving:(1)identifyalloperationsneeded(readproblem:add,subtract,multiply,divide?),(2)sequenceoperations(ordermatters:(a+b)÷c≠a+(b÷c)),(3)applyoperationrules(signrulesforallfour:same→positivequotient/product,different→negative),(4)convertformsifneeded(2/3and1.5tocommonform),(5)trackthroughsteps(runningvalueaftereachoperation),(6)interpret(resultincontext:−51.67 average daily profit; or temperature: start -12°C, rise 8° (add): -12+8=-4°C, then drop half the rise: -4-4=-8°C; or recipe: 2/3 cup for 4 servings, make 6 (multiply by 6/4=1.5): (2/3)×(3/2)=1 cup. To solve, -0.6 + 0.35 = -0.25, then drain (2/5)×0.35 = 0.14, so -0.25 - 0.14 = -0.39 m. A common error is sign error like treating addition of 0.35 as subtraction to -0.6 - 0.35 = -0.95, then subtracting 0.14 to -1.09 (not an option), or wrong fraction like 2/5 × 0.35 as 0.7/5 = 0.14 but misapplying. Solving: (1) identify all operations needed (read problem: add, subtract, multiply, divide?), (2) sequence operations (order matters: (a+b)÷c≠a+(b÷c)), (3) apply operation rules (sign rules for all four: same→positive quotient/product, different→negative), (4) convert forms if needed (2/3 and 1.5 to common form), (5) track through steps (running value after each operation), (6) interpret (result in context: -5 means owes $5, -8°C means below zero). Operation priority: handle within parentheses or natural groups first, then multiply/divide, then add/subtract (or left-to-right if equal precedence). Context clues: "share" suggests divide, "total" suggests add/multiply, "difference" suggests subtract, "of" with fraction suggests multiply. Mistakes: operation order, sign errors (most common across all four operations), arithmetic with decimals/fractions, context interpretation (negative meaning).

Question 4

At sunrise, the temperature is −6.5∘C-6.5^\circ\text{C}. By midday it increases by 9∘C9^\circ\text{C}. In the afternoon, it drops by 23\frac{2}{3} of the midday increase. What is the temperature after the afternoon drop?

  1. −3.5∘C-3.5^\circ\text{C} (correct answer)
  2. −0.5∘C-0.5^\circ\text{C}
  3. 3.5∘C3.5^\circ\text{C}
  4. −1.5∘C-1.5^\circ\text{C}
Explanation: Tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start -6.5°C, add 9°C→2.5°C at midday, multiply 9 by 2/3→6°C drop, subtract 6°C from 2.5°C→-3.5°C). Context: negative temperatures below zero, positive changes for increases, negative changes for decreases. Correct solution: -6.5°C + 9°C = 2.5°C (midday temp), then 2/3 × 9°C = 6°C (afternoon drop amount), finally 2.5°C - 6°C = -3.5°C. Error like dropping 2/3 of current temperature instead of 2/3 of increase (2/3×2.5=1.67→0.83°C wrong), sign error when adding to negative (-6.5+9=-15.5), or arithmetic with fractions (2/3×9=3 instead of 6). Solving: (1) identify all operations needed (add morning increase, find 2/3 of that increase, subtract afternoon drop), (2) sequence operations (must find midday temp first, then calculate drop amount), (3) apply operation rules (negative plus positive: -6.5+9=2.5), (4) convert forms if needed (keep as decimals throughout), (5) track through steps (-6.5°C→2.5°C→drop 6°C→-3.5°C), (6) interpret (-3.5°C means 3.5 degrees below freezing).

Question 5

A student records their net change in a class points system for four days: Day 1: +12.5+12.5 points, Day 2: −7-7 points, Day 3: +92+\frac{9}{2} points, Day 4: −3.5-3.5 points. What is the average net change per day?

