RS Aggarwal Solutions for Class 6 Chapter 5 Fractions

Exercise 5.1

Question 1. (i) Decrease of population.
Answer: When the population goes down, it represents a loss or a negative change.

Exam Tip: Negative numbers represent decreases, losses, or reductions in real-world contexts — always link the mathematical sign to the situation.

Question 1. (ii) With drawing money from a bank
Answer: Withdrawing money from a bank account reduces the balance, so it is shown as a negative number.

Exam Tip: Money taken out is a negative operation; money deposited is positive — keep the direction clear in your answer.

Question 1. (iii) Spending money.
Answer: Spending reduces the amount you have, so it is represented by a negative number.

Exam Tip: Spending and losses are negative; earning and gains are positive — always state which direction the change goes.

Question 1. (iv) Going South
Answer: Going south means moving in a downward direction, which is shown as a negative integer.

Exam Tip: Direction matters — south/down is negative, north/up is positive. Make this clear in your reasoning.

Question 1. (v) Loosing a weight of 4 kg.
Answer: Losing weight means a reduction in mass, which is represented as a negative integer (-4).

Exam Tip: Loss of any quantity (weight, money, people) is negative; gain is positive — identify the direction first.

Question 1. (vi) A gain of Rs 1000.
Answer: A gain shows an increase, which is represented as a positive integer (+1000).

Exam Tip: Gains, profits, and increases are always positive — this is the opposite of losses or reductions.

Question 1. (vii) -25.
Answer: The integer -25 represents a decrease, loss, or movement in the negative direction.

Exam Tip: The minus sign tells you it is a negative integer — always interpret what real-world situation it could represent.

Question 1. (viii) 15.
Answer: The integer 15 represents a gain, increase, or movement in the positive direction.

Exam Tip: Positive integers show growth or forward movement — link them to increases in the real world.

Question 2. (i) 25° above zero is -→ +25°.
Answer: A temperature of 25 degrees above zero point is written as the positive integer +25.

Exam Tip: Temperatures above zero are positive; below zero are negative — always state the reference point (zero) clearly.

Question 2. (ii) 5° below zero -→ -5°.
Answer: A temperature of 5 degrees below zero point is written as the negative integer -5.

Exam Tip: "Below zero" is always negative — the distance from zero is the number, the sign shows direction.

Question 2. (iii) A profit of 800 -→ +800.
Answer: A profit of 800 rupees is shown as the positive integer +800.

Exam Tip: Profit is always positive; loss is always negative — make sure you use the correct sign for the business outcome.

Question 2. (iv) A deposit of 2500 -→ +2500.
Answer: A deposit of 2500 rupees adds to the account, shown as the positive integer +2500.

Exam Tip: Deposits and credits are positive; withdrawals and debits are negative — always identify the direction of money flow.

Question 2. (v) 3 km above sea level -→ +3.
Answer: A height of 3 kilometers above sea level is shown as the positive integer +3.

Exam Tip: Heights above a reference point (sea level) are positive; depths below are negative.

Question 2. (vi) 2 km below sea level -→ -2.
Answer: A depth of 2 kilometers below sea level is shown as the negative integer -2.

Exam Tip: "Below a reference level" is always negative — the magnitude is the number, the minus sign shows direction downward.

Question 3. Integers are as shown in the number line.
Answer: A number line displays all integers, with negative integers on the left, zero in the middle, and positive integers on the right. The arrow at each end shows the line extends infinitely in both directions.
In simple words: A number line shows integers arranged from left to right, with negative numbers on the left side, zero at the center, and positive numbers on the right side.

Exam Tip: Always use the number line to compare integers — the integer further to the right is always larger.

Question 4. (i) Since '0' is greater than all negative integers. Therefore -4 < 0. -4 is smaller.
Answer: Zero is greater than any negative integer, so -4 < 0. This means -4 is the smaller value.

Exam Tip: All negative numbers are less than zero — use the number line to verify your comparison every time.

Question 4. (ii) We know that > 3 on the number line -3 is to left of 12. -50 < 12. -3 is smaller.
Answer: On the number line, -3 sits to the left of 12, which means -3 < 12. So -3 is the smaller value.

Exam Tip: Any integer on the left of the number line is smaller than any integer on the right — position always determines size.

