CBSE Class 6 Mathematics Integers Worksheet Set 05

1. Using number line find the following :

Question 1(i). -3 + 5
Answer: Start at 0, move 3 units to the left to reach -3, then move 5 units to the right to reach 2.
\(-3 + 5 = 2\)
In simple words: Moving right on the number line increases the value.

Exam Tip: Always start from 0 for the first number, then move right for positive numbers and left for negative numbers.

Question 1(ii). -4 + (-3)
Answer: Start at 0, move 4 units to the left to reach -4, then move another 3 units to the left to reach -7.
\(-4 + (-3) = -7\)
In simple words: Adding a negative number means moving further left.

Exam Tip: Two negative steps in the same direction add up to a larger negative number.

Question 1(iii). 5 + (-2)
Answer: Start at 0, move 5 units to the right to reach 5, then move 2 units to the left to reach 3.
\(5 + (-2) = 3\)
In simple words: Adding a negative number is the same as subtracting.

Exam Tip: A positive and a negative movement partially cancel each other out.

Question 1(iv). -5 + 3
Answer: Start at 0, move 5 units to the left to reach -5, then move 3 units to the right to reach -2.
\(-5 + 3 = -2\)
In simple words: Start at -5 and take 3 steps back toward zero.

Exam Tip: The result takes the sign of the number with the larger absolute value.

Question 1(v). -3 - (-2)
Answer: Subtracting a negative integer is the same as adding its positive counterpart: \(-3 + 2 = -1\). On a number line, start at -3 and move 2 units to the right to reach -1.
\(-3 - (-2) = -1\)
In simple words: Negative of a negative becomes positive.

Question 1(vi). 5 - (-2)
Answer: \(5 - (-2) = 5 + 2 = 7\). On a number line, start at 5 and move 2 units to the right to reach 7.
In simple words: Subtracting negative 2 is like adding 2.

Exam Tip: Change consecutive minus signs to a plus sign before solving.

Question 1(vii). -4 - (+1)
Answer: \(-4 - 1 = -5\). On a number line, start at -4 and move 1 unit to the left to reach -5.
In simple words: Take 1 away from -4 to get -5.

Exam Tip: Subtracting a positive integer moves you to the left.

Question 1(viii). -7 + 4
Answer: Start at -7, move 4 units to the right to reach -3.
\(-7 + 4 = -3\)
In simple words: Combine -7 and 4 to get -3.

Exam Tip: Find the difference between 7 and 4, which is 3, and keep the sign of 7.

Question 1(ix). 3 more than -5
Answer: \(-5 + 3 = -2\). Start at -5 and move 3 units to the right.
In simple words: "More than" means add.

Exam Tip: "More than" translates to a positive addition.

Question 1(x). -2 more than -3
Answer: \(-3 + (-2) = -5\). Start at -3 and move 2 units to the left.
In simple words: Add -2 to -3.

Exam Tip: Adding a negative amount decreases the total value.

Question 1(xi). -2 less than -4
Answer: \(-4 - (-2) = -4 + 2 = -2\). Start at -4 and move 2 units to the right.
In simple words: "Less than" means subtract.

Exam Tip: Be careful with signs: subtracting a negative becomes addition.

Question 1(xii). 3 less than -2
Answer: \(-2 - 3 = -5\). Start at -2 and move 3 units to the left.
In simple words: Subtract 3 from -2.

Exam Tip: "Less than" means you move left on the number line.

Question 1(xiii). -4 less than -1
Answer: \(-1 - (-4) = -1 + 4 = 3\). Start at -1 and move 4 units to the right.
In simple words: Subtracting negative 4 from -1 gives 3.

Exam Tip: Watch out for double negatives when dealing with "less than".

2. Evaluate the following :

Question 2(1). -25 + 72
Answer: \(72 - 25 = 47\)
In simple words: Subtract 25 from 72.

Exam Tip: The sign of the larger number wins.

Question 2(2). -75 + 32
Answer: \(-(75 - 32) = -43\)
In simple words: Find the difference and keep the negative sign.

Question 2(3). 25 - 79
Answer: \(-(79 - 25) = -54\)
In simple words: Subtracting a larger number from a smaller one yields a negative result.

Exam Tip: Flip the subtraction and make the result negative.

Question 2(4). -32 - (-58)
Answer:
\(= -32 + 58\)
\(= 58 - 32 = 26\)
In simple words: Convert the double negative into addition.

Exam Tip: Always clear parentheses by multiplying adjacent signs first.

Question 2(5). 48 - (-92)
Answer:
\(= 48 + 92 = 140\)
In simple words: Add 48 and 92.

Exam Tip: Subtracting a negative is the same as adding a positive.

Question 2(6). -85 + 78
Answer:
\(= -(85 - 78) = -7\)
In simple words: Subtract 78 from 85 and make it negative.