  1. 2.52.5 points
  2. 1.6251.625 points (correct answer)
  3. 6.56.5 points
  4. 0.6250.625 points
Explanation: Tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (Day 1: +12.5, Day 2: -7, Day 3: +9/2=+4.5, Day 4: -3.5, sum all→6.5 total, divide by 4→1.625 average). Context: point changes with gains (positive) and losses (negative), finding average requires sum then divide. Correct solution: 12.5 + (-7) + 4.5 + (-3.5) = 12.5 - 7 + 4.5 - 3.5 = 6.5 total change, then 6.5 ÷ 4 = 1.625 points average per day. Error like forgetting to convert 9/2 to 4.5 before adding, sign error (treating -7 as +7→20.5 total), or dividing each day by 4 then adding (wrong order). Solving: (1) identify all operations needed (add all daily changes accounting for signs, divide total by number of days), (2) sequence operations (must sum all changes before dividing for average), (3) apply operation rules (positive changes add, negative changes subtract from total), (4) convert forms if needed (9/2 = 4.5), (5) track through steps (12.5→5.5→10→6.5→1.625), (6) interpret (positive 1.625 means average daily gain in points).

Question 6

A recipe uses 34\frac{3}{4} cup of yogurt for 6 smoothies. A student wants to make 12\frac{1}{2} of the recipe, and then make 3 batches of that smaller amount. How many cups of yogurt are needed?

  1. 94\frac{9}{4} cups
  2. 38\frac{3}{8} cup
  3. 32\frac{3}{2} cups
  4. 98\frac{9}{8} cups (correct answer)
Explanation: Making half of the original recipe means multiplying 3/4 cup by 1/2, which gives 3/8 cup of yogurt for one smaller batch. Since the student wants to make 3 batches of that smaller amount, multiply 3/8 by 3, which gives 9/8 cups total, matching choice D. Choice A, 9/4 cups, comes from multiplying the original 3/4 cup by 3 without first taking half. Choice B, 3/8 cup, stops after finding the amount for one smaller batch and forgets to multiply by 3. Choice C, 3/2 cups, comes from multiplying 3/4 by 2 instead of by 1/2, reversing the halving step. Working through each step in order, halving first and then multiplying by the number of batches, is the key to avoiding these mix-ups.

Question 7

During a winter morning, the temperature is −6.5∘C-6.5^\circ\text{C}. By lunchtime it rises 4∘C4^\circ\text{C}. In the afternoon, the temperature drops by an amount equal to 1.51.5 times the number of degrees it rose that morning. What is the final temperature?

  1. −16.5∘C-16.5^\circ\text{C}
  2. −0.5∘C-0.5^\circ\text{C}
  3. −2.5∘C-2.5^\circ\text{C}
  4. −8.5∘C-8.5^\circ\text{C} (correct answer)
Explanation: First add the rise: -6.5 + 4 = -2.5 degrees C. Next, the afternoon drop is 1.5 times the 4-degree rise, which is 1.5 x 4 = 6 degrees. Subtracting this drop gives -2.5 - 6 = -8.5 degrees C, the final temperature. Choice A results from subtracting the morning rise instead of adding it before applying the drop. Choice C stops after finding the temperature at lunchtime and never accounts for the afternoon drop. Choice B miscalculates the size of the afternoon drop, using a value too small for 1.5 times the rise.

Question 8

A student has $35.00 in a lunch account. On Monday, they buy lunch for $6.75 (subtract). On Tuesday, they deposit $12.50 (add). On Wednesday, the school charges a fee equal to 1/5 of the current balance (multiply and subtract). What is the balance after the fee?

  1. $32.20
  2. $32.75
  3. $32.60 (correct answer)
  4. $25.76
Explanation: Start with $35.00, subtract the $6.75 lunch purchase: $35.00 - $6.75 = $28.25. Add the $12.50 deposit: $28.25 + $12.50 = $40.75. The fee is 1/5 of that balance: (1/5) x $40.75 = $8.15, so the balance after the fee is $40.75 - $8.15 = $32.60, matching choice C. A common error is calculating the fee using the wrong balance, such as using $28.25 before adding the Tuesday deposit.

Question 9

A science class records the elevation of a drone relative to the launch point (launch point is 00 m). The drone rises 121212\frac{1}{2} m, then drops 18.7518.75 m, then rises again by 23\frac{2}{3} of 99 m. What is the drone's final elevation relative to the launch point?

