Q1: What is the sum of \(-8\) and \(+5\)? (a) \(-13\) (b) \(-3\) (c) \(+3\) (d) \(+13\)
Solution:
Ans: (b) Explanation: When adding integers with different signs, we subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. Here, \(|-8| = 8\) and \(|+5| = 5\). Since \(8 - 5 = 3\) and \(-8\) has the larger absolute value, the answer is negative: \(-3\).
Q2: Which expression represents "7 degrees below zero increased by 12 degrees"? (a) \(-7 + (-12)\) (b) \(+7 - 12\) (c) \(-7 + 12\) (d) \(+7 + 12\)
Solution:
Ans: (c) Explanation: Seven degrees below zero is represented by \(-7\). Increased by 12 degrees means we add \(+12\). Therefore, the expression is \(-7 + 12\), which equals \(+5\).
Q3: What is \((-15) - (+9)\)? (a) \(-24\) (b) \(-6\) (c) \(+6\) (d) \(+24\)
Solution:
Ans: (a) Explanation: Subtracting a positive integer is the same as adding its opposite. So \((-15) - (+9) = (-15) + (-9)\). When adding two negative integers, we add their absolute values and keep the negative sign: \(15 + 9 = 24\), so the answer is \(-24\).
Q4: The additive inverse of \(-18\) is: (a) \(-18\) (b) \(0\) (c) \(+18\) (d) \(\frac{1}{18}\)
Solution:
Ans: (c) Explanation: The additive inverse of a number is the number that, when added to the original number, gives zero. Since \((-18) + (+18) = 0\), the additive inverse of \(-18\) is \(+18\).
Q5: Which of the following has the greatest value? (a) \((-10) + (+15)\) (b) \((+8) - (+12)\) (c) \((-5) - (-9)\) (d) \((+3) + (-7)\)
Solution:
Ans: (a) Explanation: Evaluating each option: (a) \((-10) + (+15) = +5\) (b) \((+8) - (+12) = +8 + (-12) = -4\) (c) \((-5) - (-9) = (-5) + (+9) = +4\) (d) \((+3) + (-7) = -4\) The greatest value is \(+5\) from option (a).
Q6: What is the result of \((+20) - (-15)\)? (a) \(+5\) (b) \(-5\) (c) \(+35\) (d) \(-35\)
Solution:
Ans: (c) Explanation: Subtracting a negative integer is the same as adding its opposite. So \((+20) - (-15) = (+20) + (+15) = +35\). This is a common rule: two negatives make a positive when subtracting.
Q7: A submarine was at a depth of \(-250\) meters. It rose \(80\) meters. What is its new depth? (a) \(-330\) meters (b) \(-170\) meters (c) \(+170\) meters (d) \(+330\) meters
Solution:
Ans: (b) Explanation: The submarine starts at \(-250\) meters. Rising \(80\) meters means adding \(+80\): \((-250) + (+80) = -170\) meters. The submarine is still underwater but at a shallower depth.
Ans: (b) Explanation: Solving step by step: \((-7) + (+3) = -4\) \((-4) - (-5) = (-4) + (+5) = +1\) \((+1) + (-2) = -1\) The final answer is \(-1\).
Section B: Fill in the Blanks
Q9:When adding two integers with the same sign, add their absolute values and use the __________ sign.
Solution:
Ans: common Explanation: When adding integers with the same sign (both positive or both negative), we add their absolute values and keep the common sign. For example, \((-5) + (-3) = -8\).
Q10:The result of \(0 - (+14)\) is __________.
Solution:
Ans: \(-14\) Explanation: Subtracting a positive integer from zero gives the opposite of that integer. So \(0 - (+14) = -14\).
Q11:The sum of an integer and its additive inverse is always __________.
Solution:
Ans: \(0\) or zero Explanation: By definition, the additive inverse of a number is the number that, when added to it, produces zero. For example, \(7 + (-7) = 0\).
Q12:Subtracting an integer is the same as adding its __________.
Solution:
Ans: opposite or additive inverse Explanation: This is a fundamental rule for integer subtraction. For example, \(5 - 3 = 5 + (-3)\) and \((-8) - (-2) = (-8) + (+2)\). We change subtraction to addition of the opposite.
Q13:The value of \((-12) + (+12)\) is __________.
Solution:
Ans: \(0\) or zero Explanation: Since \(+12\) and \(-12\) are additive inverses of each other, their sum is zero.
Q14:If the temperature was \(-6°C\) and it drops by \(4°C\), the new temperature is __________.
Solution:
Ans: \(-10°C\) Explanation: Dropping by \(4°C\) means subtracting \(4\) or adding \(-4\): \((-6) + (-4) = -10\). The temperature becomes colder.
Section C: Word Problems
Q15:A football team gains \(15\) yards on the first play and then loses \(22\) yards on the second play. What is the overall change in their position?
Solution:
Ans: Gain of \(15\) yards: \(+15\) Loss of \(22\) yards: \(-22\) Overall change: \((+15) + (-22) = -7\) Final Answer: The team has a loss of \(7\) yards.
Q16:The lowest temperature recorded in a city on Monday was \(-18°C\). On Tuesday, the temperature was \(9°C\) higher than Monday. What was Tuesday's lowest temperature?
Solution:
Ans: Monday's temperature: \(-18°C\) Tuesday is \(9°C\) higher: \((-18) + (+9)\) \((-18) + (+9) = -9\) Final Answer: Tuesday's lowest temperature was \(-9°C\).
Q17:A bank account has a balance of \(-\$45\) (overdrawn by \(\$45\)). After depositing \(\$60\), what is the new balance?
Solution:
Ans: Starting balance: \(-\$45\) Deposit: \(+\$60\) New balance: \((-45) + (+60) = +15\) Final Answer: The new balance is \(+\$15\) or \(\$15\).
Q18:A diver descends \(35\) meters below sea level and then ascends \(12\) meters. What is the diver's current depth relative to sea level?
Solution:
Ans: Descending \(35\) meters: \(-35\) meters Ascending \(12\) meters: \(+12\) meters Current depth: \((-35) + (+12) = -23\) Final Answer: The diver is at \(-23\) meters or \(23\) meters below sea level.
Q19:In a game, Sarah scores \(+25\) points in round one, loses \(18\) points in round two, and loses \(9\) points in round three. What is her total score after three rounds?
Solution:
Ans: Round one: \(+25\) Round two: \(-18\) Round three: \(-9\) Total score: \((+25) + (-18) + (-9)\) Step 1: \((+25) + (-18) = +7\) Step 2: \((+7) + (-9) = -2\) Final Answer: Sarah's total score is \(-2\) points.
Q20:The elevation of Death Valley is \(-86\) meters. The elevation of a nearby hill is \(+42\) meters. What is the difference in elevation between the hill and Death Valley?
Solution:
Ans: Elevation of hill: \(+42\) meters Elevation of Death Valley: \(-86\) meters Difference: \((+42) - (-86)\) Rewrite subtraction as addition: \((+42) + (+86)\) \((+42) + (+86) = +128\) Final Answer: The difference in elevation is \(128\) meters.
The document Worksheet (with Solutions): Integers: Addition And Subtraction is a part of the Grade 7 Course Math Grade 7.
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