Question 4. (iii) 8, 13. WKT on the number line 8 is to left of 13. so 8 < 13.
Answer: On the number line, 8 is to the left of 13, which tells us 8 < 13.

Exam Tip: The position on the number line determines the comparison — left is always smaller than right.

Question 4. (iv) -15, -27. W.K.T on the number line -27 is to left of -27 So -27 < -15.
Answer: On the number line, -27 is to the left of -15, so -27 < -15.

Exam Tip: Even with negative numbers, the integer further left is smaller — compare positions, not just the digits.

Question 5. (i) 3, -4. Sr. WKT on the number line 3 is to right of -4. So 3 > -4. 3 is larger.
Answer: On the number line, 3 is to the right of -4, so 3 > -4. Therefore, 3 is the larger value.

Exam Tip: Any positive integer is always larger than any negative integer — use this rule as a quick check.

Question 5. (ii) -12, -8. WKT on the number line -12 is to left of -8 so -12 < -8 -8 is larger
Answer: On the number line, -12 is to the left of -8, so -12 < -8. This means -8 is the larger value.

Exam Tip: For two negative numbers, the one closer to zero is larger — remember, -1 is greater than -100.

Question 5. (iii) 0,7. Since '0' is less than all positive integers. Therefore 7 > 0 7 is Larger
Answer: Zero is less than any positive integer, so 7 > 0. Therefore, 7 is the larger value.

Exam Tip: Zero is smaller than all positive integers but larger than all negative integers — it is the boundary.

Question 5. (iv) 12, -18. WKT on the number line -18 is to left of 12. So 12 > -18 12 is Larger.
Answer: On the number line, -18 is to the left of 12, so 12 > -18. Therefore, 12 is the larger value.

Exam Tip: Any positive integer is always greater than any negative integer — this is a fundamental rule in integer ordering.

Question 6. (i) Integers between -7 and 3 are -6, -5, -4, -3, -2, -1, 0, 1, 2.
Answer: The integers that lie between -7 and 3 are: -6, -5, -4, -3, -2, -1, 0, 1, 2. These are all the whole numbers starting from one more than -7 and ending at one less than 3.

Exam Tip: When listing integers between two numbers, exclude the endpoints themselves — start at one step in from each boundary.

Question 6. (ii) Integers between -2 and 2 are. -1, 0, 1
Answer: The integers that lie between -2 and 2 are: -1, 0, 1. These are all the whole numbers strictly between the two endpoints.

Exam Tip: A small range produces fewer integers — always count carefully and avoid including the boundary values.

Question 6. (iii) Integers between -4 and 0 are. -3, -2, -1.
Answer: The integers that lie between -4 and 0 are: -3, -2, -1. These are the whole numbers greater than -4 and less than 0.

Exam Tip: When one boundary is zero, count backward from -1 to find all integers in the range.

Question 6. (iv) Integers between 0 and 3 are 1, 2.
Answer: The integers that lie between 0 and 3 are: 1, 2. These are the positive whole numbers greater than 0 and less than 3.

Exam Tip: Between 0 and any positive integer n, there are exactly n-1 integers — this is a quick way to check your count.

Question 7. (i) Integers between -4 and 3 are -3, -2, -1, 0, 1, 2. Therefore, no of integers between -4 and 3 are 6.
Answer: The integers that lie between -4 and 3 are -3, -2, -1, 0, 1, 2, giving a total of 6 integers.

Exam Tip: To find the count, list all integers and then count them — this method prevents errors from miscalculation.

Question 7. (ii) Integers between 5 and 12 are 6, 7, 8, 9, 10, 11. Therefore, no of integers between 5 and 12 are 6.
Answer: The integers that lie between 5 and 12 are 6, 7, 8, 9, 10, 11, for a total of 6 integers.

Exam Tip: The number of integers between a and b equals b - a - 1 (excluding the endpoints) — use this formula to verify.

Question 7. (iii) Integers between -9 and -2 are -8, -7, -6, -5, -4, -3. Therefore, no of integers between -9 and -2 are 6.
Answer: The integers that lie between -9 and -2 are -8, -7, -6, -5, -4, -3, totaling 6 integers.

Exam Tip: The formula works for negative integers too — count from -8 up to -3 without including the boundaries themselves.

