RS Aggarwal 2021-2022 for Class 6 Maths Chapter 4 - Integer
RS Aggarwal Class 6 Math Solution Chapter 4 - Integer Exercise 4A is available here. RS Aggarwal Class 6 Math Solutions are solved by expert teachers in step by step, which help the students to understand easily. RS Aggarwal textbooks are responsible for a strong foundation in Maths. These textbook solutions help students in exams as well as their daily homework routine. The solutions included are easy to understand, and each step in the solution is described to match the students’ understanding.
RS Aggarwal Class 6 Math Solution Chapter 4 - Integer
Exercise 4A
1. Write the opposite of each of the following:
(i) An increase of 8
(ii) A loss of Rs. 7
(iii) Gaining a weight of 5 kg.
(iv) 10 km above sea level.
(v) 5 oC below the freezing point.
(vi) A deposit of Rs. 100
(vii) Earning Rs. 500.
(viii) Going 6 km to the east
(ix) 24
(x) -34
Solution:
(i) A decrease of 8
(ii) A gain of Rs 7
(iii) Losing a weight of 5 kg
(iv) 10 km below the sea level
(v) 5 oC above the freezing point
(vi) A withdrawal of Rs 100
(vii) Spending Rs 500
(viii) Going 6 m to the west
(ix) The opposite of 24 is -24.
(x) The opposite of -34 is 34.
2. Indicate the following using ' + ' or ' - ' sign:
(i) A gain of Rs. 600
(ii) A loss of Rs. 800
(iii) 7 oC below the freezing point
(iv) Decrease of 9
(v) 2 km above sea level
(vi) 3 km below sea level
(vii) A deposit of Rs. 200
(viii) A withdrawal of Rs. 300
Solution:
(i) + Rs 600
(ii) - Rs 800
(iii) -7 oC
(iv) - 9
(v) + 2 km
(vi) - 3 km
(vii) + Rs 200
(viii) - Rs 300
3. Mark the following integers on a number line:
(i) -5
(ii) -2
(iii) 0
(iv) 7
(v) -13
Solution:
(i)
(4) Which number is larger in each of the following pairs.
(i) 0, -2
(ii) - 3, - 5
(iii) -5, 2
(iv) - 16, 8
(v) -365, -913
(vi) -888, 8
Solution:
(i) 0 > -2
Because zero is greater than every negative integer.
(ii) -3 > -5
Smaller negative number is always greater than bigger negative number
(iii) 2 > -5
Every positive integer is greater than every negative integer.
(iv) 8 > -16
Every positive integer is greater than every negative integer.
(v) -365 > -913
Smaller negative number is always greater than bigger negative number
(vi) 8 > -888
Every positive integer is greater than every negative integer.
(5) Which number is smaller in each of the following pairs.
(i) 6, -7
(ii) 0, -1
(iii) -13, -27
(iv) -26, 17
(v) -317, -603
(vi) -777, 7
Solution:
(i) -7 < 6
Every negative integer is smaller than every positive integer.
(ii) -1 < 0
Because negative integer is always smaller than zero
(iii) -27 < -13
Bigger negative number is always smaller than smaller negative number
(iv) -26 < 17
Every negative integer is smaller than every positive integer.
(v) -603 < -317
Bigger negative number is always smaller than smaller negative number
(vi) -777 < 7
Every negative integer is smaller than every positive integer.
(6) Write all integer between
(i) 0 and 6
(ii) -5 and 0
(iii) -3 and 3
(iv) -7 and -5
Solution:
(i) 1, 2, 3, 4, 5
(ii) -4, -3, -2, -1
(iii) -2, -1, 0, 1, 2
(iv) -6
(7) Fill in the blanks by appropriate symbol > or < :
(i) 0 ..... 7
(ii) 0 ..... -3
(iii) -5 .... -2
(iv) -15 .... 13
(v) -231 ..... -132
(vi) -6 .... 6
Solution:
(i) 0 < 7
This is because 0 is less than any positive integer.
(ii) 0 > -3
This is because 0 is greater than any negative integer.