Exam Tip: Check which absolute value is greater.

Question 2(7). -95 - 99
Answer:
\(= -(95 + 99) = -194\)
In simple words: Combine two negative debts.

Exam Tip: Same signs mean add the numbers and keep the common sign.

Question 2(8). -105 + 105
Answer:
\(= 0\)
In simple words: A number plus its opposite equals zero.

Exam Tip: These are additive inverses.

Question 2(9). -28 - 108
Answer:
\(= -(28 + 108) = -136\)
In simple words: Add both numbers and attach a negative sign.

Question 2(10). -203 + 702
Answer:
\(= 702 - 203 = 499\)
In simple words: Subtract 203 from 702.

Exam Tip: Positive number is larger, so the result is positive.

Question 2(11). -405 + (-208)
Answer:
\(= -(405 + 208) = -613\)
In simple words: Add 405 and 208, then make the result negative.

Exam Tip: Sum of two negative integers is always negative.

Question 2(12). -300 - (-215)
Answer:
\(= -300 + 215\)
\(= -(300 - 215) = -85\)
In simple words: Change to -300 + 215 and find the difference.

Question 2(13). 500 - 700
Answer:
\(= -(700 - 500) = -200\)
In simple words: Subtract 700 from 500.

Exam Tip: Smaller minus larger gives a negative result.

Question 2(14). -200 + 150
Answer:
\(= -(200 - 150) = -50\)
In simple words: Find the difference between 200 and 150.

Exam Tip: Keep the sign of the number with the greater absolute value.

Question 2(15). -173 + -293
Answer:
\(= -(173 + 293) = -466\)
In simple words: Add both negative numbers together.

Exam Tip: "-173 + -293" is the same as "-173 - 293".

Question 2(16). -28 + 75 + -56 + -28
Answer:
\(= (-28 - 56 - 28) + 75\)
\(= -112 + 75 = -37\)
In simple words: Group all negatives together, sum them up, then add the positive number.

Exam Tip: Grouping like signs makes addition much easier.

Question 2(17). -108 - (-210) - 408 + 709
Answer:
\(= -108 + 210 - 408 + 709\)
\(= (-108 - 408) + (210 + 709)\)
\(= -516 + 919 = 403\)
In simple words: First remove parentheses, then group positives and negatives separately.

Exam Tip: Handle signs carefully before grouping.

Question 2(18). +739 - 710 - (-210) + (-80)
Answer:
\(= 739 - 710 + 210 - 80\)
\(= (739 + 210) - (710 + 80)\)
\(= 949 - 790 = 159\)
In simple words: Simplify signs and combine terms.

Exam Tip: Convert all double signs first.

Question 2(19). 709 + 483 - 1009 + (-403)
Answer:
\(= 709 + 483 - 1009 - 403\)
\(= (709 + 483) - (1009 + 403)\)
\(= 1192 - 1412 = -220\)
In simple words: Sum positives, sum negatives, then find the difference.

Exam Tip: Double check your addition and subtraction steps.

Question 2(20). 208 - [-73 - (43 - 78)]
Answer:
\(= 208 - [-73 - (-35)]\)
\(= 208 - [-73 + 35]\)
\(= 208 - [-38]\)
\(= 208 + 38 = 246\)
In simple words: Solve inside the innermost parentheses first, then brackets.

Exam Tip: Follow BODMAS order of operations.

Question 2(21). 513 - {-89 - [58 - (7 - 8 - 10)]}
Answer:
\(= 513 - {-89 - [58 - (-11)]}\)
\(= 513 - {-89 - [58 + 11]}\)
\(= 513 - {-89 - 69}\)
\(= 513 - {-158}\)
\(= 513 + 158 = 671\)
In simple words: Work from the innermost brackets outwards.

Exam Tip: Clear parentheses one level at a time.

Question 2(22). -403 + [703 - (-48) + (-1085)]
Answer:
\(= -403 + [703 + 48 - 1085]\)
\(= -403 + [751 - 1085]\)
\(= -403 + [-334]\)
\(= -403 - 334 = -737\)
In simple words: Simplify inside the square bracket first.

Question 2(23). -4532 + -7351 + 1532
Answer:
\(= (-4532 + 1532) - 7351\)
\(= -3000 - 7351 = -10351\)
In simple words: Combine -4532 and 1532 first to get -3000, then subtract 7351.

Exam Tip: Look for numbers that make clean round values when combined.

Question 2(24). 728 - (-425) - 9285
Answer:
\(= 728 + 425 - 9285\)
\(= 1153 - 9285 = -8132\)
In simple words: Add 728 and 425, then subtract 9285.

Exam Tip: Convert subtraction of a negative into addition first.

