RD Sharma Solutions Class 7 Integers Exercise 1.1

RD Sharma Class 7 Solutions Chapter 1 Ex 1.1 PDF Free Download

RD Sharma Solutions Class 7 Chapter 1 Exercise 1.1

Exercise 1.1

Q1) Determine each of the following products:

(i) 12 × 7

(ii) (-15) × 8

(iii) (- 25) × (- 9)

(iv) (125) × (- 8)

Solution:

(i) Given: 12 × 7

From the property, the product of two integers of like signs is equal to the product of their absolute value

12 × 7 = 84

Therfore the product of 12 and 7 is 84

(ii) Given:  (- 15) × 8

From the property, The product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values

(- 15) × 8

= (- 15 × 8)

= –120

Therfore the product of – 15 and 8  is –120

(iii) Given: (-25) × (-9)

From the property, the product of two integers of like signs is equal to the product of their absolute value

(-25) × (-9)

= + (25 × 9)

= 225

Therfore the product of -25 and -9 is 225

(iv) Given: (125) × (- 8)

From the property, The product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values

(125) × (- 8)

= – (125 × 8)

= –1000

Therfore the product of 125 and -8 is –1000

Q2) Find each of the following products:

(i) 3 × (- 8) × 5

(ii) 9 × (- 3) × (- 6)

(iii) (- 2) × 36 × (- 5)

(iv) (- 2) × (- 4) × (- 6) × (- 8)

Solution:

(i) Given:3 × (- 8) × 5

Perform the multiplication operation of the given integers by applying the properties,

3 × (- 8) × 5

= – (3 × 8) × 5

= (- 24) × 5

= – (24 × 5)

= – 120

Therefore, the product of 3, -8 and 5 is -120

(ii) Given:9 × (-3) × (- 6)

Perform the multiplication operation of the given integers by applying the properties,

9 × (-3) × (- 6)

= – (9 × 3) × (- 6)

= (- 27) × (- 6)

= + (27 × 6)

= 162

Therefore, the product of 9, -3 and -6 is 162

(iii) Given:(-2) × 36 × (- 5)

Perform the multiplication operation of the given integers by applying the properties,

(-2) × 36 × (- 5)

= – (2 × 36) × (- 5)

= (- 72) × (- 5)

= (72 × 5)

= 360

Therefore, the product of -2, 36 and -5 is 360

(iv) Given: (- 2) × (- 4) × (- 6) × (- 8)

Perform the multiplication operation of the given integers by applying the properties,

(- 2) × (- 4) × (- 6) × (- 8)

= (2 × 4) × (6 × 8)

= (8 × 48)

= 384

Therefore, the product of 2, -4, -6 and -8 is 384

Q3) Find the value of:

(i) 1487 × 327 + (- 487) × 327

(ii) 28945 × 99 – (- 28945)

Solution:

(i) Given: 1487 × 327 + (- 487) × 327

First perform the multiplication operation

1487 × 327 + (- 487) × 327

Now subtract the values

= 486249 – 159249

= 327000

Therefore, the value of 1487 × 327 + (- 487) × 327 is  327000

(ii) Given: 28945 × 99 – (- 28945)

First perform the multiplication operation

28945 × 99 – (- 28945)

Now add the values

= 2865555 + 28945

= 2894500

Therefore, the value of 28945 × 99 – (- 28945) is 2894500

Q4) Complete the following multiplication table:

 

X -4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4

Is the multiplication table symmetrical about the diagonal joining the upper left corner to the lower right corner?

Solution:

The multiplication table is

X -4 -3 -2 -1 0 1 2 3 4
-4 16 12 8 4 0 -4 -8 -12 -16
-3 12 9 6 3 0 -3 -6 -6 -12
-2 8 6 4 2 0 -2 -4 -6 -8
-1 4 3 2 1 0 -1 -2 -3 -4
0 0 0 0 0 0 0 0 0 0
1 -4 -3 -2 -1 0 1 2 3 4
2 -8 -6 -4 -2 0 2 4 6 8
3 -12 -9 -6 -3 0 3 6 9 12
4 -16 -12 -8 -4 0 4 8 12 16

Yes, the multiplication table is symmetrical about the diagonal joining the upper left corner to the lower right corner.

Q5) Determine the integer whose product with ‘-1’ is

(i) 58

(ii) 0

(iii) – 225

Solution:

(i)  Given Number: 58

The product with -1 becomes

58 x (–1) = – (58 x 1)

= – 58

Therefore, the obtained integer is -58

(ii) Given Number: 0

0 x (–1) = 0

Because when 0 is multiplied with any number, the product is zero.

