12 multiple-choice questions, progressively harder.
Which expression has the greatest value?
Solution
Correct answer: B
Evaluate each. The second rewrites as −3+5=2-3 + 5 = 2−3+5=2, while the others give −8-8−8, −6-6−6, and −7-7−7.
−3−(−5)=−3+5=2-3 - (-5) = -3 + 5 = 2−3−(−5)=−3+5=2
Only that one is positive, so it is the greatest.
Start at −5-5−5 on the number line. Which number, taken away, lands you at 444?
Going from −5-5−5 up to 444 is a move of nine units to the right. Taking away a positive number would step left, so the number taken away has to be negative, and taking away −9-9−9 steps nine units right.
−5−(−9)=−5+9=4-5 - (-9) = -5 + 9 = 4−5−(−9)=−5+9=4
Check: taking away −9-9−9 adds 999 and reaches 444.
What is 20−35−(−10)20 - 35 - (-10)20−35−(−10)?
Correct answer: C
Rewrite the subtractions as adding opposites and work left to right.
20+(−35)+10=−15+10=−520 + (-35) + 10 = -15 + 10 = -520+(−35)+10=−15+10=−5
First 20+(−35)=−1520 + (-35) = -1520+(−35)=−15, then −15+10=−5-15 + 10 = -5−15+10=−5.
Which statement is true?
Subtracting −4-4−4 is adding 444, so 10−(−4)=10+410 - (-4) = 10 + 410−(−4)=10+4.
10−(−4)=10+4=1410 - (-4) = 10 + 4 = 1410−(−4)=10+4=14
The others are wrong: −10+4=−6-10 + 4 = -6−10+4=−6 and −10−4=−14-10 - 4 = -14−10−4=−14.
What is (−6+10)−(3−8)(-6 + 10) - (3 - 8)(−6+10)−(3−8)?
Evaluate inside each set of parentheses first. The first group is −6+10=4-6 + 10 = 4−6+10=4 and the second is 3−8=−53 - 8 = -53−8=−5.
4−(−5)=4+5=94 - (-5) = 4 + 5 = 94−(−5)=4+5=9
Subtracting the negative result −5-5−5 adds 555.
What is −3−(−8)+(−5)−2-3 - (-8) + (-5) - 2−3−(−8)+(−5)−2?
Correct answer: D
Rewrite the subtractions as adding opposites, then combine.
−3+8+(−5)+(−2)=8+(−10)=−2-3 + 8 + (-5) + (-2) = 8 + (-10) = -2−3+8+(−5)+(−2)=8+(−10)=−2
The positive part is 888, the negatives total −3+(−5)+(−2)=−10-3 + (-5) + (-2) = -10−3+(−5)+(−2)=−10, and 8+(−10)=−28 + (-10) = -28+(−10)=−2.
What is −50−(−30)−(−20)-50 - (-30) - (-20)−50−(−30)−(−20)?
Rewrite both subtractions of negatives as additions.
−50+30+20=−50+50=0-50 + 30 + 20 = -50 + 50 = 0−50+30+20=−50+50=0
The two positive steps total 505050, which exactly cancels the −50-50−50.
The roof of a building is 424242 m above ground level, and its garage floor is 181818 m below ground level. How much higher is the roof than the garage floor?
Correct answer: A
Ground level is 000, so the garage floor sits at −18-18−18 m. How much higher one is than the other is the roof with the garage floor taken away.
42−(−18)=42+18=6042 - (-18) = 42 + 18 = 6042−(−18)=42+18=60
The climb from −18-18−18 m runs 181818 m up to ground level and 424242 m more above it, and those two distances add because the trip crosses zero.
What is 7−9+4−(−2)−67 - 9 + 4 - (-2) - 67−9+4−(−2)−6?
7+(−9)+4+2+(−6)=13+(−15)=−27 + (-9) + 4 + 2 + (-6) = 13 + (-15) = -27+(−9)+4+2+(−6)=13+(−15)=−2
The positives total 7+4+2=137 + 4 + 2 = 137+4+2=13, the negatives total −9+(−6)=−15-9 + (-6) = -15−9+(−6)=−15, and 13+(−15)=−213 + (-15) = -213+(−15)=−2.
What is −1−1−1−1−1-1 - 1 - 1 - 1 - 1−1−1−1−1−1?
Each subtraction adds a −1-1−1, so all five steps go left and the distances add.
−1+(−1)+(−1)+(−1)+(−1)=−5-1 + (-1) + (-1) + (-1) + (-1) = -5−1+(−1)+(−1)+(−1)+(−1)=−5
What is −2−(−11)−4−(−1)-2 - (-11) - 4 - (-1)−2−(−11)−4−(−1)?
Rewrite every subtraction as adding the opposite.
−2+11+(−4)+1=12+(−6)=6-2 + 11 + (-4) + 1 = 12 + (-6) = 6−2+11+(−4)+1=12+(−6)=6
The positives total 11+1=1211 + 1 = 1211+1=12, the negatives total −2+(−4)=−6-2 + (-4) = -6−2+(−4)=−6, and 12+(−6)=612 + (-6) = 612+(−6)=6.
The opposite of (−7+3)(-7 + 3)(−7+3) is which number?
First evaluate inside the parentheses: −7+3=−4-7 + 3 = -4−7+3=−4. The opposite of −4-4−4 is the number the same distance from zero on the other side.
opposite of −4=4\text{opposite of } -4 = 4opposite of −4=4
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