Exercise 1.6

Exercise 1.6

Miscellaneous Practice problems

1. What Should be added to −1 to get 10?

Answer: 11

2. −70 + 20 = –40 −10

3. Subtract 94860 from ( −86945)

 –86945 – 94860 = – 1,81,805

4. Find the value of (–25)+60+(–95)+(–385)

(–25) + 60 (–95) + (–385)

 + 60 + (–25 – 95 – 385)

+ 60 –505 = – 445

5. Find the sum of (–9999) ( −2001)and ( −5999)

–9999 +

–2001

–5999

---------

–17999

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6. Find the product of (−30) × ( −70) ×15

2100 × 15 = 31500

7. Divide (−72) by 8

–72 ÷ 8 = –9

8. Find two pairs of integers whose product is +15 .

(–3,–5), (3, 5)

9. Check the following for equality

(i) (11 + 7) +10 and 11 + (7 +10)

(11 + 7) + 10 = 18 + 10 = 28

11 + (7 + 10) = 11 + 17 = 28

(11 + 7) + 10 = 11 + (7 + 10)

They are equal

(ii) (8 − 13) × 7 and 8 − (13 × 7)

(8–13) × 7 = –5 × 7 = –35

8 – (13 × 7) = 8 – 91 = –83

(8–13) × 7 ≠ 8 – (13 × 7)

They are not equal

(iii) [(−6) − (+8)] × (−4) and ( −6) −[ 8 × ( −4)]

[(–6) – (+8)] × (–4) = (–6 – 8) × (–4) = –14 × –4 = 56

(–6) – [8 × (–4) = (–6) – [–32] = –6 + 32 = 26

[(–6) – (+8)] × (–4) ≠ (–6) – [8 × (–4)]

They are not equal

(iv) 3 × [(−4) + ( −10)] and [ 3 × ( −4) + 3 × (−10)]

3 × [(–4) + (–10)] = [3 × (–14) = –42

[3 × (–4) + 3 × (–10) = –12 – 30 = –42

3 × [(–4) + (–10)] = [3 × (–4) + 3 × (–10)]

They are equal 

10. Which is Not true?

(i) 15 + 5 = 5 × (3+1)

(ii) (8 + 4) × 2 = 8 + (4 + 2)

(iii) 7 + (8 – 8) = 7

(iv) 6 +(3 × 2) = (3 × 2) + 6

(v) 4 × (25 × 7) = (4 × 25) × 7

(i) 15 + 5 = 5 × (3+1)

15 + 5 = 5 × (3 + l)

 20 = 5 × 4

 20 = 20 True

(ii) (8 + 4) × 2 = 8 + (4 + 2)

(8 + 4) × 2 = 8 + (4 + 2)

 12 × 2 = 8 + 6

 24 = 14 Not True

(iii) 7 + (8 – 8) = 7

 7 + (8 – 8) = 7

 7 + 0 = 7

 7 = 7 True

(iv) 6 +(3 × 2) = (3 × 2) + 6

 6 + (3 × 2) = (3 × 2) + 6

 6 + 6 = 6 + 6

 12 = 12 True

(v) 4 × (25 × 7) = (4 × 25) × 7

 4 × (25 × 7) = (4 × 25) × 7

 4 × 175 = 100 × 7

 700 = 700 True

11. Kalaivani had ₹ 5000 in her bank account on 01.01.2018. She deposited ₹ 2000 in January and withdrew ₹ 700 in February. What was Kalaivani’s bank balance on 01.04.2018, if she deposited ₹ 1000 and withdrew ₹ 500 in March?

01.01.2018 Amount in bank = ₹ 5000 +

Amount deposited in January = ₹ 2000

                                               = ₹ 7000 –

Amount withdrew in February = ₹ 700 

                                             = ₹ 6300 +

Amount deposited in March = ₹ 1000

                                            = ₹ 7300 –

Amount withdrew in March = ₹ 500

                                              ₹ 6800

Balance amount on 01–04–2018 = ₹ 6800

12. The price of an item x increases by ₹ 10 every year and an item y decreases by ₹ 15 every year. If in 2018, the price of x is ₹ 50 and y is ₹ 90, then which item will be costlier in the year 2020.

In 2018, the price of x = ₹ 50

In 2020 the price of x increases = ₹ 2 × 10 = ₹ 20

In 2020 the price of x = ₹ 50 + 20 = ₹ 70

In 2018 the price of y = ₹ 90

In 2020 the price of y decreases = ₹ 2 × l5 = ₹ 30

In 2020 the price of y = ₹ (90–30) = ₹ 60

The item x will be costlier in 2020.

13. Match the statements in column A and column B

Answer : 1. d 2. a 3. e 4. C 5. b

1. For any two integers 72 and 108, 72 +108 is an also an integer. (d) Closed under addition.

2. For any three integers 68, 25 and 99 68 × (25 + 99) = (68 × 25)+ (68 × 99) (a) Distributive property of multiplication over addition.

3. 0 +(–138) = (–138) = (–138) + 0 (e) Additive identity.