Question 7. (iv) Integers between 0 and 5 are 1, 2, 3, 4. Therefore, no of integers between 0 and 5.
Answer: The integers that lie between 0 and 5 are 1, 2, 3, 4, for a total of 4 integers.

Exam Tip: Between 0 and n, there are always n - 1 integers — this is a quick way to check without listing.

Question 8. (i) 2 < 5
Answer: This is a valid comparison because 2 is smaller than 5 on the number line.

Exam Tip: Always ensure the inequality symbol points toward the smaller number — it is like a mouth eating the bigger value.

Question 8. (ii) 0 < 3
Answer: This is correct because zero is less than the positive integer 3.

Exam Tip: Zero is smaller than all positive integers — always remember this boundary rule.

Question 8. (iii) 0 > -7
Answer: This is valid because zero is greater than the negative integer -7.

Exam Tip: Zero is always larger than all negative integers — use this to quickly order mixed-sign numbers.

Question 8. (iv) -18 < 15
Answer: This is valid because any negative integer is smaller than any positive integer.

Exam Tip: Always compare the signs first — any negative is less than any positive, regardless of magnitude.

Question 8. (v) -235 > -532
Answer: This is valid because -235 is closer to zero than -532, making it larger.

Exam Tip: For negative numbers, the one closer to zero is always bigger — compare their distances from zero, not just the digits.

Question 8. (vi) -20 < 20
Answer: This is valid because -20 is negative and 20 is positive, making -20 the smaller value.

Exam Tip: Opposite numbers always have opposite relationships to zero — -a is always less than +a.

Question 9. (i) -12, -9, -8, 0, 1, 5, 15.
Answer: Arranging these integers in increasing order: -12, -9, -8, 0, 1, 5, 15. Negative integers come first (smallest to largest), then zero, then positive integers.

Exam Tip: Sort negatives first from most negative to least negative, then zero, then positives from smallest to largest — this is the natural order.

Question 9. (ii) -320, -106, -7, 107, 186.
Answer: Arranging these integers in increasing order: -320, -106, -7, 107, 186. For negatives, the one with the smallest value (most negative) comes first; positive integers follow in increasing order.

Exam Tip: Negative numbers in order go from smallest (most negative) to largest (closest to zero) — do not mix up the digit size with the integer size.

Question 10. (i) 8, 7, 6, 0, 2, -5, -9, -15.
Answer: Arranging these integers in decreasing order: 8, 7, 6, 0, 2, -5, -9, -15. Start with the largest positive integers, then zero, then negative integers from least negative to most negative.

Exam Tip: Decreasing order is the reverse of increasing — start with the largest and work toward the smallest, treating negatives carefully.

Question 10. (ii) 124, -74, -89, -154, -205.
Answer: Arranging these integers in decreasing order: 124, -74, -89, -154, -205. The positive integer is largest, followed by negative integers arranged from least negative to most negative.

Exam Tip: Place all positive integers first, then arrange negatives from those closest to zero to those furthest from zero.

Exercise 5.2

Question 1. (i) 5 + (-2)
Answer: To find 5 + (-2), start at 0 on the number line and move 5 units right to reach +5. Since the second number is -2 (negative), move 2 units left from +5 to arrive at 3. Therefore, 5 + (-2) = 3.

Exam Tip: When adding a negative number, move left on the number line — think of it as subtracting the absolute value.

Question 1. (ii) (-9) + 4.
Answer: To find (-9) + 4, begin at 0 and move 9 units left to reach -9. The second number is +4 (positive), so move 4 units right from -9 to land at -5. Therefore, (-9) + 4 = -5.

Exam Tip: When adding a positive number to a negative one, move right on the number line — the result depends on which absolute value is larger.

Question 1. (iii) (-3) + (-5).
Answer: To find (-3) + (-5), begin at 0 and move 3 units left to reach -3. The second number is -5 (negative), so move 5 more units left from -3 to arrive at -8. Therefore, (-3) + (-5) = -8.

Exam Tip: When adding two negative numbers, keep moving left — the result is always negative with a magnitude equal to the sum of both absolute values.

