This MCQ module is based on: Integers on the Number Line
TOPIC 38 OF 41
Integers on the Number Line
🎓 Class 6
Mathematics
CBSE
Theory
Ch 10 — The Other Side of Zero
⏱ ~30 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Integers on the Number Line
Targeting Class 6 level in Integers, with Basic difficulty.
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10.4 The Integer Number Line
We extend the number line to the left of 0 to include the negative integers.
The integer number line runs in both directions without end. 0 is the centre.
Definition
The set of integers, denoted by the letter Z (from the German Zahlen, meaning "numbers"), is:\[Z = \{\ldots, -4, -3, -2, -1, 0, +1, +2, +3, +4, \ldots\}\] It has no smallest and no largest member.
Opposite Numbers (Inverses)
For every positive integer, there is a corresponding negative integer the same distance from 0 on the other side. These are called opposite numbers? or additive inverses.
The opposite of +3 is −3; the opposite of −7 is +7. The opposite of 0 is 0 itself.
Key Property
A number and its opposite always add to 0:\((+3) + (-3) = 0, \quad (-5) + (+5) = 0, \quad (+a) + (-a) = 0\) for every integer \(a\).
10.5 Comparing Integers
On the number line, numbers to the right are always greater. Numbers to the left are smaller.
Rules of Ordering
(i) Every positive number is greater than every negative number and greater than 0.(ii) 0 is greater than every negative number.
(iii) Between two negative numbers, the one closer to 0 (smaller in magnitude) is greater. So −2 > −5 (because −2 is to the right of −5).
Worked Examples
Compare: Is −3 or −7 greater? On the number line, −3 lies to the right of −7, so −3 > −7.
Compare: Is 0 or −1 greater? 0 is to the right of −1, so 0 > −1.
Arrange in ascending order: −6, +2, 0, −1, +5, −9 → from smallest to largest: −9 < −6 < −1 < 0 < +2 < +5.
The "Floor Model"
Think of the shopping mall: Floor +5 is higher than Floor +1. Floor −1 (basement 1) is lower than Floor 0 (ground), and Floor −3 is lower than Floor −1. Going up means bigger; going down means smaller.
Ordering integers via mall floors: higher floor = bigger integer.
Absolute Value (Size without Sign)
The distance of a number from 0 on the number line is called its absolute value. Written with vertical bars: \(|+5| = 5, \; |-5| = 5, \; |0| = 0\). Absolute value is always zero or positive.
🔵 Which is farther from 0: −12 or +8? \(|-12| = 12\) and \(|+8| = 8\). So −12 is farther from 0, even though +8 is the greater number.
Activity: Elevator Ride
L3 ApplyMaterials: Paper strip marked with floors −5 to +5, a paper clip as "elevator"
Predict: Starting at Floor 0, if you go up 3 floors and then down 7 floors, where will you be? Make a guess before you check.
- Place the paper clip at 0.
- "Up" means slide the clip toward +. "Down" means slide toward −.
- Try these trips: (i) up 5, down 8 → position? (ii) down 3, up 10 → position? (iii) down 2, down 4 → position?
- Write each trip as an integer sum, e.g. \(0 + 5 - 8 = -3\).
(i) 0 + 5 − 8 = −3 (ii) 0 − 3 + 10 = +7 (iii) 0 − 2 − 4 = −6.
Figure it Out — Part B
Q1. Write the integer represented by each situation:
(a) Lift at floor +3 goes down 5 floors. (b) Temperature rises from −4°C to +2°C. (c) A submarine at −120 m rises by 40 m.
(a) Lift at floor +3 goes down 5 floors. (b) Temperature rises from −4°C to +2°C. (c) A submarine at −120 m rises by 40 m.
(a) 3 − 5 = −2 (2nd basement). (b) Change = +2 − (−4) = +6°C. (c) New depth = −120 + 40 = −80 m.
Q2. Fill >, < or = :
(a) −5 ___ −8 (b) 0 ___ −3 (c) −1 ___ +1 (d) |−7| ___ |+7| (e) −10 ___ −2.
