CBSE Class 6 > Class 6 Notes > Mathematics > RS Aggarwal Solutions: Integers (Exercise 6D)
RS Aggarwal Solutions: Integers (Exercise 6D)
Solution 1:
(i) 15 by 8
= 15 × 8
= 120
(ii) 16 by -9
= 16 × (-9)
= -144
(iii) (-20) by 15
= (-20) × 15
= -300
(iv) -18 by 11
= (-18) × 11
= -198
(v) (-27) by 1
= (-27) × 1
= -27
(vi) (-30) by (-1)
= (-30) × (-1)
= 30
(vii) (-13) by (-8)
= (-13) × (-8)
= 104
(viii) 36 by (-1)
= 36 × (-1)
= -36
(ix) 0 by (-6)
= 0 × (-6)
= 0
(x) (-40) by (-10)
= (-40) × (-10)
= 400
(xi) (-12) by (-12)
= (-12) × (-12)
= 144
(xii) (-1) by (-1)
= (-1) × (-1)
= 1
Solution 2:
= 15 × 8
= 120
(ii) 16 by -9
= 16 × (-9)
= -144
(iii) (-20) by 15
= (-20) × 15
= -300
(iv) -18 by 11
= (-18) × 11
= -198
(v) (-27) by 1
= (-27) × 1
= -27
(vi) (-30) by (-1)
= (-30) × (-1)
= 30
(vii) (-13) by (-8)
= (-13) × (-8)
= 104
(viii) 36 by (-1)
= 36 × (-1)
= -36
(ix) 0 by (-6)
= 0 × (-6)
= 0
(x) (-40) by (-10)
= (-40) × (-10)
= 400
(xi) (-12) by (-12)
= (-12) × (-12)
= 144
(xii) (-1) by (-1)
= (-1) × (-1)
= 1
Solution 2:
(i) (-3) × 4 × (-5)
= (-3 × 4) × (-5)
= -12 × (-5)
= 60
(ii) 3 × (-5) × (-6)
= {3 × (-5)} × (-6)
= (-15) × (-6)
= 90
(iii) (-8) × 5 × 3
= (-8 × 5) × 3
= (-40) × 3
= -120
(iv) 9 × 7 × (-10)
= (9 × 7) × (-10)
= 63 × (-10)
= -630
(v) (-5) × (-8) × (-9)
= {(-5) × (-8)} × (-9)
= 40 × (-9)
= -360
(vi) (-10) × (-11) × (-12)
= {(-10) × (-11)} × (-12)
= 110 × (-12)
= -1320
Solution 3:
= (-3 × 4) × (-5)
= -12 × (-5)
= 60
(ii) 3 × (-5) × (-6)
= {3 × (-5)} × (-6)
= (-15) × (-6)
= 90
(iii) (-8) × 5 × 3
= (-8 × 5) × 3
= (-40) × 3
= -120
(iv) 9 × 7 × (-10)
= (9 × 7) × (-10)
= 63 × (-10)
= -630
(v) (-5) × (-8) × (-9)
= {(-5) × (-8)} × (-9)
= 40 × (-9)
= -360
(vi) (-10) × (-11) × (-12)
= {(-10) × (-11)} × (-12)
= 110 × (-12)
= -1320
Solution 3:
(i) (-25) × 9 × (-4)
= (-25) × (-4) × 9
= 100 × 9
= 900
(ii) (-16) × (-20) × (-5)
= (-16) × (+100)
= -1600
(iii) (-15) × (-7) × (-20)
= (300) × (-7)
= -2100
(iv) 18 × (-25) × (-5)
= 18 × (-5) × (-25)
= (-90) × (-25)
= -2250
(v) (-35) × 21 × (-6)
= 210 × 21
= 4410
(vi) (-12) × (-9) × (-25)
= (-12) × (-25) × (-9)
= 300 × (-9)
= -2700
Solution 4:
= (-25) × (-4) × 9
= 100 × 9
= 900
(ii) (-16) × (-20) × (-5)
= (-16) × (+100)
= -1600
(iii) (-15) × (-7) × (-20)
= (300) × (-7)
= -2100
(iv) 18 × (-25) × (-5)
= 18 × (-5) × (-25)
= (-90) × (-25)
= -2250
(v) (-35) × 21 × (-6)
= 210 × 21
= 4410
(vi) (-12) × (-9) × (-25)
= (-12) × (-25) × (-9)
= 300 × (-9)
= -2700
Solution 4:
(i) 16 × {9 + (-5)} = (16 × 9) + 16 × (-5)
L.H.S.
