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6th Grade Integers Worksheet
In 6th grade integers worksheet contains various types of questions on integers, absolute value of an integer, addition of integer, properties of integer, subtraction of integer, properties of subtraction of integers and word problems on integers.
Summary of Integers
✅ A collection (or set) of all whole numbers along with the negative numbers -1, -2, -3, -4, -5, ..., is called the set of integers.
✅ There is no largest and smallest integers.
✅ An integer occurring to the right on a number line is greater than that to the left, and, the integer to the left is smaller than that the right one.
✅ The absolute value of an integer is the numerical value of the integer regardless of its sign.
✅ Addition of Integers:
(i) If both the integers are of the same sign (either positive or negative), add their absolute values and assign the sign of addend to their sum.
(ii) If both integers are of opposite signs, find the difference of their absolute values and assign the sign of the addend having greater value.
✍️ Addition of Integers on a Number Line:
(i) When we add a positive integer, we move to the right on the number line.
(ii) When we add a negative integer, we move to the left on the number line.
✅ Subtraction of Integers:
When we subtract an integer from another integer, change the sign of integer which is to be subtracted and then add.
✍️ Subtraction of Integers on a Number Line:
(i) When we subtract a positive integer, we move to the left on the number line.
(ii) When we subtract a negative integer, we move to the right on the number line.
I. Multiple Choice Questions (MCQ) on Integers.
Tick (✔) the correct option.
1. The value of |-67| - |-28| is
(i) -29
(ii) 39
(iii) 56
(iv) -76
2. The predecessor of -209 is
(i) -109
(ii) 901
(iii) -210
(iv) -208
3. The additive inverse of -1 is
(i) -1
(ii) 0
(iii) -2
(iv) 1
4. The sum of two integers is -178. If one of them is 119, then the other one is
(i) -297
(ii) 178
(iii) -119
(iv) 290
5. On subtracting -24 from -12, we get
(i) -12
(ii) 36
(iii) -36
(iv) 12
6. The smallest positive integer is
(i) 0
(ii) 1
(iii) -1
(iv) None of these
7. The successor of greatest negative integer is
(i) 0
(ii) -1
(iii) -2
(iv) None of these
8. Which of the following is the smallest?
(i) 0
(ii) -1
(iii) -100
(iv) 1
9. A car is at -5 m, a bird is flying at 18 m, a helicopter is flying at 66 m and a balloon is at 9 m. Which is closer to the sea level?
(i) Car
(ii) Bird
(iii) Balloon
(iv) Helicopter
10. Which of the following is correct?
(i) 0 > - 3 > 5 > - 7 > 1
(ii) 5 > - 7 > - 3 > 0 > 1
(iii) - 7 > - 3 > 0 > 1 > 5
(iv) - 7 < - 3 < 0 < 1 < 5
11. Which of the following is correct?
(i) The smallest integer is 0.
(ii) A positive integer is less than its opposite.
(iii) A negative integer is more than its opposite.
(iv) The predecessor of -385 is -386.
12. What is the value of |-15| - |7 - 2|?
(i) -20
(ii) 10
(iii) 20
(iv) -10
13. The sum of 400 + (- 25) + (- 12) is:
(i) 128
(ii) 363
(iii) -128
(iv) None of these
14. Which of the following is (are) correct?
(i) The sum of two negative integers is a positive integer.
(ii) Zero is a positive integer.
(iii) The negative of a negative integer is a positive integer.
(iv) Zero is less than every negative integer.
15. The sum of two integers is -452. If one of them is 87, the other integer is
(i) 469
(ii) -459
(iii) -539
(iv) None of these
16. The value of -17 - [(- 19) + (-6) - 4] is
(i) -70
(ii) -15
(iii) 50
(iv) 12
17. The absolute value of -113 is
(i) 13
(ii) 113
(iii) -113
(iv) None of these
18. What should be added to -19 to get 57?
(i) -76
(ii) 76
(iii) 72
(iv) -38
19. Subtracting the sum of -115 and 42 from the sum of -38 and 452, we get
(i) 123
(ii) -98
(iii) 87
(iv) 487
20. When 15 is subtracted from an integer, the result is the same as subtracting -3 from -7. What is the integer?
(i) 11
(ii) 2
(iii) 4
(iv) 5
Answer:
I. 1. The value of |-67| - |-28| is (ii) 39
2. The predecessor of -209 is (iii) -210
3. The additive inverse of -1 is (iv) 1
4. The sum of two integers is -178. If one of them is 119, then the other one is (i) -297
5. On subtracting -24 from -12, we get (iv) 12
6. The smallest positive integer is (ii) 1
7. The successor of greatest negative integer is (i) 0
8. (iii) -100
9. (i) Car
10. (iv) - 7 < - 3 < 0 < 1 < 5
11. (iv) The predecessor of -385 is -386.