  1. −0.25 m-0.25\text{ m} (correct answer)
  2. 0.25 m0.25\text{ m}
  3. −12.25 m-12.25\text{ m}
  4. −6.25 m-6.25\text{ m}
Explanation: This problem tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. The four operations with rationals include addition/subtraction using sign rules where same signs add magnitudes and different signs subtract while taking the larger's sign, and subtraction as adding the inverse like p - q = p + (-q), while multiplication/division follow sign rules where same signs give positive and different signs give negative; in multi-step problems, track values through the sequence such as start 0, add 12.5 to 12.5, subtract 18.75 to -6.25, then add (2/3)×9=6 to -0.25 m, with negatives for below launch point. For example, in a profit/loss average: Monday +120,Tuesday−120, Tuesday -45, Wednesday +$80, calculate (120 + (-45) + 80) ÷ 3 = (120 - 45 + 80) ÷ 3 = 155 ÷ 3 ≈ $51.67 average daily profit; or temperature: start -12°C, rise 8° (add): -12 + 8 = -4°C, then drop half the rise: -4 - 4 = -8°C; or recipe: 2/3 cup for 4 servings, make 6 (multiply by 6/4 = 1.5): (2/3) × (3/2) = 1 cup. To solve correctly, 0 + 12 1/2 =12.5, 12.5 -18.75= -6.25, -6.25 + (2/3 9)= -6.25 +6= -0.25 m. A common error is sign error like 12.5 -18.75 as 6.25 positive, or fraction wrong 2/39 as 3 or 6 wrong to 5.4, or order wrong adding before subtracting, or arithmetic like -6.25+6 as -0.25 wrong to 0.25 ignoring sign. To solve these, (1) identify operations: add, subtract, multiply then add, (2) sequence: after each move, (3) apply sign rules for subtraction leading to negative, (4) convert mixed 12 1/2 to 12.5, (5) track: +12.5=12.5, -18.75=-6.25, +6=-0.25, (6) interpret as -0.25 m below launch. Context 'rises, drops, rises again by 2/3 of 9 m' suggests add, subtract, multiply then add, with negative meaning below zero.

Question 10

A water bottle holds 34\frac{3}{4} liter when full. A student drinks 0.20.2 liter, then refills the bottle by adding 13\frac{1}{3} liter. Finally, they pour the total amount equally into 22 cups. How many liters are in each cup?

  1. 53120\frac{53}{120} L (correct answer)
  2. 5360\frac{53}{60} L
  3. 1630\frac{16}{30} L
  4. 1330\frac{13}{30} L
Explanation: Tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start 34\frac{3}{4} L, subtract 0.20.2 L→1120\frac{11}{20} L, add 13\frac{1}{3} L→5360\frac{53}{60} L total, divide by 2→53120\frac{53}{120} L per cup). Context: liquid measurements requiring fraction-decimal conversions and equal division. Correct solution: 34−0.2=34−15=1520−420=1120\frac{3}{4} - 0.2 = \frac{3}{4} - \frac{1}{5} = \frac{15}{20} - \frac{4}{20} = \frac{11}{20} L, then 1120+13=3360+2060=5360\frac{11}{20} + \frac{1}{3} = \frac{33}{60} + \frac{20}{60} = \frac{53}{60} L, finally 5360÷2=5360×12=53120\frac{53}{60} ÷ 2 = \frac{53}{60} × \frac{1}{2} = \frac{53}{120} L per cup. Error like forgetting to divide by 2 (answer 5360\frac{53}{60}), converting 0.2 wrong (as 210\frac{2}{10} not simplified to 15\frac{1}{5}), or adding before subtracting (34+13−0.2\frac{3}{4}+\frac{1}{3}-0.2). Solving: (1) identify all operations needed (subtract amount drunk, add refill amount, divide total by 2), (2) sequence operations (subtract→add→divide), (3) apply operation rules (convert 0.2 to fraction 15\frac{1}{5} for easier calculation), (4) convert forms if needed (all to fractions with common denominators), (5) track through steps (34→1120→5360→53120\frac{3}{4}→\frac{11}{20}→\frac{53}{60}→\frac{53}{120}), (6) interpret (53120\frac{53}{120} L is amount in each of the 2 cups).

Question 11

A science class has 1.81.8 liters of salt solution in a container. They remove 14\frac{1}{4} of it for a test, then add 0.350.35 liters of water, and finally split the mixture equally into 55 small jars. How many liters are in each jar?

