12 multiple-choice questions, progressively harder.
What is −7−(−12)-7 - (-12)−7−(−12)?
Solution
Correct answer: B
Subtracting a negative is the same as adding its opposite, so rewrite first.
−7−(−12)=−7+12=5-7 - (-12) = -7 + 12 = 5−7−(−12)=−7+12=5
The signs now differ; subtract (12−7=512 - 7 = 512−7=5) and take the positive sign of the larger distance.
What is 13+(−20)13 + (-20)13+(−20)?
Correct answer: C
The signs differ, so subtract the smaller distance from the larger. The distances are 131313 and 202020.
13+(−20)=−(20−13)=−713 + (-20) = -(20 - 13) = -713+(−20)=−(20−13)=−7
The larger distance belongs to the negative −20-20−20, so the answer is negative.
What is −15+(−8)-15 + (-8)−15+(−8)?
Correct answer: A
Both numbers are negative, so both steps go left and the distances add.
−15+(−8)=−(15+8)=−23-15 + (-8) = -(15 + 8) = -23−15+(−8)=−(15+8)=−23
What is 6−(−6)6 - (-6)6−(−6)?
Subtracting a negative becomes adding its opposite.
6−(−6)=6+6=126 - (-6) = 6 + 6 = 126−(−6)=6+6=12
Taking away a negative moves to the right, so the result grows.
What is −4+11+(−9)-4 + 11 + (-9)−4+11+(−9)?
Work left to right. First −4+11-4 + 11−4+11 has different signs: 11−4=711 - 4 = 711−4=7, positive.
−4+11=7,7+(−9)=−2-4 + 11 = 7, \qquad 7 + (-9) = -2−4+11=7,7+(−9)=−2
Then 7+(−9)7 + (-9)7+(−9) has different signs: 9−7=29 - 7 = 29−7=2, with the negative sign of the larger distance.
A diver descends to −18-18−18 meters, then rises 777 meters. What is the diver's new elevation?
Rising 777 meters adds 777 to the elevation. Start at −18-18−18 and add 777.
−18+7=−(18−7)=−11-18 + 7 = -(18 - 7) = -11−18+7=−(18−7)=−11
The diver is now at −11-11−11 meters, still below the surface but closer to it.
The temperature is −3-3−3 degrees and falls 888 degrees. What is the new temperature?
Correct answer: D
Falling 888 degrees subtracts 888, which is the same as adding −8-8−8.
−3−8=−3+(−8)=−11-3 - 8 = -3 + (-8) = -11−3−8=−3+(−8)=−11
Both steps go left, so the temperature drops to −11-11−11 degrees.
What is −2+(−7)+(−5)-2 + (-7) + (-5)−2+(−7)+(−5)?
All three numbers are negative, so the distances all add and the answer stays negative.
−2+(−7)+(−5)=−(2+7+5)=−14-2 + (-7) + (-5) = -(2 + 7 + 5) = -14−2+(−7)+(−5)=−(2+7+5)=−14
Start at −8-8−8 on the number line. Which number, added on, lands you at −3-3−3?
Adding a number is a walk from where you start. Going from −8-8−8 up to −3-3−3 is a walk of five units to the right, and a walk to the right is what adding a positive number does.
−8+5=−3-8 + 5 = -3−8+5=−3
Check: five steps right from −8-8−8 passes −7-7−7, −6-6−6, −5-5−5, −4-4−4 and lands on −3-3−3.
A bank account holds −45-45−45 dollars (overdrawn). A deposit of 606060 dollars is made. What is the new balance?
A deposit adds to the balance. Start at −45-45−45 and add 606060.
−45+60=60−45=15-45 + 60 = 60 - 45 = 15−45+60=60−45=15
The larger distance belongs to the positive deposit, so the account is now 151515 dollars in the positive.
What is 18+(−25)18 + (-25)18+(−25)?
The signs differ, so subtract the smaller distance from the larger. The distances are 181818 and 252525.
18+(−25)=−(25−18)=−718 + (-25) = -(25 - 18) = -718+(−25)=−(25−18)=−7
The larger distance belongs to the negative −25-25−25, so the answer is negative.
Start at 444 on the number line. Which number, taken away, lands you at 999?
Going from 444 up to 999 is a move of five units to the right. Subtracting a positive number steps left, so the missing number has to be negative, and subtracting −5-5−5 steps five units right.
4−(−5)=4+5=94 - (-5) = 4 + 5 = 94−(−5)=4+5=9
Check: taking away −5-5−5 adds 555 and lands on 999.
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