This MCQ module is based on: Addition of Integers
TOPIC 39 OF 41
Addition of Integers
🎓 Class 6
Mathematics
CBSE
Theory
Ch 10 — The Other Side of Zero
⏱ ~30 min
🌐 Language: [gtranslate]
🧠 AI-Powered MCQ Assessment
▲
📐 Maths Assessment
▲
This mathematics assessment will be based on: Addition of Integers
Targeting Class 6 level in Integers, with Basic difficulty.
Upload images, PDFs, or Word documents to include their content in assessment generation.
10.6 Adding Integers
Now that we know what integers are, let us learn to add them. We'll use two powerful pictures: the token model and the number-line model.
Case 1: Adding Two Positives
This is the familiar case. (+3) + (+4) = +7. On the number line: start at 0, jump 3 right, then 4 more right — land on +7.
Case 2: Adding Two Negatives
(−3) + (−4) = −7. With tokens: 3 red + 4 red = 7 red → −7. On the number line: start at 0, jump 3 left, then 4 more left — land on −7.
Rule — Same Signs
When adding two integers with the same sign: add their absolute values, and keep the common sign.Case 3: Adding a Positive and a Negative
(+6) + (−2): start with 6 yellow tokens, add 2 red tokens. Two yellows cancel with two reds → 4 yellow remain → +4.
(+2) + (−6): 2 yellow + 6 red. Two zero pairs cancel → 4 red remain → −4.
Token method: cancel zero pairs, what remains is the answer.
Rule — Opposite Signs
When adding two integers with opposite signs: subtract the smaller absolute value from the larger; the sign of the answer is the sign of the integer with the larger absolute value.The Number-Line Method
Start at the first number. Positive means jump right, negative means jump left. The arrival point is the sum.
Number-line addition: start at −3, jump 5 right, land on +2.
Worked Examples
Ex 1: \((-7) + (-4) = -11\). Same sign → add magnitudes (7 + 4 = 11), keep sign (−) → −11.
Ex 2: \((+9) + (-5) = +4\). Opposite signs → bigger magnitude is 9 (positive) → answer is positive; 9 − 5 = 4 → +4.
Ex 3: \((-8) + (+3) = -5\). Opposite signs; 8 > 3, bigger sign is negative; 8 − 3 = 5 → −5.
Ex 4: \((+15) + (-15) = 0\). Opposite numbers always sum to 0.
Properties of Addition
Key Properties
For all integers \(a\), \(b\), \(c\):Closure: \(a + b\) is always an integer.
Commutative: \(a + b = b + a\).
Associative: \((a + b) + c = a + (b + c)\).
Additive identity: \(a + 0 = 0 + a = a\).
Additive inverse: For every \(a\), there is \(-a\) such that \(a + (-a) = 0\).
🔵 Quick check: Are the whole numbers (0, 1, 2, 3, …) closed under subtraction? No — e.g., 3 − 5 is not a whole number. But integers are closed under subtraction, since any integer subtraction gives an integer. That is one of the main reasons integers were invented.
Activity: Token Duels
L3 ApplyMaterials: 20 yellow and 20 red tokens (paper chits or counters)
Predict: You will hold 8 red and 3 yellow tokens, and your partner 4 red and 9 yellow. When your piles are combined, what total integer will result?
- Pair up. Each player secretly builds a pile from yellow and red tokens.
- Announce your pile's value (e.g., "mine is −5").
- Without combining yet, both players try to predict the total using the addition rule.
- Combine the two piles and cancel zero pairs. Whose prediction was correct?
- Play 10 rounds. Keep a score of correct predictions.
Tip: if both piles have the same sign, add magnitudes. If opposite signs, find the difference and take the sign of the larger magnitude. With practice this becomes instant.
Figure it Out — Part C
Q1. Add: (a) (+3) + (+8) (b) (−5) + (−9) (c) (+12) + (−7) (d) (−15) + (+8) (e) (−6) + (+6) (f) 0 + (−4).
(a) +11 (b) −14 (c) +5 (d) −7 (e) 0 (f) −4.
Q2. Find the sum: (−3) + (+5) + (−2) + (+4) + (−6).
Group positives: +5 + 4 = +9. Group negatives: −3 + (−2) + (−6) = −11. Total: 9 − 11 = −2.
