by Integers class 7
Contents
What are Integers ?
It includes all natural numbers , 0 and negative of natural numbers . It is denoted by ,
representation of integers on number line
Properties of integers:
- 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
Sums on integers for class 7(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)
Integers Class 7 Maths quiz
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
Integers class 7 extra questions word problems
(i) A spacecraft is at 4525km above the earth’s surface.if it descends at the rate of 5km per minute. What will be its position after 9 hours.
(ii)A fruit merchant earns a profit of Rs. 66 per bag of orange sold and a loss of Rs. 44 per bag of grapes sold.
(a)Merchant sells 1800 bags of orange and 2500 bags of grapes. What is the profit or loss?
(b) What is the number of bags of oranges to be sold to have neither profit nor loss if the number of grapes bags are sold is 900 bags?
(iii) Nathan ended round one of a quiz with 200 points. In round two, he scored -300 points and in the third round, he gained 200 points. What was his total score at the end of the third round?
(iv) A submarine submerges from the surface of the sea at the rate of 10 m/min. How long will it take to reach 300 m below the sea level?
(v)Roman civilization began in 509 B.C. and came to an end in 476 A.D. How long did Roman civilization last?
(vi)Metal mercury is a liquid at room temperature. Its melting point is -39°C. The freezing point of alcohol is -114°C. How much warmer is the melting point of mercury than the freezing point of alcohol?
(vii)The temperature in city-X was 10°C in the morning which dropped by 15°C in the evening. What is the temperature in the evening?
(viii)Everest, the highest peak in Asia, is 29,028 feet above sea level. The Dead Sea is 1,312 feet below sea level. What is the level difference between these two places? 7.
(ix)The temperature recorded in a city on Monday is 50°. If the temperature increases by 10° on Tuesday and falls by 11° on Wednesday. Find the temperature recorded on Wednesday
(x)In an examination,3 marks are awarded for every correct answer and1mark is deducted for every incorrect answer. If a student gets 15questions correct and7questions incorrect, find the marks scored by him.
(xi)Andrew has deposited $5500 and has withdrawn $4800 two times consecutively. Find the amount in his account.
(xii) A bird is flying 1200 feet above the sea level. At a particular point, it is directly above a fish floating at 400 feet below the sea level. By how much the bird must descend its flight to be as far as from the sea level, as the fish is?
(xiii)Ryan was playing a game where catching a fish in the basket adds 10 points to his score. If he catches an octopus instead, he loses 5 points. What is his total if he catches 3 fish and 5 octopus?
(xiv)Jason is moving from his hometown to Alaska. He is expecting a big temperature change, and he is getting ready. The hottest it gets in his hometown is 32 degrees celsius. The coldest it gets in Alaska is approximately – 45 degrees celsius. What temperature change will Jason experience?
(xv)The temperature of a hot iron rod drops by 8°𝐶 every hour. If the temperature of the iron rod is 118°𝐶, find the temperature after 4 hours.
(xvi)A submarine submerges at the rate of 5 m/min. If it descends from 20 m above the sea level, how long will it take to reach 250 m below sea level?
(xvii)At Srinagar temperature was − 5°C on Monday and then it dropped by 2°C on Tuesday. What was the temperature of Srinagar on Tuesday? On Wednesday, it rose by 4°C. What was the temperature on this day?
(xviii)A plane is flying at the height of 5000 m above the sea level. At a particular point, it is exactly above a submarine floating 1200 m below the sea level. What is the vertical distance between them?
(xix)Mohan deposits Rs 2,000 in his bank account and withdraws Rs 1,642 from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan’s account after the withdrawal.
(xx)Rita goes 20 km towards east from a point A to the point B. From B, she moves 30 km towards west along the same road. If the distance towards east is represented by a positive integer then, how will you represent the distance travelled towards west? By which integer will you represent her final position from A?
(xxi) A cement company earns a profit of Rs 8 per bag of white cement sold and a loss of Rs 5 per bag of grey cement sold.
(a) The company sells 3, 000 bags of white cement and 5,000 bags of grey cement in a month. What is its profit or loss?
(b) What is the number of white cement bags it must sell to have neither profit nor loss, if the number of grey bags sold is 6,400 bags.
(xxii) An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 m above the ground level, how long will it take to reach − 350 m.
Ans. (i) 1825 km (ii) (a) profit amount is rupees 8800 . (b) 600 bags of oranges
(iii) 300 (iv) 30 minutes (v) 985 degrees (vi) -75 (vii) -5 (viii) 30340 feet
(ix) 49 degrees (x) 38 (xi) $ -4100 (xii) 800 feet (xiii) 5 points (xiv)77
degrees (xv) 86 degrees celcius (xvi) 54 minutes (xvii) Monday = −5°C, on
tuesday −7°C , on Wednesday −3ºC (xviii) 6200 m (xix) rs. 358 (xx) −10 km (i.e.,
Rita is now in west direction) (xxi) (a) loss of Rs 1000 (b) 4000 bags of white
cement (xxii) 1 hour
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