Rd Sharma Solutions Class 6 Chapter 5 Negative Numbers and Integers
Welcome to NCTB Solution. Here with this post we are going to help 6th class students for the Solutions of Rd Sharma Class 6 Mathematics, Chapter 5, Negative Numbers and Integers. Here students can easily find Exercise wise solution for chapter 5, Negative Numbers and Integers. Students will find proper solutions for Exercise 5.1, 5.2, 5.3 and 5.4. Our teachers solved every problem with easily understandable methods so that every students can understand easily. Here all solutions are based on the CBSE latest curriculum.
Negative Numbers and Integers Exercise 5.1 Solution
Question no – (1)
Solution :
(i) Opposite of Increase in population is
= Decrease in population.
(ii) Opposite of Depositing money in a bank is
= Withdrawing money from bank.
(iii) Opposite of Earning money is
= Spending money.
(iv) Opposite of Going North is
= Going south.
(v) Opposite of Gaining a weight of 4 kg is
= Losing weight of 4 kg.
(vi) Opposite of A loss Rs 1000 is
= Gain of Rs 100.
(vii) Opposite of 25 is
= -25
(viii) Opposite of -15 is
= 15
Question no – (2)
Solution :
(i) 25° above Zero using integers
= +25° C
(ii) 5° below zero using integers
= -5°
(iii) A profit of Rs 800 using integers
= +800
(iv) A deposit of Rs 2500 using integers
= +2500
(v) 3 km above sea level using integers
= + 3
(vi) 2 km below sea level using integers
= -2
Question no – (3)
Solution :
Given numbers are,
(i) 7,
(ii) -4,
(iii) 0
Now, on number line,
Question no – (4)
Solution :
(i) 0, – 4
Here, – 4 is smaller
(Negative integers are always smaller then Positive integers)
(ii) -3, 12
Here, – 3 is smaller
(iii) 8, 13
Here, 8 is smaller
(iv) -15, – 27
Here, – 27 is smaller
Question no – (5)
Solution :
(i) 3, -4
= 3 is larger
(ii) -12, -8
= -8 is larger
(ii) 0, 7
= 7 is larger
(iv) 12, -18
= 12 is larger
Question no – (6)
Solution :
(i) The integers between -7 and 3 are,
= 6, -5, -4, -3, -2, -1, 0, 1, 2
(ii) The integers between –2 and 2 are,
= 1, 0, 1
(iii) The integers between –4 and 0 are,
= 3, -2, -1
(iv) The integers between 0 and 3 are,
= 1, 2
Question no – (7)
Solution :
(i) -4 and 3
Between -4 and 3, there integers are, -3, -2, -1, 0, 1, 2
The integers total in 6.
(ii) 5 and 12
The integers between 5 and 12 are, 6, 7, 8, 9, 10, 11
Total integers are in 6.
(iii) -9 and -2
= The integers between -9 and -2 are, -8, -7, -6, -5, -4, -3
Total no of integers are 6.
(iv) 0 and 5
The integers between 0 and 5 are, 1, 2, 3, 4
Total integers are 4.
