Middle School Math Quiz: Rational Number Word Problems

7 questions · exam conditions

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Rational Number Word ProblemsQuestion 1 of 7

A weather station records temperature changes over four hours. The temperature drops $3.5°F$ in the first hour, rises $2.25°F$ in the second hour, drops $4.75°F$ in the third hour, and rises $1.5°F$ in the fourth hour. If the final temperature is $-2.5°F$ , what was the initial temperature?

2.0°F

4.0°F

6.5°F

1.0°F

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Middle School Math Quiz

Middle School Math Quiz: Rational Number Word Problems

Practice Rational Number Word Problems 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 Rational Number Word Problems, 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

$2.0°F$ (correct answer)
$4.0°F$
$6.5°F$
$1.0°F$

Explanation: Let the initial temperature be

x

. The total change is:

-3.5 + 2.25 - 4.75 + 1.5 = -4.5°F

. So

x + (-4.5) = -2.5

, which gives us

x = -2.5 + 4.5 = 2.0°F

. Choice B adds instead of subtracting the net change. Choice C miscalculates the total change as

-6.5

. Choice D results from calculation errors in the temperature changes.

Question 2

A football team's field position changes during a series of plays. Starting at their own 25-yard line, they gain $12.5$ yards, lose $8.25$ yards, gain $15.75$ yards, lose $4.5$ yards, and gain $7.25$ yards. Field position is measured as yards from their own goal line. If they need to reach the 50-yard line to be in the opponent's territory, how many more yards do they need?

$22.75$ yards
$7.75$ yards
$2.25$ yards (correct answer)
$27.25$ yards

Explanation: This problem tests your ability to work with positive and negative numbers in a real-world context. When a team gains yards, you add to their position; when they lose yards, you subtract from their position. Starting at the 25-yard line, let's track each play:

25 + 12.5 - 8.25 + 15.75 - 4.5 + 7.25

. Work left to right:

25 + 12.5 = 37.5

, then

37.5 - 8.25 = 29.25

, then

29.25 + 15.75 = 45

, then

45 - 4.5 = 40.5

, and finally

40.5 + 7.25 = 47.75

. The team ends up at the 47.75-yard line. Since they need to reach the 50-yard line, they need

50 - 47.75 = 2.25

more yards, which is answer C. Answer A (

22.75

yards) likely comes from incorrectly subtracting their final position from their starting position:

47.75 - 25 = 22.75

. This tells you how far they've moved total, not how far they need to go. Answer B (

7.75

yards) might result from calculation errors in tracking the plays, perhaps by mixing up signs or decimal places. Answer D (

27.25

yards) could come from subtracting their starting position from the target:

50 - 25 = 25

, then making a small arithmetic error. Remember: in multi-step problems involving gains and losses, carefully track each change in sequence, then compare your final result to the target. Don't confuse "distance traveled" with "distance remaining."

Question 3

A scientist measures the change in a chemical solution's pH level during an experiment. The pH starts at $7.5$ , decreases by $2.25$ , then increases by $0.75$ , decreases by $1.5$ , and finally increases by $3.25$ . If a solution is considered acidic when pH < 7, basic when pH > 7, and neutral when pH = 7, what type of solution resulted, and by how much did the pH change from the starting point?

Neutral solution; no net change
Acidic solution; decreased by $0.25$
Basic solution; decreased by $0.25$
Basic solution; increased by $0.25$ (correct answer)

Explanation: This question tests your ability to track sequential changes using positive and negative numbers, then interpret the final result. When you see a series of increases and decreases, work through them step-by-step while keeping track of the cumulative effect. Starting at pH

7.5

, let's trace each change:

Decreases by $2.25$ : $7.5 - 2.25 = 5.25$
Increases by $0.75$ : $5.25 + 0.75 = 6.0$
Decreases by $1.5$ : $6.0 - 1.5 = 4.5$
Increases by $3.25$ : $4.5 + 3.25 = 7.75$

The final pH is

7.75

. Since

7.75 > 7

, this is a basic solution. To find the net change, subtract the starting value:

7.75 - 7.5 = +0.25

, meaning an increase of

0.25

. Answer A is wrong because the solution isn't neutral (pH ≠ 7) and there was a net change. Answer B incorrectly classifies the solution as acidic when

7.75 > 7

makes it basic. Answer C correctly identifies that the pH changed by

0.25

but wrongly calls it a decrease and misclassifies the solution as acidic. Answer D correctly identifies both the basic nature (pH > 7) and the net increase. Study tip: For sequential change problems, work step-by-step rather than trying shortcuts. Always distinguish between the direction of individual changes and the overall net change from start to finish.

