by Integers class 7
It includes all natural numbers , 0 and negative of natural numbers . It is denoted by
representation of integers on number line
- Negative integers are on the left side of 0
- Positive integers are on the right side of the zero
- 0 is neither +ve nor -ve.
- Integers are closed under addition. It means, for any two integers a and b, a + b is an integer.
- Integers are also closed under subtraction. Thus, if a and b are two integers then a – b is also an integer.
- Addition is commutative for integers. In general, for any two integers a and b, we can say a + b = b + a
- Subtraction is not commutative for integers. Consider the integers 5 and (–3) , 5 – ( –3) = 5 + 3 = 8 and (–3) – 5
= – 3 – 5 = – 8 Thus 5 – ( –3)(–3) – 5
- Addition is associative for integers. In general for any integers a, b and c, we can say a + (b + c) = (a + b) + c
- For any two positive integers a and b, we can say a × (– b) = (– a) × b = – (a × b)
- Integers are closed under multiplication. In general, a × b is an integer, for all integers a and b
- Multiplication is commutative for integers. For any two integers a and b, a × b = b × a
- Distributivity of multiplication over addition is true for integers. In general, for any integers a, b and c,
a × (b + c) = a × b + a × c - Integers are not closed under division.
- Division is not commutative for integers.
Questions on integers for class 7 pdf
Solved Examples
Example 1: Arrange the following integers in ascending order -102, -39, -51, -5 , 0 , -6, 35 and 7 .
Sol. Ascending order of the given integers are : -102 < -51< -39 < -6< -5 < 0< 7< 35
Example 2: Find the sum of -72 , 237 , 84 , 72, -184 , -37 .
Sol. (-72) +237+84+72+(-184)+(-37)=(-72) +393 +(-184)+(-37)
= -72+393-184-37
=393-293 =100
Example 3: Write down a pair of integers whose (a) sum is –3 (b) difference is –5 (c) difference is 3 (d) sum is 0
Sol. (a) (–1) + (–2) = –3 or (–5) + 2 = –3 or (-7)+(4) =-3
(b) (–9) – (– 4) = –5 or (–2) – 3 = –5 or (-7) -(-2)= -5
(c) (–7) – (–10) = 3 or 1 – (–2) = 2 or +7 -(+4) =3
(d) (–10) + 10 = 0 or 4 + (–4) = 0 or 3 +(-3) =0 (You can make more pairs.)
Example 4: Solve the following:
(i) (-10) × (-5) + (-6)
(ii) (-10) × [(-13) + (-10)]
(iii) (-5) × [(-6) + 5]
Sol. (i) (-10) × (-5) + (-6) = 50 – 6 = 44
(ii) (-20) × [(-13) + (-10)] = (-20) × (-23) = 460
(iii) (-5) × [(-6) + 5]= (-5) x (-1) =5
Example 5: In a class test containing 15 questions, 4 marks are given for every correct answer and (–2) marks are given for every incorrect answer. Anil attempts all questions but only 10 of her answers are correct. What is his total score?
Sol. (i) Marks given for one correct answer = 4
So, marks given for 10 correct answers = 4 × 10 = 40
Marks given for one incorrect answer = – 2
So, marks given for 5 (= 15 – 10) incorrect answers = (–2) × 5 = –10
Therefore, Gurpreet’s total score = 40 + ( –10) = 30
Example 6: Is (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)?
Sol. (–15) × [(–7) + (–1)]= (-15) x (-8) = 120
(–15) × (–7) + (–15) × (–1)= 105 + 15 = 120
Hence (–15) × [(–7) + (–1)] = (–15) × (–7) + (–15) × (–1)
Example 7: Find each of the following products: (a) (–20) × (–2) × (–5) × 7 (b) (–1) × (–5) × (– 4) × (– 6)
Sol. (a) (–20) × (–2) × (–5) × 7 =– 20 × (–2 × –5) × 7 = [–20 × 10] × 7 = – 1400
(b) (–1) × (–5) × (– 4) × (– 6) = [(–1) × (–5)] × [(– 4) × (– 6)] = 5 × 24 = 120
Example 8: A certain freezing process requires that room temperature be lowered from 40°C at the rate of 5°C every hour. What will be the room temperature 10 hours after the process begins?
