Operations with Integers Class 7 Maths Worksheet with Answers Chapter 2

Ganita Prakash Part-II, Grade 7, Textbook of Mathematics – Chapter 2 is titled “Operations with Integers”. You have already covered Integers in Class 6. The whole family of numbers that includes positive numbers, zero, and negative numbers. In this chapter, we go one big step ahead. We learn how to multiply and divide integers, and how their signs behave when we do these operations.

The chapter begins with carrom coin sliding left and right on a number line reminds us that a rightward move is positive and a leftward move is negative. Green and red tokens help us picture addition and subtraction once more. From here, the real fun starts.

The heart of the chapter is the sign rule. Learn it well, because you will use it everywhere in higher classes.

This worksheet pulls together every skill taught in the chapter. The key areas are:

• Recap of integers using the number line and tokens
• Multiplying two integers and getting the sign right
• Patterns in the multiplication tables of integers
• Dividing integers and their signs
• Brahmagupta’s old “fortune and debt” rules for signs
• Properties of integers – commutative, associative and distributive
• Finding the sign of a product of many integers
• Simplifying long integer expressions with brackets
• Word problems – test marks, temperature, profit and loss, elevators

Very important rules and formulas to keep in mind:

• Multiplication sign rule: (+) × (+) = +, (−) × (−) = +, (+) × (−) = −, (−) × (+) = −. Same signs give plus, different signs give minus.
• Division sign rule: It works exactly like multiplication. Same signs give a positive answer, different signs give a negative answer.
• Multiply by −1: −1 × a = −a. It just flips the sign of the number.
• Sign of many numbers: Count the negative signs. An even number of negatives gives a positive answer. An odd number gives a negative answer.
• Commutative: a × b = b × a (order does not matter).
• Associative: a × (b × c) = (a × b) × c (grouping does not matter).
• Distributive: a × (b + c) = (a × b) + (a × c).

Most mistakes in this chapter are sign mistakes, not calculation mistakes. So first find the answer, then decide its sign carefully. Slow down at the minus signs and you will not make any mistakes.

You will find the questions arranged from easy to challenging – Basic, Standard, Advanced and HOTS. Practise step by step and grow in confidence. Once you are done, the complete answer key is at the end.

Class 7 Maths Worksheet – Chapter 2: Operations with Integers

Basic

1. Find the values:
   • (+7) + (−12)
   • (−15) + (+9)
   • (−8) + (−13)
   • (+24) + (−24)
2. Find the values:
   • 7 − 18
   • 4 − (−12)
   • −9 − 5
   • −15 − (−8)
3. Find the additive inverse of:
   • 17
   • −25
   • 0
   • −101
4. Multiply:
   • 6 × (−7)
   • (−8) × 5
   • (−9) × (−4)
   • 12 × 3
5. Divide:
   • 42 ÷ (−6)
   • (−56) ÷ 8
   • (−72) ÷ (−9)
   • 63 ÷ 7
6. Complete the statements:
   • (−3) × _____ = 27
   • 5 × _____ = −35
   • _____ × (−8) = −56
   • _____ ÷ 12 = −11
7. A carrom coin starts at 0. It moves +8 units, then −13 units, and then +6 units.
   What is its final position?
8. Find two integers whose:
   • Sum is 27 and difference is 9
   • Sum is 0 and difference is −10

Standard

1. Find the values:
   • (−5) × (18 + (−3))
   • (−7) × 4 × (−1)
   • (−2) × (−1) × (−5) × (−3)
   • 5 × (4 + (−2))
2. Use the distributive property to evaluate:
   • 18 × (25 − 7)
   • (−6) × (14 + 3)
   • 27 × (−12 + 8)
3. Given that 123 × 456 = 56,088, write the values of:
   • (−123) × 456
   • (−123) × (−456)
   • 123 × (−456)
4. A freezing process lowers the temperature from 32°C at the rate of 5°C every hour.
   What will the temperature be after 10 hours?
5. A cement company earns ₹8 per bag of white cement and loses ₹5 per bag of grey cement.
   It sells 3,000 white bags and 5,000 grey bags. Find its total profit or loss.
6. The company sells 6,400 grey cement bags. How many white cement bags must it sell to have neither profit nor loss?
7. In a test, +4 marks are awarded for each correct answer and −2 marks for each incorrect answer.
   Anita scores 40 marks with 15 correct answers. How many answers are incorrect? How many questions did she answer?
8. Arrange the following in increasing order:
   • (−348) + (−1064)
   • (−348) − (−1064)
   • 348 − (−1064)
   • (−348) × (−1064)
   • 348 × (−1064)