Q3. A submarine is 120 m below sea level. It rises 50 m, then dives 30 m more. Where is it now?
Start: −120. Rise 50: −120 + 50 = −70. Dive 30: −70 + (−30) = −100 m (100 m below sea level).
Q4. Fill in the blanks:
(a) (−7) + ___ = 0 (b) ___ + (−4) = −10 (c) (+12) + ___ = +3 (d) ___ + (+5) = −2.
(a) (−7) + ___ = 0 (b) ___ + (−4) = −10 (c) (+12) + ___ = +3 (d) ___ + (+5) = −2.
(a) +7 (b) −6 (c) −9 (d) −7.
Q5. A bank account shows deposits and withdrawals during a week: +500, −200, +300, −100, −150, +50. Find the net balance change.
Positives: 500 + 300 + 50 = 850. Negatives: 200 + 100 + 150 = 450. Net = 850 − 450 = +400 (balance grew by ₹400).
Competency-Based Questions
Scenario: A climber starts at the base camp at 4,000 m above sea level. On Day 1 she climbs +600 m, on Day 2 she climbs +400 m, on Day 3 she descends −300 m due to bad weather, and on Day 4 she climbs +500 m.
Q1. What is her altitude at the end of Day 4?
L3 Apply4000 + 600 + 400 − 300 + 500 = 5,200 m.
Q2. Analyse which day produced the largest absolute change in altitude.
L4 Analyse|+600| = 600, |+400| = 400, |−300| = 300, |+500| = 500. Day 1 had the largest change (600 m).
Q3. Evaluate the climber's statement: "Since I went up on 3 days and down on only 1 day, my net climb is 3 − 1 = 2 days' worth of climbing." Is this reasoning correct?
L5 EvaluateIncorrect reasoning. Net change is not about counting the number of positive/negative days but about summing the signed amounts: +600 + 400 − 300 + 500 = +1200 m. The "3 − 1 = 2 days" argument ignores magnitudes.
Q4. Design a 5-day plan for a different climb that begins and ends at the same altitude, with at least one descent day and a total of five daily movements. Show the plan.
L6 CreateSample plan: +800, +500, −400, +200, −1100. Sum: 800 + 500 − 400 + 200 − 1100 = 0. Starting and ending altitude are equal. Many answers are possible — the sum of all 5 signed movements must be 0.
Assertion–Reason Questions
Assertion (A): The sum of two negative integers is always negative.
Reason (R): When two integers have the same sign, we add the magnitudes and keep that sign.
Reason (R): When two integers have the same sign, we add the magnitudes and keep that sign.
(a) Both negatives → sum has sign (−). R is the general same-sign rule.
Assertion (A): Integer addition is commutative: \(a + b = b + a\).
Reason (R): The order of jumping on a number line affects the final position.
Reason (R): The order of jumping on a number line affects the final position.
(c) A is true (commutativity holds). R is false — the order of jumps on a number line does not change the final position.
Assertion (A): For every integer \(a\), \(a + (-a) = 0\).
Reason (R): \(a\) and \(-a\) are opposite numbers equidistant from 0 on the number line.
Reason (R): \(a\) and \(-a\) are opposite numbers equidistant from 0 on the number line.
(a) Opposite numbers always sum to zero. R is the correct geometric explanation.
Frequently Asked Questions
How do you add two negative integers?
Add the absolute values and keep the negative sign. Example: (-4) + (-7) = -(4+7) = -11.
What is a zero pair?
A zero pair is a pair of opposite integers that add to zero, like +3 and -3. Zero pairs cancel out during integer addition using tokens.
What is (-5) + 9?
(-5) + 9 = 4. Subtract 5 from 9 because they have different signs, then use the sign of 9 (positive) which has the larger absolute value.
Is integer addition commutative?
Yes. a + b = b + a for all integers, so (-3) + 5 = 5 + (-3) = 2. Order does not change the sum.
What is (-7) + 7?
(-7) + 7 = 0. Any integer plus its opposite equals zero - this is the additive inverse property.
How does the number-line method work?
Start at the first integer. For positive addend, move right by that many steps; for negative addend, move left. The final position is the sum.
AI Tutor
Mathematics Class 6 — Ganita Prakash
Ready