  1. 0.370.37 L
  2. 0.430.43 L
  3. 0.340.34 L (correct answer)
  4. 0.250.25 L
Explanation: Tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start 1.8 L, remove 1/4: multiply by 3/4→1.35 L, add 0.35 L→1.7 L total, divide by 5→0.34 L per jar). Context: liquid measurements with removal (multiply by fraction remaining), addition, and equal division. Correct solution: Remove 1/4 means keep 3/4: 1.8 × 3/4 = 1.35 L remaining, then 1.35 + 0.35 = 1.7 L total, finally 1.7 ÷ 5 = 0.34 L per jar. Error like removing 1/4 L instead of 1/4 of total (1.8-0.25=1.55), or calculating 1/4×1.8=0.45 then forgetting to subtract (keeps 1.8 L), or arithmetic error in division. Solving: (1) identify all operations needed (calculate 1/4 of total to remove, subtract from total OR multiply by 3/4, add water, divide by jars), (2) sequence operations (remove first, then add, then divide), (3) apply operation rules (removing 1/4 = keeping 3/4, multiply by 3/4), (4) convert forms if needed (1/4 of 1.8 = 0.45 L removed), (5) track through steps (1.8→1.35→1.7→0.34), (6) interpret (0.34 L is amount in each of 5 jars).

Question 12

A gamer starts a round with 5050 points. They lose 18.518.5 points, then earn 3030 points, and then their final score is split equally among 44 teammates for a team average. What is the average score per teammate?

  1. 15.5015.50
  2. 30.7530.75
  3. 15.37515.375 (correct answer)
  4. 20.37520.375
Explanation: Tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start 50 points, subtract 18.5→31.5 points, add 30→61.5 points, divide by 4→15.375 points per teammate). Context: gaming points with losses (negative change) and gains (positive change), then averaging. Correct solution: 50 - 18.5 = 31.5 points, then 31.5 + 30 = 61.5 points, finally 61.5 ÷ 4 = 15.375 points per teammate. Error like dividing final score by 4 teammates plus original player (÷5 instead of ÷4→12.3), arithmetic error (50-18.5=32.5), or wrong operation order (50÷4=12.5, then subtract/add). Solving: (1) identify all operations needed (subtract loss, add gain, divide by number of teammates), (2) sequence operations (must find final total before dividing), (3) apply operation rules (subtraction for point loss, addition for gain), (4) convert forms if needed (keep as decimals), (5) track through steps (50→31.5→61.5→15.375), (6) interpret (15.375 is average score each teammate receives).

Question 13

A recipe calls for 2132\frac{1}{3} cups of flour. Sarah wants to make 1121\frac{1}{2} times the recipe, but she only has 3143\frac{1}{4} cups of flour available. How much more flour does she need, expressed as a mixed number?

  1. 14\frac{1}{4} cup (correct answer)
  2. 12\frac{1}{2} cup
  3. 34\frac{3}{4} cup
  4. 1141\frac{1}{4} cups
Explanation: Amount needed: 213×112=73×32=216=3122\frac{1}{3} \times 1\frac{1}{2} = \frac{7}{3} \times \frac{3}{2} = \frac{21}{6} = 3\frac{1}{2} cups. Amount available: 3143\frac{1}{4} cups. Additional needed: 312−314=324−314=143\frac{1}{2} - 3\frac{1}{4} = 3\frac{2}{4} - 3\frac{1}{4} = \frac{1}{4} cup. Choice B represents a common error of subtracting incorrectly. Choice C might result from calculation errors. Choice D could come from adding instead of subtracting or other computational mistakes.

Question 14

A student has $25.00 in lunch money. They buy a sandwich for $6.75, then their friend pays them back $4.50 they owed. After that, the student donates 15\frac{1}{5} of the money they have left to a school fundraiser. How much money does the student have after the donation?