Question 1. (iv) (-1) + (-2) + 2.
Answer: To find (-1) + (-2) + 2, start at 0 and move 1 unit left to reach -1. Then move 2 more units left from -1 to arrive at -3. Finally, move 2 units right from -3 (because the third number is +2) to land at -1. Therefore, (-1) + (-2) + 2 = -1.

Exam Tip: When combining multiple steps, trace each move on the number line carefully — this prevents sign errors.

Question 1. (v) 6 + (-6)
Answer: To find 6 + (-6), start at 0 and move 6 units right to reach +6. Since the second number is -6 (negative), move 6 units left from +6 to return to 0. Therefore, 6 + (-6) = 0.

Exam Tip: Adding a number to its opposite always gives zero — they cancel each other out perfectly.

Question 1. (vi) (-2) + 5 + (-a).
Answer: To solve (-2) + 5 + (-a), start at 0 and move 2 units left to reach -2. Then move 5 units right to get to +3. Next, move a units left to reach (3 - a). Simplifying the algebraic steps: -2 + 5 + (-a) = 5 - 2 + (-a) = 3 - a. If a = 9, the final result is -6.

Exam Tip: When variables are present, rearrange using the commutative law of addition — combine like terms before applying the final steps.

Question 2. (i) -557 and 488
Answer: The integers to be added have opposite signs. To add them, we find the difference of their absolute values and assign the sign of the number with the greater absolute value. Since |-557| = 557 and |488| = 488, we have: (-557) + 488 = -(557 - 488) = -69.

Exam Tip: For opposite-sign addition, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.

Question 2. (ii) -522 + (-160) = -522 - 160
Answer: Adding two negative integers: (-522) + (-160) means combining them as -522 - 160 = -682. Both negative, so the result is negative with magnitude equal to the sum of both magnitudes.

Exam Tip: Two negatives always produce a negative result — just add the absolute values and put a minus sign in front.

Question 2. (iii) 2567 and -325
Answer: These integers have opposite signs. To add them: 2567 + (-325) = (2567) - (325) = 2567 - 325 = 2242. Since the positive number has the larger absolute value, the result is positive.

Exam Tip: When adding a negative to a positive, subtract the smaller absolute value from the larger and keep the sign of the larger.

Question 2. (iv) -10025 and 139
Answer: These have opposite signs. Adding: [-10025] + [139] = -10025 + 139 = -9886. The negative number has a much larger absolute value, so the result stays negative.

Exam Tip: Always compare absolute values first to determine the sign of the result — the bigger absolute value wins.

Question 2. (v) 2567 + (-2578) = 2547 - 2548
Answer: To add these: 2567 + (-2578) = 2567 - 2578 = -1. Since the negative number has a slightly larger absolute value, the result is negative.

Exam Tip: Even when absolute values are close, subtract carefully — a small difference in absolute values gives a result with minimal magnitude.

Question 2. (vi) 2884 + (-2884) = 2884 - 2884 = 0.
Answer: Adding a number and its opposite: 2884 + (-2884) = 0. Any integer plus its additive inverse equals zero.

Exam Tip: Additive inverses cancel perfectly — this is a shortcut in many computation problems.

Exercise 5.3

Question 1. (i) Additive inverse of 52 is -52.
Answer: The additive inverse of 52 is -52, because 52 + (-52) = 0. The additive inverse is the opposite-signed integer that sums to zero.

Exam Tip: To find an additive inverse, flip the sign — positive becomes negative and vice versa.

Question 1. (ii) 176
Answer: The additive inverse of 176 is -176, since 176 + (-176) = 0.

Exam Tip: The additive inverse of any positive integer a is -a — a simple sign change.

Question 1. (iii) 0
Answer: The additive inverse of 0 is 0, because 0 + 0 = 0. Zero is its own additive inverse.

Exam Tip: Zero is unique — it is the only integer that is its own additive inverse.

Question 1. (iv) -1
Answer: The additive inverse of -1 is 1, because (-1) + 1 = 0.

Exam Tip: The additive inverse of any negative integer b is -b (which is positive) — always flip the sign.

Question 2. (i) Success - or -42 is = -42 + (-1)
Answer: Finding the successor of -42: the successor is the next integer going forward, which is -42 + 1 = -41.

Exam Tip: The successor of any integer n is n + 1 — always add 1 to find the next integer.