Question no – (8)
Solution :
(i) 2 < 5
(ii) 0 < 3
(iii) 0 > -7
(iv) -235 > -532
(v) -18 < 15
(vi) -20 < 20
Question no – (9)
Solution :
(i) -8, 5, 0, -12, 1, -9, 15
∴ In increasing order,
= -12, -9, -8, 0, 1, 5, 15
(ii) -106, 107, -320, -7, 185
∴ In increasing order,
= -320, -106, – 7, 107, 185
Question no – (10)
Solution :
(i) -15, 0, -2, -9, 7, 6. -5, 8
∴ In increasing order,
= -15, -9, -5, -2, 0, 6, 7, 8
(ii) -154, 123, -205, -89, -74
∴ In increasing order,
= -205, -154, -89, -79, 123
Question no – (11)
Solution :
Given integers,
2 more than 3
5 less than 3
4 more than -9
Now, on number line :
Question no – (12)
Solution :
(i) 14
= The absolute value of 14 is |14| = 14
(ii) -25
= The absolute value of -25 is |-25| = 25
(iii) 0
= The absolute value of 0 is |0| = 0
(iv) -125
= The absolute value of |-125| is 125
(v) -248
= The absolute value of -248 is |-248| = 248
(vi) a -7, if a is greater than 7
= The absolute value of a -7 is |a -7| = a -7 where a > 7
(vii) a -7, if a -2 is less than 7
= The absolute value of a -7 if a -2 is less than
7 is |a -7| = -(a–7) where a | 2 < 7
(viii) a + 4, if a is greater than -4
= The absolute value of a + 4 if a is than -4 is |a + 4| = a + 4
(ix) a + 4 if a is less than -4
= The absolute value of where a > -4
(x) |-3|
= The absolute value of |-3| is |-3| = 3
(xi) -|-5|
= The absolute value of -|-5| is = 5
(xii) |12-5|
= The absolute value of |12 – 5| is = 7
Question no – (13)
Solution :
(i) 4 negative integers less than -10 are -11, -12, -13, -14.
(ii) 6 negative integers just greater than -12 are -11, -10, -9, -8, -7, -6.
Question no – (14)
Solution :
(i) The smallest integers is Zero
= False.
(ii) The opposite of zero is zero
= True.
(iii) Zero is not n integers.
= False.
(iv) 0 is larger than every negative integer.
= True.
(v) The absolute value of an integer is greater than the integer.
= False.
(vi) A positive integer is greater than its opposite.
= True.
(vii) Every negative integer is less than every natural number
= True.
(viii) 0 is smallest positive integer.
= False.
Negative Numbers and Integers Exercise 5.2 Solution
Question no – (1)
Solution :
(i) 5 + (-2)
= 5 – 2
= 3
Now, on the number line :
(ii) (-9) + 4
= – 9 + 4
= -5
Now, on the number line :
(iii) (-3) + (-5)
= -3 – 8
= -8
Now, on the number line :
(iv) 6 + (-6)
= 6 – 6
= 0
Now, on the number line :
(v) (- 1) + (- 2) + 2
= -1 – 2 + 2
= -1
Now, on the number line :
(vi) (-2) + 7 + (-9)
= -2 + 7 – 9
= -4
Now, on the number line :
Question no – (2)
Solution :
(i) Given, -557 and 488
∴ |-557|- |488|
= 557 – 488
= 69
Thus, the sum is 69.
(ii) Given, -522 and -160
= – 522 – 160
= – 682
Therefore, the sum is -682
(iii) Given, 2567 and -325
= 2567 – 325
= 2242
Therefore, the sum is 2242.
(iv) Given, -10025 and 139
= – 10025 + 139
= – 9886
Hence, the sum is -9886
(v) Given, 2547 and -2548
= 2547 – 2548
= -1
Thus, the sum is -1
(vi) Given, 2884 and -2884
= 2884 – 2884
= 0
Therefore, the sum is 0
Negative Numbers and Integers Exercise 5.3 Solution
Question no – (1)
Solution :
(i) Given, 52
= The addition integer of 52 is -52
(ii) Given, -176
= The addition integer of -176 is 176
(iii) Given, 0
= The addition integer of 0 is 0
(iv) Given, 1
= The addition integer of 1 is -1
Question no – (2)
Solution :
(i) Given, -42
∴ The successor of -42 is
= -42 + 1
= -41
Hence, -41 is the successor.
(ii) Given, -1
∴ The successor of -1 is
= -1 + 1
= 0
Thus, 0 is the successor.
(iii) Given, 0
∴ The successor of 0 is
= 0 + 1
= 1
Therefore, 1 is the successor.
(iv) Given, -200
∴ The successor of -200 is
= -200 + 1
= -199
Hence, -199 is the successor.
(v) Given, -99
∴ The successor of –99 is
= -99 + 1
= -98
Thus, -98 is the successor.