(iii) -5 < -2
Bigger negative number is always smaller than smaller negative number
(iv) -15 < 13
Every positive integer is greater than every negative integer.
(v) -231 < -132
Bigger negative number is always smaller than smaller negative number
(vi) -6 < 6
Because every positive integer is greater than every negative integer.
(8) Write the following integer in the
(i) increasing order : 5, -7, -2, 0, 8
(ii) -23, 12, 0, -6, -100, -1
(iii) -17, 15, -363, -501, 165
(iv) 21, -106, -16, 16, 0, -2, -81
Solution:
(i) -7 < -2 < 0 < 5 < 8
(ii) -100 < -23 < -6 < -1 < 0 < 12
(iii) -501 < -363 < -17 < 15 < 165
(iv) -106 < -81 < -16 < -2 < 0 < 16 < 21
(9) Write the following integer in the decreasing order:
(i) 0, 7, -3, -9, -132, 36
(ii) 51, -53, -8, 0, -2
(iii) -71, -81, 36, 0, -5
(iv) -365, -515, 102, 413, -7
Solution:
(i) 36 > 7 > 0 > -3 > -9 > -132
(ii) 51 > 0 > -2 > -8 > -53
(iii) 36 > 0 > -5 > -71 > -81
(iv) 413 > 102 > -7 > -365 > -515
(10) Using the number line, write the integer which is
(i) 4 more than 6
(ii) 5 more than -6
(iii) 6 less than 2
(iv) 2 less than -3
Solution:
(i)
To get an integer that is 4 more than 6. We will start from 6 and proceed 4 steps to the right to obtain 10.
To get an integer that is 5 more than -6. We will start from -6 and proceed 5 steps to the right to obtain -1.
To get an integer that is 6 less than 2. We will start from 2 and proceed 6 steps to the left to obtain -4.
(i) The smallest integer is zero.
(ii) Zero is not an integer.
(iii) The opposite of zero is zero.
(iv) -10 is greater than -6.
(v) The absolute value of an integer is always greater than the integer.
(vi) 0 is larger then every negative integer.
(vii) Every negative integer is less than every natural number.
(viii) The successor of -187 is -188.
(ix) The predecessor of -215 is -214.
Solution:
(i) False
This is because 0 is greater than every negative integer.
(ii) False
Every whole number is an integer and 0 is a whole number.
(iii) True
0 is an integer that is neither positive nor negative. So, the opposite of zero is zero.
(iv) False
Bigger negative number is always smaller than smaller negative number
(v) True
An absolute value is a positive number. For example, -2 is an integer, but its absolute value is 2 and it is greater than -2.
(vi) True
This is because all negative integers are to the left of 0.
(vii) True
This is because natural numbers are positive and every positive integer is greater than every negative integer.
(viii) False
This is because the successor of -187 is equal to -186 (-186 + 1). In succession, we move from the left to the right along a number line.
(ix) False
This is because the predecessor of -215 is -216 (-216 - 1). To find the predecessor, we move from the right to the left along a number line.
(12) Find the value of
(i) | -9 |
(ii) | 36 |
(iii) | 0 |
(iv) | 15 |
(v) - | -13 |
(vi) 7 + | -3 |
(vii) | 7 - 4 |
(viii) 8 - | -7 |
Solution:
(i) The value of |-9| is 9
(ii) The value of |-36| is 36
(iii) The value of |0| is 0
(iv) The value of |15| is 15
(v) The value of |-3| is 3
(vi) 7 + |-3|
= 7 + 3 (The value of |-3| is 3)
= 10
(vii) |7 - 4|
= |3|
= 3 (The value of |3| is 3)
(viii) 8 - |-7|
= 8 - 7 (The value of |-7| is 7)
= 1
(13) (i) Write five negative integer greater than -7.
(ii) Write five negative integer less than -20.
Solution:
(i) Every negative integer that is to the right of -7 is greater than -7.
So, five negative integers that are greater than -7 are -6, -5, -4, -3, -2 and -1.
(ii) Every negative integer that is to the left of -20 is less than -20.
So, five negative integers that are less than -20 are -21, -22, -23, -24 and -25.
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