Sol. Temperature of the room in the beginning = 40°C
Temperature drop after 10 hour= =
Thus the temperature of the room after 10 hours = 40°C – 50°C = -10°C
Example 9: Find: (a) 125 ÷ (–25) (b) 80 ÷ (–5)
Sol. (a) 125÷ (-25) = (-125) ÷ 25 = =5
(b) 80 ÷ (-5) =(-80) ÷ 5 = -16
Example 10: Find: (a) (–36) ÷ (– 4) (b) (–201) ÷ (–3)
Sol. (a) (-36) ÷ (-4)= 36 ÷ 4 = 9
(b) (-201) ÷ (-3) = 201÷ 3 = 67
Example 11: Solve the following :
(a) 3+2-1 x 4 ÷ 2
Sol. 3+2-1 x 4 ÷ 2 = 3+2-1 x 2 = 3+2-2 = 3
(b) 53 x 2 -1 x 6
Sol. 53 x 2 -1 x 6 = 106-6 =100
(c) 7 x 3 +8-2
Sol. 7 x 3 +8-2= 21 +8 – 2 = 29-2 = 27
(d) 12+(-3) +5 – (-2)
Sol. 12+(-3) +5 – (-2) = 12-3+5+2 =9+7 = 16
Unsolved Examples with answers
(i) Complete the following pattern:
(a) 7, 3, – 1, – 5, _____, _____, _____.
(b) – 2, – 4, – 6, – 8, _____, _____, _____.
(c) 15, 10, 5, 0, _____, _____, _____.
(d) – 11, – 8, – 5, – 2, _____, _____, _____.
(ii)Use the sign of >, < or = in the box to make the statements true.
(a) (– 8) + (– 6) (–8) – (– 6)
(b) (– 3) + 7 – 19 15 – 8 + (– 9)
(c) 23 – 41 + 10 23 – 41 – 10
(d) 39 + (– 24) – 15 36 + (– 52) – (– 36)
(e) – 231 + 79 + 51 (–399) + 159 + 81
(iii) Solve the following: (a) (-15) × 8 + (-15) × 4 (b) [32 + 2 × 17 + (-6)] ÷ 15
(iv) a × (b – c) = a × b – …………
(v) (a) For any integer a, what is (–1) × a equal to? (b) Determine the integer whose product with (–1) is 24
(vi) Replace the blank with an integer to make it a true statement.
(a) (–3) × _____ = 24 (b) 5 × _____ = –40
(c) _____ × (– 9) = –63 (d) _____ × (–12) = 132
(vii) For any integer a, a ÷ 1 = ……………..
(viii) For any integer a, a ÷ (- 1) =………….
(ix) Evaluate the following : (a) (-526)-(-217) (b) (-31) +31 (c) [(-6) x (-8) ] x 5 (d) -13 x (7-8) (e) (-3) x 8 x (-5)
(x) Match the following
Column I Column II
(a) a × 1 (i) Additive inverse of a
(b) 1 (ii) Additive identity
(c) ( – a) ÷ ( – b) (iii) Multiplicative identity
(d) a × ( – 1) (iv) a ÷ ( – b)
(e) a × 0 (v) a ÷ b
(f) ( –a) ÷ b (vi) a
(g) 0 (vii) – a
(h) a ÷ (–a) (viii) 0
(i) –a (ix) –1
Ans. (i) (a) -9, -13, -17, -21 (b) -10, -12, -14, -16 (c) -5, -10, -15, -20 (d) 1, 4, 7, 10
(ii) (a) < (b) < (c) > (d) < (e) > (iii) (a) -180 (b) 4 (iv) a x c
(v) (a) -a (b) -24 (vi) (a) -8 (b) -8 (c) 7 (d) -11 (vii) a (viii) -a
(ix) (a) -309 (b) 0 (c) 240 (d) 13 (e) 120
(x) (a) → (vi), (b) → (iii), c → (v), d → (vii), e → (viii), f → (iv) g → (ii), h → (ix), i → (i)
DOWNLOAD PDF Integers class 7 worksheet
MCQ questions for class 7 maths integers
(i) Put the correct sign <, > or = . (-11)+(-7) (-11) -(-7)
(a) < (b) > (c) = (d) none of these
(ii) Solve 40-(-39) + (-5)
(a) 74 (b) 64 (c) 60 (d) 0
(iii) When the integers 12, 0, 5, – 5, – 8 are arranged in descending or ascending order, then find out which of the following integers always remains in the middle of the arrangement.