Question no – (3)
Solution :
(i) Given, 0
∴ The predecessor of 0 is
= 0 – 1
= -1
Therefore, -1 is the predecessor.
(ii) Given, 1
∴ The predecessor of 1 is
= 1 – 1
= 0
Hence, 0 is the predecessor.
(iii) Given, -1
∴ The predecessor of – 1 is
= – 1 – 1
= -2
Thus, -2 is the predecessor.
(iv) Given, -125
∴ The predecessor of -125 is
= -125 – 1
= -126
Therefore, -126 is the predecessor.
(v) Given, 1000
∴ The predecessor of 1000 is
= 1000 – 1
= 999
Hence, 999 is the predecessor.
Question no – (4)
Solution :
(i) Given statement is True.
(ii) Given statement is False.
(iii) Given statement is False.
(iv) Given statement is False.
(v) Given statement is False.
Question no – (5)
Solution :
The integers whose absolute value is less than 5 are -4, -3, -2, -1, 0, 1, 2, 3, 4.
Question no – (6)
Solution :
(i) Given,|4 + 2| = |4| + |2|
∴ L.H.S |4 + 2|
= 161
= 6
∴ R.H.S |4| + |2|
= 4 + 2
= 6
∴ It is True.
(ii) Given, |2 – 4| = |2| + |4|
∴ L.H.S = |-2 – 4|
= | -2|
= 2
∴ R.H.S = |2| + |4|
= 2 + 4
= 6
∴ It is False
(iii) Given, |4 – 2| = |4| – |2|
∴ L.H.S = |4 – 2|
= 2
∴ R.H.S = |4| – |2|
= 4 – 2
= 2
∴ It is True.
(iv) Given, |(2) + (- 4) | = |- 2| + |4|
∴ L.H.S
|(- 2) + (- 4)|
= |2 + 4|
= 6
∴ R.H.S
|- 2| + |- 4| = 2 + 4 = 6
∴ It is True
Question no – (8)
Solution :
(i) x + 1 = 0
= x + 1 – 1
∴ x = – 1
(ii) x + 5 = 0
= x + 5 – 5 = 0 – 5
∴ x = – 5
(iii) – 3 + x = 0
= – 3 + 3 + x = 0 + 3
∴ x = 3
(iv) x + (-8) = 0
= x – 8 + 8 = 0 + 8
∴ x = 8
(v) 7 + x = 0
= 7 + x – 7 = 0 – 7
= x = – 7
(vi) x + 0 = 0
∴ x = 0
Negative Numbers and Integers Exercise 5.4 Solution
Question no – (1)
Solution :
(i) Given, 12, -5
= – 5 – 12
= – 17
(ii) Given, -12, 8
= 8 – (-12)
= 8 + 12
= 20
(iii) Given, -225, -135
∴ -135 – (-225)
= -135 + 225
= 90
(iv) Given, 1001, 101
= 101 – 1001
= -900
(v) Given, -812, 3126
= 3126 – (-812)
= 3126 + 812
= 3938
(vi) Given, 7560, -8
= -8 – 7560
= -7568
(vii) Given, -3978, -4109
= – 4109 – (- 3978)
= -131
(viii) Given, 0, -1005
= -1005 – 0
= -1005
Question no – (2)
Solution :
(i) Given, -27 – (-23)
= -27 + 23
= -4
Hence, the value is -4
(ii) Given, -17 – 18 – (-35)
= -17 – 18 + 35
= -35 + 35
= 0
Therefore, the value is 0
(iii) Given, -12 – (-5) – (-125) + 270
= -12 + 5 + 125 + 270
= 388
Thus, the value is 388
(iv) Given, 373 + (-245) + (-373) + 145 + 3000
= 373 – 245 – 373 + 145 + 3000
= 3145 – 245
= 2900
Therefore, the value is 2900.
(v) Given, 1 + (-475) + (-475)+ (-475) + (-475) + 1900
= 1 – 950 – 950 + 1900
= 1
So, the value is 1.