12. (ii) 10
13. The sum of 400 + (- 25) + (- 12) is: (ii) 363
14. (iii) The negative of a negative integer is a positive integer.
15. The sum of two integers is -452. If one of them is 87, the other integer is (iii) -539
16. The value of -17 - [(- 19) + (-6) - 4] is (iv) 12
17. The absolute value of -113 is (ii) 113
18. (ii) 76
19. Subtracting the sum of -115 and 42 from the sum of -38 and 452, we get (iv) 487
20. (i) 11
6th Grade Integers Worksheet
II. State True or False:
(i) -7 and 7 are equidistant from 0 on the number line.
(ii) Integers are closed under subtraction.
(iii) On the number line -10 lies on the right of 0
(iv) The value of -14 - (-6) is -20.
(v) The sum of two integers is 45. If one of them is -38, then the other is 83.
Answer:
II. (i) True
(ii) True
(iii) False
(iv) False
(v) True
III. Fill in the blanks.
(i) The smallest 5-digit negative integer is __________.
(ii) The sum of two integers is always an __________.
(iii) __________ is the smallest +ve integer.
(iv) Opposite of going 55 km to the East is going 55 km to the __________.
(v) 17 km below the sea level can be indicated using integers as __________.
Answer:
III. (i) -99999
(ii) integer
(iii) 1
(iv) West
(v) -17
6th Grade Integers Worksheet
IV. Match the columns.
|
Column A |
Column B |
|
(i) -37 - (-15) |
(a) 101 |
|
(ii) - (-500) |
(b) -26 |
|
(iii) -19 + (-12) - (-5) |
(c) -22 |
|
(iv) Negative of -999 |
(d) 500 |
|
(v) The value of |-101| |
(e) 999 |
Solution:
IV. (i) → (c)
(ii) → (d)
(iii) → (b)
(iv) → (e)
(v) → (a)
6th Grade Integers Worksheet
V. Word Problems on Integers.
(i) Two integers have a difference of 6 and a sum of -40. What are the integers?
(ii) A fruit-seller had a profit of $178 on Saturday, a loss of $70 on Sunday and a loss of $89 on Monday. Find his net profit or loss in these three days.
Answer:
V. (i) -17 and -23
(ii) Profit $19
VI. Write the integers lying between -21 and -13.
Answer:
VI. -20, -19, -18, -17, -16, -15, -14
VII. Which number will you get on moving 5 steps to the right of -6?
Answer:
VII. -1
VIII. Using a number line, arrange the following integers in ascending order:
-5, -1, 0, -3, -8, 1, -2, 6
IX. Subtract the sum of 150 and -24 from the sum of 43 and -66.
Answer:
IX. -149
X. Find the value of each of the following:
(i) |-18| - |8 - 3|
(ii) -|5| + |8| - (-37) + 74
Answer:
X. (i) 13
(ii) 124
XI. Nitheeya walks 100 m due east and then 59 m due west. Find her position with respect to her starting point.
Answer:
XI. Nitheeya's final position is 41 m due east of her starting point.
XII. Evaluate:
(i) 1 - 7 + 5 - 8 + 6 - 9 + 38 - 50
(ii) 7 + (-3) + 9 + (-3) + 11 + (-15) + 17 + (-13) + 17 + (-24)
Answer:
XII. (i) -24
(ii) 3
XIII. If -11 represent 11 m below water surface in a sea, what does 21 + (- 34) + 22 represent?
Answer:
XIII. 9 m above the water surface
XIV. If $400 represents a gain of $400, what does -13 show?
Answer:
XIV. A loss of $400.
XV. If is an operation between p and q such that p * q = p - q then simplify the following:
(i) 4 * 7
(ii) 4 * (-9)
(iii) -2 * 24
(iv) (-5) * (-3)
Answer:
XV. (i) -3
(ii) 13
(iii) -26
(iv) -2
XVI. Find the missing numbers in the alternating sequence.
(i) -9 Subtract 6 → ___ Subtract (-7) → ___ Subtract 6 → ___ Subtract (-7) → ___
(ii) 3 Subtract (-5) → ___ Subtract 4 → ___ Subtract (-5) → ___ Subtract 4 → ___
Answer:
XVI. (i) -9 Subtract 6 → -15 Subtract (-7) → -8 Subtract 6 → -14 Subtract (-7) → -7
(ii) 3 Subtract (-5) → 8 Subtract 4 → 4 Subtract (-5) → 9 Subtract 4 → 5
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