📝 Add and Subtract Integers (7 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 7 questions available

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What is Add and Subtract Integers?

Definition:
Adding and subtracting integers involves combining positive and negative whole numbers, where addition of a positive increases the value, addition of a negative decreases it, and subtraction can be interpreted as adding the opposite (or additive inverse) of the number being subtracted.

Working:
For addition, if signs are same, add absolute values and keep the sign; if different, subtract smaller absolute value from larger and use sign of larger; for subtraction, change to addition of the opposite: $a - b = a + (-b)$ , then apply addition rules.

Example:
Calculate $-5 + 3$ and $-2 - (-6)$ .
Solution: For $-5+3$ , signs differ, subtract $5-3=2$ , use sign of larger absolute value (negative), so $-2$ ; for $-2 - (-6)$ , rewrite as $-2 + 6 = 4$ .

Reason:
Integer operations are foundational for algebra, as they apply to variable expressions, solving equations, and modeling real-life situations like temperature changes, financial transactions, and elevation differences.

Easy

Medium

Hard

📝 All Add and Subtract Integers MCQs

Q1. A submarine is at $-18$ meters relative to sea level. It rises $7$ meters and then descends $12$ meters. What is its final position?

-23

meters ✅

-5

meters

1

meter

23

meters

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Representing upward movement as positive and downward movement as negative gives $-18+7-12=-23$ . The final position is therefore $23$ meters below sea level. The distractors reflect common errors such as reversing a direction or combining magnitudes without signs.

Q2. A student claims that $-14-(-9)=-23$ because subtracting always makes a number smaller. Which reasoning best evaluates the claim?

A.The claim is correct because subtraction always decreases the first number.

B.The claim is incorrect because subtracting a negative is equivalent to adding its positive, so the result is

-5

. ✅

C.The claim is incorrect because two negative numbers always produce a positive answer.

D.The claim is correct because

14+9=23

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The key idea is that subtracting a negative changes the operation: $-14-(-9)=-14+9=-5$ . The student's error comes from treating every subtraction as movement farther left, ignoring that subtracting a negative moves the value to the right.

Q3. A bank account has a balance of $-\<span class="katex-error" title="ParseError: KaTeX parse error: Can't use function '$ ' in math mode at position 3: 35\̲)̲. A deposit of …" style="color:#cc0000">35\). A deposit of $\</span>50$ is made, followed by a withdrawal of $\$18$ . What balance remains, and what does it mean?

-\$103

, meaning the account is deeply overdrawn

-\$3

, meaning the account is still overdrawn ✅

\$3

, meaning the account has a positive balance

\$67

, meaning the account has a positive balance

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The balance can be modeled as $-35+50-18=-3$ . Thus, the account remains overdrawn by $\$3$ . The distractors represent errors such as treating the initial debt as positive or adding the withdrawal instead of subtracting it.

Q4. On a number line, a point starts at $-6$ , moves $11$ units right, and then moves $8$ units left. Where does it finish?

-25

-3

C.3 ✅

D.-13

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: Moving right corresponds to adding a positive integer, while moving left corresponds to adding a negative integer. Therefore, the position is $-6+11-8=3$ . The incorrect choices come from reversing one direction or combining all movements as positive distances.

Q5. Two students solve $-8-(-13)$ . Student A writes $-8+13=5$ . Student B writes $-8-13=-21$ . Which comparison is correct?

A.Student A is correct because subtracting a negative becomes addition. ✅

B.Student B is correct because both numbers have negative signs.

C.Both are correct because different methods can give different results.

D.Neither is correct because subtraction of integers cannot involve negative numbers.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: Student A correctly rewrites $-8-(-13)$ as $-8+13$ , giving $5$ . Student B incorrectly treats the second negative sign as if it should remain unchanged. The important reasoning is recognizing that subtracting a negative reverses the direction.

Q6. A temperature chart records changes during four hours as $+6^\circ$ , $-9^\circ$ , $+4^\circ$ , and $-7^\circ$ . If the starting temperature was $-2^\circ C$ , what is the final temperature?

-8^\circ C

✅

-4^\circ C

0^\circ C

2^\circ C

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The temperature changes must be combined with their signs: $-2+6-9+4-7=-8$ . Therefore, the final temperature is $-8^\circ C$ . A correct model must preserve each increase and decrease rather than simply adding the magnitudes of all changes.

Q7. A game awards $+10$ points for a correct answer and $-6$ points for an incorrect answer. A player answers five questions, getting three correct and two incorrect. Compared with a player who gets all five incorrect, how many more points does the first player earn?

A.18 points

B.30 points

C.48 points ✅

D.60 points

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: The first player's score is $3(10)+2(-6)=18$ . The all-incorrect player's score is $5(-6)=-30$ . The difference is $18-(-30)=48$ points. This requires modeling both scores and then subtracting a negative quantity correctly.

🔗 Related Topics (MCQs)

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