Question 2(25). -58 + 98 - 40
Answer:
\(= (-58 - 40) + 98\)
\(= -98 + 98 = 0\)
In simple words: Combine negative terms to get -98, which cancels with 98.

Exam Tip: Grouping numbers that sum to zero saves time.

Question 2(26). -403 - (-375) + 102
Answer:
\(= -403 + 375 + 102\)
\(= -403 + 477 = 74\)
In simple words: Change -(-375) to +375, add positives, then combine.

Exam Tip: Add all positive terms together before subtracting.

Question 2(27). -459 - 729 - (-358) + -2085
Answer:
\(= -459 - 729 + 358 - 2085\)
\(= (-459 - 729 - 2085) + 358\)
\(= -3273 + 358 = -2915\)
In simple words: Sum all negative numbers, then add the positive number.

Exam Tip: Double check addition of multiple large negative numbers.

Question 2(28). -78 - (-532)
Answer:
\(= -78 + 532\)
\(= 532 - 78 = 454\)
In simple words: Change double negative to positive and subtract.

Exam Tip: Subtraction of negative becomes addition.

2. Use '<' or '>' or '=' to fill the box to get the correct statement :

Question 2(1). -138 [ ] -(-138)
Answer: (<) -138 < 138
Left side is -138, right side is \(-(-138) = 138\). A negative number is always less than a positive number.
In simple words: -138 is less than +138.

Exam Tip: Simplify both sides completely before comparing.

Question 2(2). -728 [ ] 0
Answer: (<) -728 < 0
Any negative integer is always less than zero.
In simple words: Negative numbers are smaller than zero.

Exam Tip: Zero is greater than all negative numbers.

Question 2(3). -238 [ ] -347
Answer: (>) -238 > -347
For negative numbers, the one with the smaller absolute value is greater.
In simple words: -238 is closer to zero than -347, so it is larger.

Question 2(4). -41 [ ] -8
Answer: (<) -41 < -8
-41 is further to the left on the number line than -8.
In simple words: -8 is greater than -41.

Exam Tip: Larger negative digits represent smaller values.

Question 2(5). 32 [ ] -78
Answer: (>) 32 > -78
Any positive number is always greater than any negative number.
In simple words: Positive is always greater than negative.

Exam Tip: You don't need to calculate magnitudes when comparing positive and negative numbers.

Question 2(6). -97 [ ] -79
Answer: (<) -97 < -79
-97 is smaller than -79 because it is further left on the number line.
In simple words: -79 is closer to zero, so it is greater.

Exam Tip: Compare the positive versions and reverse the inequality sign for negatives.

Question 2(7). 0 [ ] -79
Answer: (>) 0 > -79
Zero is greater than any negative number.
In simple words: Zero is higher than -79.

Exam Tip: 0 is always greater than negative integers.

Question 2(8). -438 [ ] -458
Answer: (>) -438 > -458
-438 is closer to zero than -458.
In simple words: -438 is greater than -458.

Exam Tip: Smaller absolute value wins in negative comparisons.

Question 2(9). 48 [ ] 408
Answer: (<) 48 < 408
48 is less than 408.
In simple words: 408 is much larger than 48.

Exam Tip: Standard positive number comparison rule applies.

3. Complete the blanks :

Question 3(1). -28, -38, -48, ______, ______, ______, ______
-287, -277, -267, ______, ______, ______, ______
Answer:
First sequence: -58, -68, -78, -88 (decreasing by 10)
Second sequence: -257, -247, -237, -227 (increasing by 10)
In simple words: Identify the pattern and continue it.

Exam Tip: Check whether numbers are increasing or decreasing in magnitude.

Question 3(2). -589, -586, -583, ______, ______, ______, ______
-13, -8, -3, ______, ______, ______, ______, ______, ______
Answer:
First sequence: -580, -577, -574, -571 (increasing by 3)
Second sequence: 2, 7, 12, 17, 22, 27 (increasing by 5)
In simple words: Find the common difference between consecutive terms.

Exam Tip: Subtract the first term from the second term to find the step size.

Write the opposite of the following :

Question 4(1). 739 above sea level.
Answer: 739 below sea level
In simple words: Opposite of above is below.

Exam Tip: Reverse the directional word while keeping the number same.

Question 4(2). Going 730m towards north
Answer: Going 730m towards south
In simple words: Opposite of north is south.

Exam Tip: North and south are opposite directions.

Question 4(3). -413
Answer: +413 (or 413)
In simple words: Change the negative sign to positive.

Exam Tip: Opposite of a negative number is its positive counterpart.

Question 4(4). +705
Answer: -705
In simple words: Change the positive sign to negative.

Exam Tip: Opposite of a positive number is its negative counterpart.

Question 4(5). Depositing Rs 750.
Answer: Withdrawing Rs 750
In simple words: Opposite of depositing money is withdrawing money.

Exam Tip: Deposit and withdrawal are financial opposites.