  1. $18.20 (correct answer)
  2. $22.75
  3. $14.95
  4. $18.75
Explanation: Tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. Four operations with rationals: addition/subtraction (sign rules: same signs add magnitudes, different signs subtract, take larger's sign; subtraction as adding inverse: p-q=p+(-q)), multiplication/division (sign rules: same signs give positive, different signs give negative). Multi-step: track values through sequence (start $25, subtract 6.75→6.75→18.25, add 4.50→4.50→22.75, multiply by 1/5 for donation→$4.55 donated, subtract from 22.75→22.75→18.20 remaining). Context: money transactions with spending (subtract), receiving (add), and fractional donation. Correct solution: $25.00 - $6.75 = $18.25, then $18.25 + $4.50 = $22.75, then 1/5 × $22.75 = $4.55 donation, finally $22.75 - $4.55 = $18.20. Error like calculating 1/5 of original 25insteadofcurrentamount(25 instead of current amount (5 donation→$17.75 final), or keeping 1/5 instead of donating 1/5 (keeps 4.55→wrong),orarithmeticerrorinsubtraction(4.55→wrong), or arithmetic error in subtraction (22.75-4.55=4.55=18.75). Solving: (1) identify all operations needed (subtract sandwich cost, add repayment, find 1/5 of current total, subtract donation), (2) sequence operations (must calculate current balance before finding 1/5), (3) apply operation rules (subtraction for spending, addition for receiving), (4) convert forms if needed (1/5 as decimal 0.2 or keep as fraction), (5) track through steps (25→25→18.25→$22.75→donation 4.55→4.55→18.20), (6) interpret (final $18.20 is money remaining after all transactions).

Question 15

A video game score changes over 4 rounds. The changes are: Round 1: +12.5+12.5, Round 2: −9-9, Round 3: +72+\frac{7}{2}, Round 4: −4.5-4.5. What is the player's average score change per round?

  1. −1.5-1.5
  2. 1.51.5
  3. 0.6250.625 (correct answer)
  4. −0.625-0.625
Explanation: This problem tests solving real-world problems with all four operations on rational numbers (positive/negative integers/fractions/decimals), requiring multi-step calculations and context interpretation. The four operations with rationals include addition/subtraction using sign rules where same signs add magnitudes and different signs subtract while taking the larger's sign, and subtraction as adding the inverse like p−q=p+(−q)p - q = p + (-q), while multiplication/division follow sign rules where same signs give positive and different signs give negative; in multi-step problems, track values through the sequence such as sum 12.5−9+3.5−4.5=(12.5+3.5)+(−9−4.5)=16−13.5=2.512.5 -9 +3.5 -4.5 = (12.5 + 3.5) + (-9 -4.5) =16 -13.5=2.5, then divide by 4 =0.625=0.625 average, with negatives for score decreases. For example, in a profit/loss average: Monday +120+120, Tuesday −45-45, Wednesday +80+80, calculate (120+(−45)+80)÷3=(120−45+80)÷3=155÷3≈$51.67averagedailyprofit;ortemperature:start$−12°C(120 + (-45) + 80) ÷ 3 = (120 - 45 + 80) ÷ 3 = 155 ÷ 3 ≈ $51.67 average daily profit; or temperature: start $-12°C, rise 8°8° (add): −12+8=−4°C-12 + 8 = -4°C, then drop half the rise: −4−4=−8°C-4 - 4 = -8°C; or recipe: 2/32/3 cup for 4 servings, make 6 (multiply by 6/4=1.56/4 = 1.5): (2/3)×(3/2)=1(2/3) × (3/2) = 1 cup. To solve correctly, sum 12.5+(−9)+72+(−4.5)=12.5−9+3.5−4.512.5 + (-9) + \frac{7}{2} + (-4.5) =12.5 -9 +3.5 -4.5, 12.5+3.5=1612.5+3.5=16, −9−4.5=−13.5-9-4.5=-13.5, 16−13.5=2.516-13.5=2.5, 2.5/4=0.6252.5 / 4 =0.625. A common error is operation order wrong like dividing each before summing, sign error like treating −9-9 as +9+9 summing to 29.5/4=7.37529.5/4=7.375, wrong operation, fraction wrong 72\frac{7}{2} as 3 or 4, treating negative as positive, or arithmetic error like 2.5/4=0.652.5/4=0.65 or 0.60.6. To solve these, (1) identify operations: add all changes then divide by 4, (2) sequence as sum first then divide, (3) apply sign rules for addition with positives/negatives, (4) convert 72\frac{7}{2} to 3.5, (5) track sum: 12.5−9=3.512.5-9=3.5, +3.5=7+3.5=7, −4.5=2.5-4.5=2.5, $/4=0.625$, (6) interpret as average change positive meaning net gain per round. Operation priority in sum before divide, context 'average' suggests sum then divide, mistakes in sign errors or forgetting to include all terms.