(a) 0 (b) 5 (c) – 8 (d) – 5
(iv) Next three consecutive numbers in the pattern 11, 8, 5, 2, –, –, –are
(a) 0, – 3, – 6 (b) – 1, – 5, – 8 (c) – 2, – 5, – 8 (d) – 1, – 4, – 7
(v)The …………… is an additive identity for integers.
(a)1 (b) 0 (c)-1 (d) 2
(vi) (–1) × (–1) × (–1) × (–1) × (–1) = ………….
(a) 1 (b) -1 (c) 0 (d) 2
(vii) …………………… is the multiplicative identity for integers.
(a) 0 (b) 1 (c) -1 (d) 2
(viii) 0 ÷ a = …………… for a ≠ 0
(a) 0 (b) 1 (c) -1 (d) not defined
(ix) any integer divided by zero is ……………………………
(a) 0 (b) meaningless (c) 1 (d) -1
(x) (– 85) × 43 + 43 × ( – 15) is equal to ?
(a) -4300 (b) 4300 (c) 430 (d) -430
Ans. (i) (a) (ii) (a) (iii) 0 (iv) (d) (v) (b) (vi)( b) (vii) (b) (viii) (a) (ix) (b) (x) (a)
Maths quiz for class 7 integers
Integers class 7 (extra questions with answers)
A. State whether the following statements are correct or incorrect.
(i) When two positive integers are added we get a positive integer.
(ii) When two negative integers are added we get a positive integer.
(iii) When a positive integer and a negative integer are added, we always get a negative integer.
(iv) Additive inverse of an integer 8 is (– 8) and additive inverse of (– 8) is 8.
(v) For subtraction, we add the additive inverse of the integer that is being subtracted, to the other integer.
(vi) (–10) + 3 = 10 – 3
(vii) 8 + (–7) – (– 4) = 8 + 7 – 4
(viii) 25 × (–21) = (–25) × 21
(ix) –1 is a multiplicative identity of integers?
(x) The distributivity of multiplication over addition is true for integers.
(xi) Is division associative for integers?
(xii) When we change the order of integers, their sum remains the same.
(xiii) When we change the order of integers their difference remains the same.
(xiv) a ÷ b = b ÷ a
(xv) a – b = b – a
B . Answer the following questions:
(i) Write a pair of integers whose sum is zero (0) but difference is 8.
(ii) Write a pair of integers whose product is – 15 and whose difference is 8.
(iii) On multiplying or dividing two integers, If the signs of both the integers are same, the sign of the answer is ………………..
(iv) On multiplying or dividing two integers, If the signs of both the integers are different, the sign of the answer is ………………
(v) If a, b and c are integers then a x (b+c)= ………….+…………..
(vi) The product of three negative integers is a …………….. integer.
(vii) The product of four negative integers is a …………………. integer.
(viii) If the number of negative integers in a product is even, then the product is a ……………….. integer; if the number of negative
integers in a product is odd, then the product is a …………………. integer.
(ix) What will be the sign of the product if we multiply together: (a) 8 negative integers and 3 positive integers?
(b) 5 negative integers and 4 positive integers?
(x) (-5) x (-10) =………… x (-5)
(xi) The sum of two integers is 116. If one of them is -79, find the other integers.
(xii) The product of three integers does not depend upon the grouping of integers and this is called the …………………….. for multiplication of integers
Ans. A. (i) True (ii) False (iii) False (iv) True (v) True (vi) False (viii) False (viii) True (ix) False (x) True (xi) False (xii) True (xiii) False (xiv) False (v) False
B. (i) 4 and -4 (ii)5, -3 and 3 ,-5. (iii) positive (iv) negative (v) (a x b)+(b x c) (vi) negative (vii) positive (viii) positive, negative (ix) (a) positive (b) negative (x) -10 (xi) 195 (xii) associative property
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