RD Sharma Solutions Class 7 Integers Exercise 1.1

RD Sharma Solutions Class 7 Chapter 1 Exercise 1.1

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

Exercise 1.1

Q1) Determine each of the following products:

(i) \(12\times 7\)

Solution:

We have,

\(12\times 7\) = 84 [The product of two integers of like signs is equal to the product of their absolute value]

(ii) \((-15)\times 8\)

Solution:

We have,

\((-15)\times 8\) [ The product of two integers of opposite

= \((-15\times 8)\) signs is equal to the additive inverse of the

= –120 product of their absolute values]

(iii) \((-25)\times (-9)\)

Solution:

We have,

\((-25)\times (-9)\)

= \(+(25\times 9)\)

= 225

(iv) \((125)\times (-8)\)

Solution:

We have,

\((125)\times (-8)\)

= \(-(125\times 8)\)

= –1000

Q2) Find each of the following products:

(i) \(3\times (-8)\times 5\)

Solution:

We have,

\(3\times (-8)\times 5\)

= \(-(3\times 8)\times 5\)

= \((-24)\times 5\)

= \(-(24\times 5)\)

= –120

(ii) \(9\times (-3)\times (-6)\)

Solution:

We have,

\(9\times (-3)\times (-6)\)

= \(-(9\times 3)\times (-6)\)

= \((-27)\times (-6)\)

= \(+(27\times 6)\)

= 162

(iii) \((-2)\times 36\times (-5)\)

Solution:

We have,

\((-2)\times 36\times (-5)\)

= \(-(2\times 36)\times (-5)\)

= \((-72)\times (-5)\)

= \((72\times 5)\)

= 360

(iv) \((-2)\times (-4)\times (-6)\times (-8)\)

Solution:

\((-2)\times (-4)\times (-6)\times (-8)\)

= \((2\times 4)\times (6\times 8)\)

= \((8\times 48)\)

= 384

Q3) Find the value of:

(i) \(1487\times 327+(-487)\times 327\)

Solution:

We have,

\(1487\times 327+(-487)\times 327\)

= 486249 – 159249

= 327000

(ii) \(28945\times 99-(-28945)\)

Solution:

We have,

\(28945\times 99-(-28945)\)

= 2865555 – 28945

= 2894500Q4) Complete the following multiplication table:

Second number

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

First number

-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:

Second number

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

First number

-3

12 9 6 3 0 -3 -6 -9 -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

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

(i) 58

Solution:

58 x (–1) = – (58 x 1)

= –58

(ii) 0

Solution:

0 x (–1) = 0

(iii) 225

Solution:

(–225) x (–1) = +(225 x 1)

= 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) Positive ∵ \([ -ve\times -ve=+ve]\)

(ii) Negative ∵ \([ -ve\times +ve=-ve]\)

(iii) Negative

Q7) State which is greater:

(i) \((8+9)\times 10\;and\;8+9\times 10\)

Solution:

\((8+9)\times 10=17\times 10\)

\(=170\)

\(8+9\times 10=8+90=98\)

\((8+9)\times 10>8+9\times 10\)

(ii) \((8-9)\times 10\;and\;8-9\times 10\)

Solution:

\((8-9)\times 10=-1\times 10\)

\(=-10\)

\(8-9\times 10=8-90=-82\)

\((8-9)\times 10>8-9\times 10\)

(iii) \(((-2)-5)\times {-6}\;and\;(-2)-5\times (-6)\)

Solution:

\(((-2)-5)\times {-6}=(-7)\times (-6)\)

= (7 x 6)

= 42

(– 2) – 5 x (– 6) = – 2 + (5 x 6)

= 30 – 2

= 28

Therefore, \(((-2)-5\times (-6))>(-2)-5\times (-6)\)

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

Solution:

When multiplied by ‘a’ negative integer, a gives a negative integer. Hence, ‘a’ should be a positive integer.

a = 30

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

Solution:

When multiplied by ‘a’ negative integer, a gives a positive integer. Hence, ‘a’ should be a negative integer.

a = –30

Q9) Verify the following:

(i) \(19\times (7+(-3))=19\times 7+19\times (-3)\)

Solution:

L.H.S = \(19\times (7+(-3))\)

= \(19\times (7-3)\)

= \(19\times 4\)

= 76

R.H.S = \(19\times 7+19\times (-3)\)

= 133 – 57

= 76

Therefore, L.H.S = R.H.S

(ii) \((-23)[(-5)+(+19)]=(-23)\times (-5)+(-23)\times (+19)\)

Solution:

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

= \((-23)[-5+19]\)

= \((-23)[14]\)

= –322

R.H.S = \((-23)\times (-5)+(-23)\times (+19)\)

= 115 – 437

= –322

Therefore, L.H.S = R.H.S

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, \(a\times b\) 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 \(a>1,\;a\times b=b\times a=b.\)<

Solution:

(i) True (vi) True

(ii) True

(iii) False

(iv) False

(v) False