12 multiple-choice questions, progressively harder.
Which integer lies exactly halfway between −11-11−11 and −3-3−3 on the number line?
Solution
Correct answer: A
The midpoint sits the same number of ticks from each end. From −11-11−11 count right and from −3-3−3 count left until they meet.
−11→ 4 −7← 4 −3-11 \xrightarrow{\,4\,} -7 \xleftarrow{\,4\,} -3−114−74−3
So −7-7−7 is the midpoint, four units from each end.
Point AAA is at −6-6−6 and point BBB is the opposite of AAA. Which integer lies exactly halfway between AAA and BBB?
Correct answer: D
The opposite of −6-6−6 is 666, so B=6B = 6B=6. Opposites are mirror images across zero, so the midpoint of −6-6−6 and 666 is the center of the line.
−6← 6 0→ 6 6-6 \xleftarrow{\,6\,} 0 \xrightarrow{\,6\,} 6−66066
So 000 is exactly halfway between AAA and BBB.
Which of these comparisons is FALSE?
Correct answer: C
Check each by position, since farther left means smaller. The point −9-9−9 lies farther left than −8-8−8, so −9-9−9 is the smaller number.
−9<−8-9 < -8−9<−8
That makes "−9>−8-9 > -8−9>−8" the false statement; the other three are all true.
Which is the greatest integer that is still less than −5-5−5?
We need a value less than −5-5−5, so it must lie to the left of −5-5−5. The greatest such integer is the one just to the left of −5-5−5.
−6<−5-6 < -5−6<−5
So −6-6−6 is the greatest integer below −5-5−5.
On the number line, −9-9−9 and another point are the same distance from −5-5−5, one on each side. What is the other point?
Correct answer: B
The point −9-9−9 is four ticks to the left of −5-5−5, so the matching point is four ticks to the right of −5-5−5.
−5→ 4 right −1-5 \xrightarrow{\,4\text{ right}\,} -1−54 right−1
So the other point is −1-1−1.
Order from least to greatest: the opposite of −8-8−8, the number −3-3−3, and the opposite of 444.
The opposite of −8-8−8 is 888, and the opposite of 444 is −4-4−4, so the three values are 888, −3-3−3, and −4-4−4. Read them left to right on the line.
−4<−3<8-4 < -3 < 8−4<−3<8
Counting ticks, how far apart on the number line are −8-8−8 and 555?
From −8-8−8, count 888 ticks to reach 000, then 555 more to reach 555, and add the parts.
8+5=13 units8 + 5 = 13 \text{ units}8+5=13 units
An account balance is −75-75−75 dollars. Which balance shows a SMALLER debt?
A smaller debt means owing less, which is a balance closer to zero, hence farther right and greater. Among the choices, the value closest to zero is −60-60−60.
−75<−60-75 < -60−75<−60
So a balance of −60-60−60 dollars is the smaller debt.
A diver descends so each new depth is more negative than the last. Which list of depths could record the dive in order?
Descending to a more negative depth means each reading is smaller (farther left) than the one before.
−5>−11>−18>−24-5 > -11 > -18 > -24−5>−11>−18>−24
So only −5,−11,−18,−24-5, -11, -18, -24−5,−11,−18,−24 decreases at every step.
One reading is the opposite of 777. A second reading is 444 ticks farther to the left. What is the second reading?
The opposite of 777 is −7-7−7, so the first reading is −7-7−7. Moving four ticks farther left counts down from there.
−7→ 4 left −11-7 \xrightarrow{\,4\text{ left}\,} -11−74 left−11
So the second reading is −11-11−11.
Which integer is NOT strictly between −15-15−15 and −9-9−9 on the number line?
Strictly between −15-15−15 and −9-9−9 means the values from −14-14−14 up to −10-10−10, with both endpoints left out. The number −9-9−9 is an endpoint, so it does not count.
−14, −13, −12, −11, −10-14,\, -13,\, -12,\, -11,\, -10−14,−13,−12,−11,−10
So −9-9−9 is not strictly between them.
Point PPP is at −4-4−4. Point QQQ is twice as far from zero as PPP and lies on the same side of zero. What is QQQ?
The point PPP at −4-4−4 is four units from zero. Twice that distance is eight units, and the same side as PPP is the negative (left) side.
2×4=8 units left of 02 \times 4 = 8 \text{ units left of } 02×4=8 units left of 0
So Q=−8Q = -8Q=−8.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.