(a) −5 ___ −8 (b) 0 ___ −3 (c) −1 ___ +1 (d) |−7| ___ |+7| (e) −10 ___ −2.
(a) > (b) > (c) < (d) = (both are 7) (e) <.
Q3. Arrange in descending order: −2, +6, −15, 0, +1, −1, +9.
+9 > +6 > +1 > 0 > −1 > −2 > −15.
Q4. Write the opposite (additive inverse) of: +12, −34, 0, +1, −1.
−12, +34, 0, −1, +1.
Q5. Write the successor and predecessor of each integer:
(a) −5 (b) 0 (c) −1 (d) +3.
(a) −5 (b) 0 (c) −1 (d) +3.
(a) succ −4, pred −6. (b) succ +1, pred −1. (c) succ 0, pred −2. (d) succ +4, pred +2.
Competency-Based Questions
Scenario: On a cross-section of the Earth's surface, heights and depths at 7 locations A–G (in metres, relative to sea level) are: A = +1500, B = −500, C = +800, D = +1200, E = −1000, F = 0 (sea level), G = −1500.
Q1. Which is the highest point? Which is the lowest?
L3 ApplyHighest: A (+1500). Lowest: G (−1500).
Q2. Arrange the 7 locations from lowest to highest.
L4 AnalyseG (−1500) < E (−1000) < B (−500) < F (0) < C (+800) < D (+1200) < A (+1500).
Q3. A geologist says, "G is three times as deep below sea level as B." Evaluate this.
L5 Evaluate|G| = 1500 m, |B| = 500 m. 1500/500 = 3. Correct — G is indeed 3 times as deep as B. Note that we compare absolute values (depths), not the signed integers.
Q4. Create a simple ruler/strip design that a geography teacher could use in class to show all 7 locations and sea level, clearly distinguishing positive from negative heights.
L6 CreateDesign: A vertical strip. Middle of the strip marked 0 (sea level, yellow line). Every 500 m marked as a tick. Above 0 mark +500, +1000, +1500 in red. Below 0 mark −500, −1000, −1500 in blue. Place a small flag at each location A–G with its name. Add clouds at top and ocean floor at bottom.
Assertion–Reason Questions
Assertion (A): −3 > −7.
Reason (R): Among two negative integers, the one with the smaller absolute value is greater.
Reason (R): Among two negative integers, the one with the smaller absolute value is greater.
(a) |−3| = 3 < 7 = |−7|, so −3 is closer to 0 and therefore greater. R is the correct reason.
Assertion (A): The smallest integer is 0.
Reason (R): Integers extend infinitely in the negative direction.
Reason (R): Integers extend infinitely in the negative direction.
(d) A is false — there is no smallest integer; you can always go one step further left. R is true and exactly the reason A is false.
Assertion (A): |−10| = |+10|.
Reason (R): Absolute value measures distance from 0, ignoring direction.
Reason (R): Absolute value measures distance from 0, ignoring direction.
(a) Both −10 and +10 are 10 units from 0, and R correctly explains why the absolute values are equal.
Frequently Asked Questions
Which integer is greater, -3 or -7?
-3 is greater than -7. On the number line -3 lies to the right of -7. Remember: for negatives, the smaller digit is the greater number.
What is the absolute value of an integer?
The absolute value is its distance from zero on the number line, without sign. |5| = 5 and |-5| = 5. Absolute value is always non-negative.
What is the predecessor of 0?
The predecessor of 0 (the integer just before 0) is -1. The successor of 0 is 1.
How do you compare two integers?
On the number line the integer lying to the right is greater. Any positive integer is greater than any negative integer, and 0 is greater than every negative integer.
What is the opposite of -8?
The opposite (additive inverse) of -8 is +8. Opposites lie at the same distance from zero on opposite sides.
Are all whole numbers integers?
Yes. Every whole number (0, 1, 2, 3, ...) is an integer, but not every integer is a whole number - negative integers are not whole numbers.
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Mathematics Class 6 — Ganita Prakash
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