12 multiple-choice questions, progressively harder.
What is −8+15−(−3)−12-8 + 15 - (-3) - 12−8+15−(−3)−12?
Solution
Correct answer: C
Rewrite every subtraction as adding the opposite, then combine.
−8+15+3+(−12)=18+(−20)=−2-8 + 15 + 3 + (-12) = 18 + (-20) = -2−8+15+3+(−12)=18+(−20)=−2
The positives total 15+3=1815 + 3 = 1815+3=18 and the negatives total −8+(−12)=−20-8 + (-12) = -20−8+(−12)=−20; combining gives −2-2−2.
The temperature at midnight is −6-6−6 degrees. It falls 444 degrees by 3 a.m., then rises 999 degrees by noon. What is the temperature at noon?
Correct answer: B
Falling subtracts and rising adds, so chain the changes from −6-6−6.
−6−4+9=−10+9=−1-6 - 4 + 9 = -10 + 9 = -1−6−4+9=−10+9=−1
First −6−4=−10-6 - 4 = -10−6−4=−10, then −10+9=−1-10 + 9 = -1−10+9=−1, so the temperature at noon is −1-1−1 degrees.
What is −100+250−175-100 + 250 - 175−100+250−175?
Rewrite as additions and combine.
−100+250+(−175)=150+(−175)=−25-100 + 250 + (-175) = 150 + (-175) = -25−100+250+(−175)=150+(−175)=−25
First −100+250=150-100 + 250 = 150−100+250=150, then 150+(−175)=−25150 + (-175) = -25150+(−175)=−25.
Start at −7-7−7 on the number line. Which number, added on, lands you at −15-15−15?
Correct answer: A
Going from −7-7−7 down to −15-15−15 is a walk of eight units to the left. Adding a negative number is what walks left, and the size of that number is how far it walks.
−7+(−8)=−15-7 + (-8) = -15−7+(−8)=−15
Check: eight steps left from −7-7−7 reaches −15-15−15.
What is −13−(−13)−13-13 - (-13) - 13−13−(−13)−13?
Rewrite each subtraction as adding the opposite.
−13+13+(−13)=0+(−13)=−13-13 + 13 + (-13) = 0 + (-13) = -13−13+13+(−13)=0+(−13)=−13
The first two form a zero pair, leaving −13-13−13.
Which statement is true?
Subtracting 999 means adding its opposite −9-9−9, so −4−9=−4+(−9)-4 - 9 = -4 + (-9)−4−9=−4+(−9).
−4−9=−4+(−9)=−13-4 - 9 = -4 + (-9) = -13−4−9=−4+(−9)=−13
Both sides equal −13-13−13, so the first statement is true. The others change the value.
A hiker starts at 120120120 m above sea level, descends 200200200 m into a canyon, then climbs 505050 m. What is the hiker's elevation?
Correct answer: D
Descending subtracts and climbing adds, starting from 120120120.
120−200+50=−80+50=−30120 - 200 + 50 = -80 + 50 = -30120−200+50=−80+50=−30
First 120−200=−80120 - 200 = -80120−200=−80, then −80+50=−30-80 + 50 = -30−80+50=−30, so the hiker ends 303030 m below sea level.
What is −1−2−3−4-1 - 2 - 3 - 4−1−2−3−4?
Each subtraction adds a negative, so all four steps go left and the distances add.
−1+(−2)+(−3)+(−4)=−(1+2+3+4)=−10-1 + (-2) + (-3) + (-4) = -(1 + 2 + 3 + 4) = -10−1+(−2)+(−3)+(−4)=−(1+2+3+4)=−10
Taking −6-6−6 away from a number lands on 111. Which number did you start from?
Taking away −6-6−6 is the same as adding 666, so the move is six units to the right. The starting point is therefore six units to the left of 111, and six steps left from 111 reaches −5-5−5.
−5−(−6)=−5+6=1-5 - (-6) = -5 + 6 = 1−5−(−6)=−5+6=1
Check: starting at −5-5−5 and adding 666 does land on 111.
A football team gains 777 yards, loses 121212 yards, then loses another 333 yards. What is the net change in field position?
A gain adds and a loss subtracts. Combine the three changes.
7−12−3=7+(−15)=−87 - 12 - 3 = 7 + (-15) = -87−12−3=7+(−15)=−8
The net change is a loss of 888 yards, written −8-8−8.
If a=−4a = -4a=−4 and b=−9b = -9b=−9, what is a−ba - ba−b?
Substitute the values, then rewrite the subtraction as adding the opposite.
a−b=−4−(−9)=−4+9=5a - b = -4 - (-9) = -4 + 9 = 5a−b=−4−(−9)=−4+9=5
Subtracting b=−9b = -9b=−9 adds 999, landing on 555.
What is −30+45−60+25-30 + 45 - 60 + 25−30+45−60+25?
Add the positive parts and the negative parts separately, then combine.
(45+25)+(−30+(−60))=70+(−90)=−20(45 + 25) + (-30 + (-60)) = 70 + (-90) = -20(45+25)+(−30+(−60))=70+(−90)=−20
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