(vi) Given, (-1) + (-304) + 304 + 304 (-304) + 1
= -1 + 1 – 304 + 304 – 304 + 304
= 0
Therefore, the value is 0.
Question no – (3)
Solution :
Sum = (-5020 + 2320)
= -2700
Now, -709 – (-2700)
= -709 + 2700
= 1991
Question no – (4)
Solution :
1st the sum,
= (-1250 + 1138)
= -112
and, (1136 – 1272) = -136
∴ We get,
= -136 – (-112)
= -136 + 112
= -24
Question no – (5)
Solution :
1st the sum
= (233 – 147)
= 86
Now, the subtract,
= 86 – (-284)
= 86 + 284
= 370
Question no – (6)
Solution :
In the given question,
Sum of two integers = 238
One of the integers = 122
Other integer = ?
∴ Other integers,
= – (-122) + 238 ‘
= + 122 + 238
= 360
Therefore, the other integer will be 360.
Question no – (7)
Solution :
In the given question,
Sum of two integers is = -223
One integers = 172
Other integers = ?
∴ Other integer,
= -233 – 172
= -395
Therefore, the other integers will be -395.
Question no – (8)
Solution :
(i) Given, -8 – 24 + 31 – 26 – 28 + 7 + 19 – 18 – 8 + 33
∴ -32 – 26 – 28 – 26 + 38 + 19 + 33
= 6 – 26 – 28 + 7 + 19
= 6 – 28 – 26 + 7 + 19
= -22
Question no – (9)
Solution :
Given, 1 – 2 + 3 – 4 + 5 – 6 __ + 15 – 16
= 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10 + 11 – 12 + 13 – 14 + 15 – 16
= -1 – 1 – 1 – 1 – 1 – 1 – 1 – 1
= -8
Question no – (10)
Solution :
(i) if the number of terms is 10.
If the number of than is 10.
We get
= 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (- 5) + 5 + 5 (- 5)
= 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5
= 0
(ii) if the number of terms is 11.
If the number of terms is 11
= 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5
= 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 + 5 – 5 + 5
= 5
Question no – (11)
Solution :
(i) (- 6) + (- 9) * (- 6) – (- 9)
= (-6) + (-9) < (-6) – (-9)
(ii) (-12) – (-2) * (- 12) + (-12)
= (-12) – (-12) > (-12) + (-12)
(iii) (- 20) – (- 20) * 20 – (65)
= (-20) – (-20) > 20 – (65)
(iv) 28 – (-10) * (-16) – (-76)
= 28 – (-10) < (-16) – (-76)
Question no – (12)
Solution :
(i) 4 △ 3
= -4 + 3 – (-2)
= 1
(ii) (-2) △ (-3)
= -(-2) + (-3) – (-2)
= 1
(iii) 6 △ (-5)
= -6 (-5) – (-2)
= 9
(iv) (-5) △ 6
= -(-5) + 6 – (-2)
= 13
Question no – (13)
Solution :
Here, a + 1 = b
= a – b
= -1
Therefore, the value of a – b is -1.
Question no – (14)
Solution :
Here,
= a – 1 = b
= a – b = 1
Therefore, the value of a – b is 1.
Question no – (15)
Solution :
(i) -13 > – 8 (- 2)
= This statement is False.
(ii) -4 + (- 2) < 2
= This statement is True.
(iii) The negative of a negative integer is positive.
= This statement is True.
(iv) If a and b are two integers such that a > b, then a – b is always a positive integer.
= This statement is True.
(v) The difference of two integers is an integer.
= This statement is True.
(vi) Additive inverse of a negative integer is negative,
= This statement is True.
(vii) Additive inverse of a positive integer in negative,
This statement is True.
(vii) Additive inverse of a negative integer is positive.
= This statement is True.
Question no – (16)
Solution :
(i) -7 + 7 = 0
(ii) 29 + (-29) = 0
(iii) 132 + (-132) = 0
(iv) -14 + 36 = 22
(v) -1256 + 514 = -742
(vi) –3305 – 1234 = -4359
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