Question 4

A delivery truck's weight changes throughout the day. It starts with $2,450$ pounds of cargo. At the first stop, it delivers $375.5$ pounds and picks up $128.25$ pounds. At the second stop, it delivers $892.75$ pounds and picks up $445.5$ pounds. At the third stop, it delivers $520.25$ pounds. If the empty truck weighs $4,200$ pounds, what is the truck's total weight after all stops?

$5,435.25$ pounds (correct answer)
$5,635.25$ pounds
$1,235.25$ pounds
$5,835.25$ pounds

Explanation: Starting cargo:

2,450

pounds. After first stop:

2,450 - 375.5 + 128.25 = 2,202.75

pounds. After second stop:

2,202.75 - 892.75 + 445.5 = 1,755.5

pounds. After third stop:

1,755.5 - 520.25 = 1,235.25

pounds of cargo. Total truck weight:

4,200 + 1,235.25 = 5,435.25

pounds. Choice B adds an extra

200

pounds. Choice C gives only the cargo weight, forgetting the truck's weight. Choice D adds an extra

400

pounds.

Question 5

Maria's checking account has a balance of $-\$47.25$ . She makes three deposits of $28.50, $15.75, and $22.00, then writes checks for $18.25 and $35.50. If her bank charges a $25.00 overdraft fee for each day her account is negative, and she started the day negative, what is her balance after all transactions and fees?

$-\$84.75$
$-\$59.75$ (correct answer)
$-\$34.75$
$-\$109.75$

Explanation: Starting balance:

-\$47.25

. After deposits:

-47.25 + 28.50 + 15.75 + 22.00 = \$19.00

. After checks:

19.00 - 18.25 - 35.50 = -\$34.75

. Since the account started negative and ended negative, she incurs one overdraft fee of $25.00. Final balance: $

-34.75 - 25.00 = -\

59.75

. Choice A forgets the overdraft fee. Choice C includes only transactions without the fee. Choice D incorrectly applies two overdraft fees.

Question 6

A stock's price changes over five days are: Monday $+\$2.75$ , Tuesday $-\$4.50$ , Wednesday $+\$1.25$ , Thursday $-\$3.75$ , Friday $+\$2.50$ . If the stock's price on Friday evening was $38.75, and an investor bought $ $150$ $ shares on Monday morning, what was the total value of their investment when they purchased it?

$5,737.50
$6,037.50 (correct answer)
$5,812.50
$6,112.50

Explanation: Total change over the week:

2.75 - 4.50 + 1.25 - 3.75 + 2.50 = -1.75

. If Friday's price was $38.75 and the total change was $

-\

1.75

, then Monday's opening price was

38.75 - (-1.75) = 38.75 + 1.75 = $40.25

. Investment value:

150 × 40.25 = $6,037.50

. Choice A uses Friday's price instead of Monday's. Choice C miscalculates the weekly change. Choice D adds the change incorrectly.

Question 7

An elevator starts at the ground floor (floor 0) and makes the following moves: up $12$ floors, down $5.5$ floors, up $8.25$ floors, down $11.75$ floors, and up $4.5$ floors. If the building charges $0.75 per floor traveled (regardless of direction) and gives a $2.50 discount for trips over $ $35$ $ floors total, what is the cost of this elevator trip?

$26.25
$31.25
$28.75 (correct answer)
$29.00

Explanation: When you see a problem involving distance traveled and cost calculations, you need to track two separate things: the total distance moved and any special conditions that affect pricing. First, calculate the total floors traveled by adding up all movements regardless of direction:

12 + 5.5 + 8.25 + 11.75 + 4.5 = 42

floors total. Notice that we count both up and down movements since the building charges per floor traveled, not net displacement. Next, apply the pricing structure. At $0.75 per floor, the base cost would be $

42 \times \

0.75 = $31.50

. However, since the total distance (42 floors) exceeds 35 floors, you qualify for the $2.50 discount. The final cost is $

\

31.50 - $2.50 = $28.75$$. Answer A (

26.25) represents a calculation error where someone might have incorrectly applied the discount or miscalculated the total distance. Answer B (

31.25) comes from calculating

\$31.50 - \$0.25

, suggesting confusion about the discount amount. Answer D ($29.00) results from applying a $2.50 discount incorrectly to a wrong base calculation. The key strategy here is to carefully read multi-step problems and identify each component: distance calculation (including all movements), base pricing, and conditional discounts. Always check whether you qualify for special conditions before applying them, and double-check your arithmetic on problems involving decimals.