Question 2. (ii) -1 + 1 = 0
Answer: The successor of -1 is 0, found by adding 1: (-1) + 1 = 0.

Exam Tip: Moving from a negative integer to zero is often the midpoint in successor problems — verify by adding 1.

Question 2. (iii) 0 + 1 = 1
Answer: The successor of 0 is 1, calculated as 0 + 1 = 1.

Exam Tip: The successor of zero moves into positive territory — always the next whole number.

Question 2. (iv) -200 + 1 = -199
Answer: The successor of -200 is -199, found by adding 1: (-200) + 1 = -199.

Exam Tip: For any integer, especially negatives, the successor is simply the original plus 1.

Question 2. (v) -99 + 1 = -98.
Answer: The successor of -99 is -98, found by adding 1: (-99) + 1 = -98.

Exam Tip: Successor problems are straightforward — add 1 every time to get the immediate next integer.

Question 3. (i) Predecessor of 0 is \( \Rightarrow \) 0 -1 = -1
Answer: The predecessor of 0 is -1. The predecessor is the integer immediately before a given number, found by subtracting 1: 0 - 1 = -1.

Exam Tip: Predecessor means "the one before" — always subtract 1 from the given integer.

Question 3. (ii) 1 - 1 = 0
Answer: The predecessor of 1 is 0, since 1 - 1 = 0.

Exam Tip: The predecessor of any positive integer moves one step backward on the number line.

Question 3. (iii) -1 - 1 = -2
Answer: The predecessor of -1 is -2, found as (-1) - 1 = -2.

Exam Tip: For negative integers, subtracting 1 makes the number more negative — you move further left on the number line.

Question 3. (iv) -125 - 1 = -126
Answer: The predecessor of -125 is -126, since (-125) - 1 = -126.

Exam Tip: Predecessor always means subtract 1, whether the number is positive or negative.

Question 3. (v) 1000 - 1 = 999
Answer: The predecessor of 1000 is 999, since 1000 - 1 = 999.

Exam Tip: For large positive integers, the predecessor is simply one less — straightforward subtraction.

Question 4. (i) True
Answer: This statement is true.

Exam Tip: Always justify your true/false answer with a reason or example in exams.

Question 4. (ii) False
Answer: This statement is false.

Exam Tip: For false statements, be ready to provide a counterexample that shows why the claim does not hold.

Question 4. (iii) False
Answer: This statement is false.

Exam Tip: False statements require justification — prepare a clear explanation or example for each one.

Question 4. (iv) False
Answer: This statement is false.

Exam Tip: When marking false, always identify what the correct statement should be instead.

Question 4. (v) False
Answer: This statement is false.

Exam Tip: Collect all false statements together and explain the concept being violated in each one.

Question 5. Integers whose absolute values less than 5 are
Answer: The integers whose absolute values are less than 5 are: -4, -3, -2, -1, 0, 1, 2, 3, 4. These are all integers n where |n| < 5, meaning they range from -4 to +4.

Exam Tip: Absolute value represents distance from zero — find all integers within distance 4 from zero (not including 5).

Question 6. (i) True
Answer: This statement is true.

Exam Tip: When a statement is true, you may be asked to provide the underlying principle or proof.

Question 6. (ii) False
Answer: This statement is false.

Exam Tip: False statements often contain a commonly made mistake — identify the misconception to strengthen your understanding.

Question 6. (iii) True
Answer: This statement is true.

Exam Tip: True statements about integer properties are often grounded in basic definitions — trace back to the fundamental rule.

Question 6. (iv) True
Answer: This statement is true.

Exam Tip: Multiple true statements in a row signal that you may need to identify a pattern or common principle linking them.

Question 7. Addition Table
Answer: The table below shows the sum of each pair of integers by adding the row value to the column value:

Question 7. (i) Pairs of integers that sum to zero are: (+6, -6), (4, -4), (3, -3), (2, -2), (1, -1), (0, 0)
Answer: Looking at the addition table, the pairs that yield a sum of 0 are: (6, -6), (4, -4), (3, -3), (2, -2), (1, -1), and (0, 0). Each pair consists of a number and its additive inverse (except zero, which is its own additive inverse).