(iii) Given Number: -225

The product with -1 becomes

(–225) x (–1) = + (225 x 1)

= 225

Therefore, the obtained integer is 225

Q6) What will be the sign of the product if we multiply together

(i) 8 negative integers and 1 positive integer?

(ii) 21 negative integers and 3 positive integers?

(iii) 199 negative integers and 10 positive integers? 

Solution:

(i) Since – ve × – ve = + ve, when 8 negative integers and 1 positive integer are multiplied, the sign of the resultant product is Positive

(ii)Since – ve × + ve = – ve,  when 21 negative integers and 3 positive integers are multiplied, the sign of the resultant product is Negative

(iii)when 199 negative integers and 10 positive integers are multiplied, the sign of the resultant product is Negative

Q7) State which is greater: 

(i) (8 + 9) × 10 and 8 + 9 × 10

(ii) (8 – 9) × 10 and 8 – 9 × 10 

(iii) ((-2) – 5) × – 6 and (-2) – 5 × (- 6)

Solution:

(i) Given: (8 + 9) × 10 and 8 + 9 × 10

(8 + 9) × 10 = 17 × 10 = 170

8 + 9 × 10 = 8 + 90 = 98

Since 170 > 98

Therefore, (8 + 9) × 10 is greater than 8 + 9 × 10

(ii) Given: (8 – 9) × 10 and 8 – 9 × 10

(8 – 9) × 10 = – 1 × 10 = – 10

8 – 9 × 10 = 8 – 90 = – 82

Since -10 >-82

Therefore, (8 – 9) × 10 is greater than 8 – 9 × 10

(iii) Given: ((-2) – 5) × – 6 and (-2) – 5 × (- 6)

((-2) – 5) × – 6 = (- 7) × (- 6) = (7 x 6) = 42

(– 2) – 5 x (– 6) = – 2 + (5 x 6)= 30 – 2 = 28

Since 42 > 28

Therefore, ((-2) – 5×(- 6)) is greater than (- 2) – 5 × (- 6)

Q8) (i) If a× (-1) = – 30, is the integer a positive or negative?

(ii) If a × (-1) = 30, is the integer a positive or negative? 

Solution:

(i) When a positive integer is multiplied by a negative integer, it gives a negative integer. So the value of “a” should be a positive integer.

It means that 30 x -1 = -30. Therefore, a = 30

(ii) When a negative integer is multiplied by a negative integer, it gives a positive integer. So the value of “a” should be a negative integer.

It means that -30 x -1 = -30. Therefore, a = -30

Q9)  Verify the following:

(i) 19 × (7 + (-3)) = 19 × 7 + 19 × (-3)

(ii) (-23)[(-5)+ (+19)] = (-23) × (- 5) + (- 23) × (+19)

Solution:

(i) To verify: 19 × (7 + (-3)) = 19 × 7 + 19 × (-3)

L.H.S = 19 × (7+ (-3))

= 19 × (7-3)

= 19 × 4

19 × (7+ (-3)) = 76

R.H.S = 19 × 7 + 19 × (-3)

= 133 – 57

19 × 7 + 19 × (-3) = 76

19 × (7+ (-3)) = 76 = 19 × 7 + 19 × (-3)

L.H.S = R.H.S

Therefore,  19 × (7 + (-3)) = 19 × 7 + 19 × (-3) 

Hence, verified

(ii)  To verify: (-23)[(-5)+ (+19)] = (-23) × (- 5) + (- 23) × (+19)

L.H.S = (-23)[(-5) + (+19)]

= (-23)[-5 + 19]

= (-23)[14]

(-23)[(-5) + (+19)]= – 322

R.H.S = (-23) × (-5) + (-23) × (+19)

= 115 – 437

(-23) × (- 5) + (- 23) × (+19) = –322

(-23)[(-5) + (+19)]= – 322 = (-23) × (-5) + (-23) × (+19)

L.H.S = R.H.S

Therefore,  (-23)[(-5)+ (+19)] = (-23) × (- 5) + (- 23) × (+19)

Hence, verified

Q10) Which of the following statements are true?

(i) The product of a positive and a negative integer is negative.

(ii) The product of three negative integers is a negative integer.

(iii) Of the two integers, if one is negative, then their product must be positive.

(iv) For all non-zero integers a and b, a × b is always greater than

either a or b.

(v) The product of a negative and a positive integer may be zero.

(vi) There does not exist an integer b such that for a >1, a × b = b × a = b. <

Solution:

(i) True

(ii) True

(iii) False

(iv) False

(v) False

(vi) True

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