4. For any two integers (–5) and 10 (–5) × 10= 10 × (–5) (c) Commutative property under multiplication.

5. 1 × (–1098) = (–1098) = (–1098) × 1 (b) Multiplicative identity.

Challenge Problems

13. Say true or false.

(i) The sum of a positive integer and a negative integer is always a positive integer. (False)

(ii) The sum of two integers can never be zero. (False)

(iii) The product of two negative integers is a positive integer. (True)

(iv) The quotient of two integers having opposite sign is a negative integer. (True)

(v) The smallest negative integer is −1. (False)

14. An integer divided by 7 gives a result –3. What is that integer?

An integer divided by 7 = –3

An integer / 7 = –3

An integer = 7 × –3 = –21

 That integer = –21

15. Replace the question mark with suitable integer in the equation

72+(−5)− |?| = 72.

 72 + (–5) – (–5) = 72.

16. Can you give 10 pairs of single digit integers whose sum is zero?

(–1) + 1 + (–2) + 2 + (–3) + 3+ (–4) + 4 + (–5) + 5 = 0

17. If P = −15 and Q = 5 find ( P − Q) ÷ ( P + Q)

P = –15, Q = 5

(P – Q) 4 ÷ (P + Q)

(–15 – 5) 4 ÷ (–15 + 5)

(–20) ÷ (–10) = 2 

18. If the letters in the English alphabets A to M represent the number from 1 to 13 respectively and N represents 0 and the letters O to Z correspond from –1 to −12 , find the sum of integers for the names given below.

For example,

MATH → sum → 13+1–6+8 = 16

(i) YOUR NAME

(ii) SUCCESS

A B C D E F G H I J K L M

1 2 3 4 5 6 7 8 9 10 11 12 13

N O P Q R S T U V W X Y Z

0 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –11 –12

i) AGNES SHEEBA

1+7 + 0 + 5 – 5 – 5 + 8 + 5 + 5 + 2+1 .

8 + 16 = 24

ii) SUCCESS

5 – 7 + 3 + 3 + 5 – 5 – 5

–22 + 11 = –11

19. From a water tank 100 litres of water is used every day. After 10 days there is 2000 litres of water in the tank. How much water was there in the tank before 10 days?

Water used in 1 day = 100 litres

Water used in 10 days = 100 × 10 = 1000 litres

Water in the tank = 2000 litres +

Water used in 10 days = 1000 litres

Water in the tank before 10 days = 3000 litres

20. A dog is climbing down in to a well to drink water. In each jump it goes down 4 steps. The water level is in 20th step. How many jumps does the dog take to reach the water level?

Water level is in the 20th step.

The dog goes down in 1 jump = 4 steps

Number of jumps the dog takes = 20 ÷ 4 = 5

The dog takes 5 jumps to reach the water level 

21. Kannan has a fruit shop. He sells 1 dozen banana at a loss of Rs.2 each because it may get rotten next day. What is his loss?

Loss on one banana = ₹ 2

Losson 1 dozen (12) bananas = ₹ 2 × 12 = ₹ 24

Loss on one dozen bananas = ₹ 24

22. A submarine was situated at 650 feet below the sea level. If it descends 200 feet, what is its new position?

Submarine was situated at 650 feet below sea level.

                                descends = 200 feet

New position of the submarine = (650 + 200) feet

                                                 = 850 feet

23. In a magic square given below each row, column and diagonal should have the same sum, Find the values of x, y and z.

II Column – 10 – 3 + 4 = – 9

I row    1 – 10 + x = –9

–9 + x = –9

x = –9 + 9 = 0

x = 0

II row   y – 3 – 2 = –9

y – 5 = – 9

y = –9 + 5 = –4

y = –4

III row

–6 + 4 + z = –9

 –2 + z = –9

         z = –9 + 2 = –7

         z = –7 

Rows

1 – 10 + 0 = –9

–4 –3–2 = –9

–6 +4–7 = –9

Columns

l – 4 – 6 = –9

–10 – 3 + 4 = –9

0 – 2 – 7 = –9

Diagonals

1 – 3 – 7 = –9

–6 – 3 + 0 = –9

ANSWERS

Exercise 1.6

1. 11

2. −40

3. –1,81,805

4. −445

5. –17,999

6. 31,500

7. −9

8. (−3,−5), (3,5)

9. (i) Equal (ii) Not equal (iii) Not equal (iv) Equal

11. ₹ 6,800

12. The item x will be costlier is 2020

13. Match the following 1. d, 2. a, 3. e, 4. c, 5. b

Challenge Problem

13. (i) False (ii) False (iii) True (iv) True (v) False

14. −21

15. −5

16. (−1)+1+(−2)+2+(−3)+3+(−4)+4+(−5)+5= 0

 (The answer is not unique. You can take any single digit with its Additive inverse)

17. 2

18. (i) −4 (ii) −11

19. 3000 litres of water

20. 5 jumps

21. ₹ 24

22. 850 feet below the sea level

23. x = 0, y = –4, z = –7