Advance

1. Evaluate:
   • (32 × (−18)) ÷ (−36)
   • (280 × (−7)) ÷ ((−8) × (−35))
   • (25 × (−12)) ÷ (45 × (−27))
2. Find the values using the correct signs:
   • (−27) ÷ 9
   • 84 ÷ (−4)
   • (−56) ÷ (−2)
   • (−144) ÷ 12
3. If 47 − 56 + 14 − 8 + 2 − 8 + 5 = −4, find the value of
   
   −47 + 56 − 14 + 8 − 2 + 8 − 5
   
   without calculating the whole expression.
4. Find three consecutive integers whose product is:
   • −6
   • 120
5. Anil gets +4 marks for each correct answer and −2 marks for each incorrect answer.
   He scores −10 marks even though he has 5 correct answers. How many answers are incorrect?
6. An integer is multiplied by −1 and the result is:
   • 27
   • −31
   • −1
   • 0

   Find the integer in each case.

7. An alien currency has coins worth +13 pibs and −9 pibs. Show one way to make:
   • +85 pibs
   • +20 pibs
   • −50 pibs
8. A number machine takes three inputs a, b and c and gives the output a + b − c.
   Find the output for:
   • 5, 8 and 3
   • −4, −1 and −6
   • −10, −12 and −9

HOTS

1. Given that (−548) × 972 = −5,32,656, find without full multiplication:
   • (−547) × 972
   • (−548) × 971
   • (−547) × 971
2. Given that 207 × (−33 + 7) = −5382, find the value of:
   
   −207 × (33 − 7).
3. Use the integers 3, −2, 5 and −6 exactly once, along with +, − and × exactly once, to make:
   • The greatest possible value
   • The smallest possible value
4. A coin starts at 0 and moves in the order:
   
   1, −2, 3, −4, 5, −6, … , −10.
   
   Find its final position.
5. How many negative factors are needed in a product for the final answer to be negative?
   State the general rule for the sign of a product of many integers.
6. A submarine is at −120 m below sea level. It rises 35 m, dives 48 m, rises 67 m, and then dives 24 m.
   What is its final position relative to sea level?
7. A lift starts at floor 3. It goes down 8 floors, up 12 floors, down 5 floors and up 3 floors.
   At which floor does it stop?
8. Show that multiplication is associative for the integers −4, 6 and −3 by evaluating:
   • (−4 × 6) × (−3)
   • −4 × (6 × −3)

Answer Key

Basic – Answers

1. • (+7) + (−12) = −5
   • (−15) + (+9) = −6
   • (−8) + (−13) = −21
   • (+24) + (−24) = 0
2. • 7 − 18 = 7 + (−18) = −11
   • 4 − (−12) = 4 + 12 = 16
   • −9 − 5 = −9 + (−5) = −14
   • −15 − (−8) = −15 + 8 = −7
3. • Additive inverse of 17 is −17.
   • Additive inverse of −25 is 25.
   • Additive inverse of 0 is 0.
   • Additive inverse of −101 is 101.
4. • 6 × (−7) = −42
   • (−8) × 5 = −40
   • (−9) × (−4) = 36
   • 12 × 3 = 36
5. • 42 ÷ (−6) = −7
   • (−56) ÷ 8 = −7
   • (−72) ÷ (−9) = 8
   • 63 ÷ 7 = 9
6. • (−3) × −9 = 27
   • 5 × −7 = −35
   • 7 × (−8) = −56
   • −132 ÷ 12 = −11
7. 8 + (−13) + 6 = 1.
   The coin finishes 1 unit to the right of 0.
8. • For sum 27 and difference 9, the integers are 18 and 9.
   • For sum 0 and difference −10, the integers are −5 and 5.