Exam Tip: Additive inverses always sum to zero — this is their defining property, visible as zeros along the main diagonal in the addition table.

Question 7. (ii) Yes by commutativity of Addition (-4) + (-2) = (-2) + (-4)
Answer: The addition operation is commutative for integers, meaning the order does not matter: (-4) + (-2) = (-2) + (-4). Both equal -6, confirming that changing the order of the addends does not change the sum.

Exam Tip: Commutativity is a key property of integer addition — always use it when simplifying or verifying addition expressions.

Question 7. (iii) By existence of additive identity 0 + (-6) = -6 [∵ 0 + a = a]
Answer: Zero is the additive identity because adding it to any integer leaves that integer unchanged. Here, 0 + (-6) = -6 demonstrates this property, since adding zero does not alter the value.

Exam Tip: The additive identity (zero) is unique — it is the only number where a + 0 = a for all integers a.

Question 8. (i) x + 1 = 0 ⇒ x + 1 - 1 = 0 - 1 [Subtract ÷ on both sides] ⇒ x = -1
Answer: To solve x + 1 = 0, subtract 1 from both sides: x + 1 - 1 = 0 - 1, which simplifies to x = -1.

Exam Tip: When solving equations, perform the same operation on both sides to maintain balance — this method works for all linear equations.

Question 8. (ii) x + 5 = 0 ⇒ x + 5 - 5 = 0 - 5 ⇒ x = -5
Answer: To solve x + 5 = 0, subtract 5 from both sides: x + 5 - 5 = 0 - 5, which gives x = -5.

Exam Tip: Solving x + a = 0 always yields x = -a — the additive inverse of a.

Question 8. (iii) -3 + x = 0 ⇒ -3 + x + 3 = 0 + 3 ⇒ x = 3
Answer: To solve -3 + x = 0, add 3 to both sides: -3 + x + 3 = 0 + 3, which simplifies to x = 3.

Exam Tip: For equations of the form a + x = 0, the solution is x = -a — find the additive inverse of the constant term.

Question 8. (iv) x + (-8) = 0 ⇒ x - 8 = 0 ⇒ x - 8 + 8 = 0 + 8 ⇒ x = 8
Answer: To solve x + (-8) = 0, rewrite as x - 8 = 0, then add 8 to both sides: x - 8 + 8 = 0 + 8, yielding x = 8.

Exam Tip: Adding a negative is the same as subtracting — convert between forms to simplify your work.

Question 8. (v) 7 + x = 0 ⇒ 7 + x - 7 = 0 - 7 ⇒ x = -7
Answer: To solve 7 + x = 0, subtract 7 from both sides: 7 + x - 7 = 0 - 7, which simplifies to x = -7.

Exam Tip: Always isolate the variable by undoing the operation — here, subtracting 7 undoes the addition of 7.

Question 8. (vi) x + 0 = 0 ⇒ x = 0.
Answer: To solve x + 0 = 0, recognize that adding zero leaves the value unchanged, so x = 0.

Exam Tip: Zero is special — it is the only number that equals its own additive inverse, so x + 0 = 0 only when x = 0.

Exercise 5.4

Question 1. Negative Numbers and Integers – Exercise – 5.4 – Q.1
Answer: Using the subtraction rule, we get -5 - 12 = -17.

(ii) To subtract -12 from 8, we calculate 8 - (-12) = 8 + 12 = 20.

(iii) -135 - (-225) = 225 - 135 = 90

(iv) 101 - 1001 = -900

(v) 3126 - (-812)6 = 3126 + 812 = 3938.

(vi) -8 - 7560 = -7568

(vii) -4109 - (-3978) = -4109 + 3978 = -131

(viii) -1005 - 0 = -1005

Exam Tip: Always remember to convert subtraction of a negative number to addition of its positive counterpart — this is key to avoiding mistakes with negative integers.

Question 2. Negative Numbers and Integers – Exercise – 5.4 – Q.2
Answer:
(i) -27 - (-23) = -27 + 12 = 23 - 27 = -4

(ii) -17 - 18 - (-35) = -35 + 35 = 0

(iii) -12 - (-5) - (-125) + 270 = -12 + 5 + 125 + 270 = 400 - 12 = 388.

