12 multiple-choice questions, progressively harder.
What is −14+9−(−6)−11-14 + 9 - (-6) - 11−14+9−(−6)−11?
Solution
Correct answer: A
Rewrite the subtractions as adding opposites, then group the parts.
−14+9+6+(−11)=15+(−25)=−10-14 + 9 + 6 + (-11) = 15 + (-25) = -10−14+9+6+(−11)=15+(−25)=−10
The positives total 9+6=159 + 6 = 159+6=15, the negatives total −14+(−11)=−25-14 + (-11) = -25−14+(−11)=−25, and 15+(−25)=−1015 + (-25) = -1015+(−25)=−10.
Which expression has the smallest value?
Correct answer: C
Evaluate each, rewriting subtractions as adding opposites. The values are −9-9−9, −5-5−5, −11-11−11, and −3-3−3.
3−14=3+(−14)=−113 - 14 = 3 + (-14) = -113−14=3+(−14)=−11
The smallest (most negative, farthest left) value is −11-11−11, from 3−143 - 143−14.
A submarine is 220220220 m below sea level, at −220-220−220 m. It rises 909090 m, then dives 150150150 m. What is its final position relative to sea level?
Rising adds and diving subtracts, starting from −220-220−220.
−220+90−150=−130−150=−280-220 + 90 - 150 = -130 - 150 = -280−220+90−150=−130−150=−280
First −220+90=−130-220 + 90 = -130−220+90=−130, then −130−150=−280-130 - 150 = -280−130−150=−280.
What is −7−(−7)−(−7)-7 - (-7) - (-7)−7−(−7)−(−7)?
Correct answer: B
Rewrite each subtraction of a negative as an addition.
−7+7+7=0+7=7-7 + 7 + 7 = 0 + 7 = 7−7+7+7=0+7=7
The first two form a zero pair, leaving 777.
What is (8−15)−(−4+1)(8 - 15) - (-4 + 1)(8−15)−(−4+1)?
Correct answer: D
Evaluate inside each set of parentheses first: 8−15=−78 - 15 = -78−15=−7 and −4+1=−3-4 + 1 = -3−4+1=−3.
−7−(−3)=−7+3=−4-7 - (-3) = -7 + 3 = -4−7−(−3)=−7+3=−4
Subtracting the negative result −3-3−3 adds 333.
What is −6+6−6+6−6-6 + 6 - 6 + 6 - 6−6+6−6+6−6?
Pair the terms from the left; each +6+6+6 and −6-6−6 form a zero pair.
(−6+6)+(−6+6)+(−6)=0+0+(−6)=−6(-6 + 6) + (-6 + 6) + (-6) = 0 + 0 + (-6) = -6(−6+6)+(−6+6)+(−6)=0+0+(−6)=−6
Four terms cancel in two zero pairs, leaving the final −6-6−6.
If a=−8a = -8a=−8 and b=5b = 5b=5, what is b−ab - ab−a?
Substitute and rewrite the subtraction as adding the opposite.
b−a=5−(−8)=5+8=13b - a = 5 - (-8) = 5 + 8 = 13b−a=5−(−8)=5+8=13
Subtracting a=−8a = -8a=−8 adds 888.
What is 100−250+80−(−20)100 - 250 + 80 - (-20)100−250+80−(−20)?
Rewrite as additions and combine the positive and negative parts.
100+(−250)+80+20=200+(−250)=−50100 + (-250) + 80 + 20 = 200 + (-250) = -50100+(−250)+80+20=200+(−250)=−50
The positives total 100+80+20=200100 + 80 + 20 = 200100+80+20=200, the negative is −250-250−250, and 200+(−250)=−50200 + (-250) = -50200+(−250)=−50.
What is the opposite of (5−12)(5 - 12)(5−12)?
Evaluate inside first: 5−12=−75 - 12 = -75−12=−7. The opposite of −7-7−7 is the same distance from zero on the other side.
opposite of −7=7\text{opposite of } -7 = 7opposite of −7=7
What is −9+4−(−9)−4-9 + 4 - (-9) - 4−9+4−(−9)−4?
Rewrite the subtraction of a negative, then group opposite pairs.
−9+4+9+(−4)=(−9+9)+(4−4)=0-9 + 4 + 9 + (-4) = (-9 + 9) + (4 - 4) = 0−9+4+9+(−4)=(−9+9)+(4−4)=0
The −9-9−9 and 999 cancel, and the 444 and −4-4−4 cancel.
At dawn the temperature is −9-9−9 degrees. It rises 555 degrees, falls 333 degrees, then rises 111111 degrees. What is the temperature now?
Chain the changes from −9-9−9, adding for a rise and subtracting for a fall.
−9+5−3+11=−4−3+11-9 + 5 - 3 + 11 = -4 - 3 + 11−9+5−3+11=−4−3+11
Step by step: −9+5=−4-9 + 5 = -4−9+5=−4, then −4−3=−7-4 - 3 = -7−4−3=−7, then −7+11=4-7 + 11 = 4−7+11=4 degrees.
An account is overdrawn at −6-6−6 dollars. After one deposit the balance is −2-2−2 dollars. How large was the deposit?
A deposit adds to the balance, which is a move to the right on the line. From −6-6−6 to −2-2−2 is four units to the right.
−6+4=−2-6 + 4 = -2−6+4=−2
So the deposit was 444 dollars. The account is still overdrawn afterwards, but it moved toward zero.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.