Standard – Answers

1. • (−5) × (18 + (−3)) = (−5) × 15 = −75
   • (−7) × 4 × (−1) = 28
   • (−2) × (−1) × (−5) × (−3) = −30
   • 5 × (4 + (−2)) = 5 × 2 = 10
2. • 18 × (25 − 7) = 18 × 25 − 18 × 7 = 324
   • (−6) × (14 + 3) = −84 − 18 = −102
   • 27 × (−12 + 8) = 27 × (−4) = −108
3. • (−123) × 456 = −56,088
   • (−123) × (−456) = 56,088
   • 123 × (−456) = −56,088
4. Temperature after 10 hours = 32 − (5 × 10) = −18°C.
5. Profit from white cement = 3000 × 8 = ₹24,000.
   Loss from grey cement = 5000 × (−5) = −₹25,000.
   Net result = ₹1,000 loss.
6. Loss from 6,400 grey bags = 6400 × 5 = ₹32,000.
   White bags needed = 32,000 ÷ 8 = 4,000 bags.
7. Marks from 15 correct answers = 15 × 4 = 60.
   Let the number of incorrect answers be x.
   60 − 2x = 40, so x = 10.
   Total questions answered = 15 + 10 = 25.
8. The values are:
   • 348 × (−1064) = −3,70,272
   • (−348) + (−1064) = −1412
   • (−348) − (−1064) = 716
   • 348 − (−1064) = 1412
   • (−348) × (−1064) = 3,70,272

   Increasing order:
   348 × (−1064) < (−348) + (−1064) < (−348) − (−1064) < 348 − (−1064) < (−348) × (−1064)

Advance – Answers

1. • (32 × (−18)) ÷ (−36) = −576 ÷ −36 = 16
   • (280 × (−7)) ÷ ((−8) × (−35)) = −1960 ÷ 280 = −7
   • (25 × (−12)) ÷ (45 × (−27)) = −300 ÷ −1215 = 20/81
2. • (−27) ÷ 9 = −3
   • 84 ÷ (−4) = −21
   • (−56) ÷ (−2) = 28
   • (−144) ÷ 12 = −12
3. Each sign in the new expression is the opposite of the corresponding sign in the given expression.
   Therefore, the new value is the additive inverse of −4, which is 4.
4. • Three consecutive integers with product −6 are −2, −1 and 0 does not work, so one correct set is −3, −2 and −1.
   • Three consecutive integers with product 120 are 4, 5 and 6.
5. Marks from correct answers = 5 × 4 = 20.
   Let incorrect answers be x.
   20 − 2x = −10, so x = 15.
6. • If x × (−1) = 27, then x = −27.
   • If x × (−1) = −31, then x = 31.
   • If x × (−1) = −1, then x = 1.
   • If x × (−1) = 0, then x = 0.
7. • +85 = 10(+13) + 5(−9)
   • +20 = 5(+13) + 5(−9)
   • −50 = 1(+13) + 7(−9)
8. • 5 + 8 − 3 = 10
   • (−4) + (−1) − (−6) = 1
   • (−10) + (−12) − (−9) = −13

HOTS – Answers

1. • (−547) × 972 = (−548 × 972) + 972 = −5,32,656 + 972 = −5,31,684
   • (−548) × 971 = (−548 × 972) + 548 = −5,32,108
   • (−547) × 971 = −5,32,656 + 548 + 972 − 1 = −5,31,137
2. −33 + 7 = −26 and 33 − 7 = 26.
   Therefore, −207 × (33 − 7) = −207 × 26 = −5382.
3. One possible greatest value is:
   
   5 × (3 − (−6)) + (−2) = 5 × 9 − 2 = 43.

   One possible smallest value is:
   
   (−6) × (5 − (−2)) + 3 = −6 × 7 + 3 = −39.

4. Pair the movements:
   
   (1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + (9 − 10)
   
   = −1 − 1 − 1 − 1 − 1 = −5.
5. The product is negative when there is an odd number of negative factors.
   It is positive when there is an even number of negative factors.
6. Final position = −120 + 35 − 48 + 67 − 24 = −90 m.
   The submarine is 90 m below sea level.
7. Final floor = 3 − 8 + 12 − 5 + 3 = 5th floor.
8. (−4 × 6) × (−3) = −24 × −3 = 72.
   −4 × (6 × −3) = −4 × −18 = 72.
   Both expressions have the same value, so multiplication is associative.

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