(iv) 373 + (-245) + (-373) + 145 + 3000 = 373 - 245 - 373 + 3145 = 3145 + 373 - 373 - 245 = 3145 - 245 = 2900.

(v) 1 - 475 - 475 - 475 + 1900 = 1 - 950 - 950 + 1900 = 1900 + 1 - 1900 = 1.

(vi) (-1) + (-304) + 304 + 304 + (-304) + 1 = -1 + 1 - 304 + 304 - 304 + 304 = 0

Exam Tip: Group positive and negative terms separately, then combine like terms to simplify calculations and reduce computational errors.

Question 3. Negative Numbers and Integers – Exercise – 5.4 – Q.3
Answer: The total of 5020 and 2320 equals -5020 + 2320 = 2320 - 5020 = -2700.

Therefore, -(-2700) + (-709) = -709 - (-2700) = -709 + 2700 = 1991

Exam Tip: When subtracting a negative number, convert it to addition and carefully track the sign change to avoid errors.

Question 4. Negative Numbers and Integers – Exercise – 5.4 – Q.4
Answer: The total of -1250 and 1138 is -1250 + 1138 = 1138 - 1250 = -112

The total of 1136 and -1272 is 1136 - 1272 = -136

Therefore, -136 - (-112) = -136 + 112 = -24

Exam Tip: Always rewrite subtraction of negative numbers as addition of positive values — this visual transformation helps prevent sign mistakes.

Question 5. Negative Numbers and Integers – Exercise – 5.4 – Q.5
Answer: The total of 233 and -147 is 233 - 147 = 86.

So 86 - (-284) = 86 + 284 = 370.

Exam Tip: Break multi-step problems into smaller calculations and verify each step before moving forward.

Question 6. Negative Numbers and Integers – Exercise – 5.4 – Q.6
Answer: We are given that the sum of two integers equals 238, and one of the integers is -122. The other integer is calculated as -(-122) + 238 = 238 + 122 = 360.

Exam Tip: To find the missing number in a sum, subtract the known integer from the total — rearrange the equation logically.

Question 7. Negative Numbers and Integers – Exercise – 5.4 – Q.7
Answer: The needed integer is -223 - 172 = -395.

Exam Tip: When subtracting two negative numbers or adding negatives, combine their absolute values and apply the negative sign.

Question 8. Negative Numbers and Integers – Exercise – 5.4 – Q.8
Answer:
(i) -8 - 24 + 31 - 26 - 28 + 7 + 19 - 18 - 8 + 33

Rearranging to group negative and positive numbers: -8 - 24 - 26 - 28 - 18 - 8 + 31 + 7 + 19 + 33

= -32 - 26 - 28 - 26 + 38 + 19 + 33

= 38 - 32 - 26 - 28 + 33 - 26 + 19.

= 6 - 26 - 28 + 7 + 19

= 6 - 28 - 26 + 26

= 6 - 28

= -22.

(ii) -26 - 20 + 33 - (-33) + 21 + 24 - (-25) - 26 - 14 - 34

= -46 + 33 + 33 + 21 + 24 + 25 - 26 - 14 - 34

= -46 + 66 + 21 + 24 + 25 - 74

= -46 + 66 + 70 - 74

= -46 - 4 + 66

= -50 + 66

= 66 - 50

= 16.

Exam Tip: Separate positive and negative terms systematically, combine them separately, then find the final difference — this method reduces careless errors.

Question 9. Negative Numbers and Integers – Exercise – 5.4 – Q.9
Answer: 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16 = -1 - 1 - 1 - 1 - 1 - 1 - 1 - 1 = -8

Exam Tip: Notice the pattern of consecutive pairs (1-2, 3-4, etc.) — each pair yields -1, so count the pairs to find the answer quickly.

Question 10. Negative Numbers and Integers – Exercise – 5.4 – Q.10
Answer:
(i) If the number of terms is 10:

5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5)

= 5 - 5 + 5 - 5 + 5 - 5 + 5 - 5

= 0

(ii) If the number of terms is 11:

5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5

= 5 - 5 + 5 - 5 + 5 - 5 + 5 - 5 + 5 - 5 + 5

= 5.

Exam Tip: When dealing with alternating series, observe whether the total number of terms is even (result = 0) or odd (result = the first/last term value) — this pattern shortcut saves time.