5. Fill up the blanks :

Question 5(1). ___________________ is neither positive nor negative.
Answer: Zero (0)
In simple words: Zero has no sign.

Exam Tip: 0 is neutral in the integer system.

Question 5(2). _____________________ is the smallest positive integer.
Answer: 1
In simple words: Counting starts at 1 for positives.

Question 5(3). _______________________ is the greatest negative integer.
Answer: -1
In simple words: -1 is closest to zero among all negatives.

Exam Tip: -1 is the largest negative number.

Question 5(4). All positive integers are ___________________ than zero and negative integers.
Answer: greater
In simple words: Positive numbers are always bigger than zero and negatives.

Exam Tip: Positives lie to the right of zero on the number line.

Question 5(5). All negative integers are __________________ than zero and positive integers.
Answer: smaller (or less)
In simple words: Negatives are always smaller than zero and positives.

Exam Tip: Negatives lie to the left of zero.

Question 5(6). -8 + _________ = 0
Answer: 8
\(-8 + 8 = 0\)
In simple words: Add the additive inverse.

Exam Tip: A number plus its opposite is zero.

Question 5(7). -78 + _________ = -68
Answer: 10
\(-68 - (-78) = -68 + 78 = 10\)
In simple words: Find what must be added to -78 to reach -68.

Exam Tip: Subtract the starting number from the target number.

Question 5(8). 48 + _________ = 0
Answer: -48
\(48 + (-48) = 0\)
In simple words: Add -48 to 48 to get zero.

Exam Tip: Additive inverse of 48 is -48.

Question 5(10). 69 + _________ = +56
Answer: -13
\(56 - 69 = -13\)
In simple words: Subtract 69 from 56.

Exam Tip: Target minus initial value gives the missing addend.

Question 5(11). -32 + _________ = -45
Answer: -13
\(-45 - (-32) = -45 + 32 = -13\)
In simple words: Add -13 to -32 to get -45.

Exam Tip: Target value minus given addend equals missing value.

Question 5(12). +100 + _________ = 80
Answer: -20
\(80 - 100 = -20\)
In simple words: Subtract 100 from 80.

Exam Tip: Decreasing from 100 to 80 requires adding -20.

Question 5(13). 43 + -35 = _________
Answer: 8
\(43 - 35 = 8\)
In simple words: Subtract 35 from 43.

Exam Tip: Adding a negative is subtraction.

Question 5(14). 43 - _________ = 52
Answer: -9
\(43 - 52 = -9\)
In simple words: 43 minus -9 equals 43 + 9 = 52.

Exam Tip: \(43 - x = 52 \implies x = 43 - 52 = -9\).

Question 5(15). _________ - (-9) = 61
Answer: 52
\(x + 9 = 61 \implies x = 61 - 9 = 52\)
In simple words: 52 minus negative 9 gives 61.

Exam Tip: Simplify to \(x + 9 = 61\) then solve.

Question 5(16). _________ + -8 = 52
Answer: 60
\(x - 8 = 52 \implies x = 52 + 8 = 60\)
In simple words: 60 plus -8 equals 52.

Exam Tip: Isolate the blank by adding 8 to both sides.

Question 5(17). -27 + _________ = -35
Answer: -8
\(-35 - (-27) = -35 + 27 = -8\)
In simple words: Add -8 to -27 to get -35.

Exam Tip: Subtract current value from target value.

Question 5(18). -48 - _________ = 0
Answer: -48
\(-48 - (-48) = -48 + 48 = 0\)
In simple words: Subtracting -48 from -48 gives zero.

Exam Tip: Any number minus itself equals zero.

1. Using the number line write the integer which is:

(a) 3 more than 5

(b) 5 more than –5

(c) 6 less than 2

(d) 3 less than –2

Solutions: (a)

Hence, 8

(b)

Hence, 0

(c)

Hence, -4

(d)

Hence,-5

2. Use number line and add the following integers: (a) 9 + (–6) (b) 5 + (–11)

(c) (–1) + (–7)

(d) (–5) + 10

(e) (–1) + (–2) + (–3) (f) (–2) + 8 + (–4)

Solutions:

(a)

Hence, 3

b)

Hence, -6

(c)

Hence, -8

(d)

Hence, 5

(e)

Hence, -6

(f)

Hence, 2

3. Add without using number line:

(a) 11 + (–7)

(b) (–13) + (+18)

(c) (–10) + (+19)

(d) (–250) + (+150)

(e) (–380) + (–270)

(f) (–217) + (–100)

Solutions:

(a) 11 + (-7) = 4

(b) (-13) + (+18) = 5

(c) (-10) + (+19) = 9

(d) (-250) + (+150) = -100

(e) (-380) + (-270) = -650

(f) (-217) + (-100) = -317

Please refer to attached file for Integers