16 × {9 + (-5)}
= 16 × 4
= 64
R.H.S.
(16 × 9) + 16 × (-5)
= 144 - 80
= 64
∴ L.H.S. = R.H.S.
Hence, verified.
(ii) 15 × {(-14) + (-6)} = 15 × (-14) + 15 × (-6)
L.H.S.
15 × {(-14) + (-6)}
= 15 × [-14 -6]
= 15 × (-20)
= -300
R.H.S.
15 × (-14) + 15 × (-6)
= -210 - 90
= -300
∴ L.H.S. = R.H.S.
Hence, verified.
(iii) (-12) × {(-8) + (-7)} = (-12) × (-8) + (-12) × (-7)
L.H.S.
= (-12) × {(-8 + (-7)}
L.H.S.
16 × {9 + (-5)}
= 16 × 4
= 64
R.H.S.
(16 × 9) + 16 × (-5)
= 144 - 80
= 64
∴ L.H.S. = R.H.S.
Hence, verified.
(ii) 15 × {(-14) + (-6)} = 15 × (-14) + 15 × (-6)
L.H.S.
15 × {(-14) + (-6)}
= 15 × [-14 -6]
= 15 × (-20)
= -300
R.H.S.
15 × (-14) + 15 × (-6)
= -210 - 90
= -300
∴ L.H.S. = R.H.S.
Hence, verified.
(iii) (-12) × {(-8) + (-7)} = (-12) × (-8) + (-12) × (-7)
L.H.S.
= (-12) × {(-8 + (-7)}
= (-12) × (-15)
= 180
R.H.S.
(-12) × (-8) + (-12) × (-7)
96 + 84
= 180
∴ L.H.S. = R.H.S.
Hence, verified.
Solution 5:
= 180
R.H.S.
(-12) × (-8) + (-12) × (-7)
96 + 84
= 180
∴ L.H.S. = R.H.S.
Hence, verified.
Solution 5:
(i) (-9) × 6 + (-9) × 4
= (-9) × (6 + 4)
= (-9) × 10
= -90
(ii) 20 × (-17) + 20 × 14
= 20 × {(-17) + 14}
= 20 × (-3)
= -60
(iii) (-15) × (-14) + (-15) (-6)
= (-15) x {-14 + (-6)}
= (-15) × (-20)
= 300
(iv) (-12) × 8 + (-12) × 7
= (-12) × (8 + 7)
= (-12) × 15
= -180
Solution 6:
= (-9) × (6 + 4)
= (-9) × 10
= -90
(ii) 20 × (-17) + 20 × 14
= 20 × {(-17) + 14}
= 20 × (-3)
= -60
(iii) (-15) × (-14) + (-15) (-6)
= (-15) x {-14 + (-6)}
= (-15) × (-20)
= 300
(iv) (-12) × 8 + (-12) × 7
= (-12) × (8 + 7)
= (-12) × 15
= -180
Solution 6:
Solution 7:
(i) True
(ii) False
(iii) True
(iv) False
(v) True
(ii) False
(iii) True
(iv) False
(v) True
The document RS Aggarwal Solutions: Integers (Exercise 6D) is a part of the Class 6 Course Mathematics for Class 6.
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FAQs on RS Aggarwal Solutions: Integers (Exercise 6D)
| 1. What are integers? |  |
Ans. Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals, and they are represented on a number line extending infinitely in both directions.
| 2. How do you add and subtract integers? | |
Ans. To add integers, if the signs are the same, you add their absolute values and keep the common sign. If the signs are different, you subtract the smaller absolute value from the larger one and take the sign of the larger absolute value. For subtraction, you can convert it to addition by changing the sign of the integer being subtracted.
| 3. What is the significance of zero in integers? | |
Ans. Zero is a unique integer that acts as the neutral element in addition. It means that adding zero to any integer does not change the value of that integer. It is also the dividing point between positive and negative integers on the number line.
| 4. Can you explain the multiplication of integers? | |
Ans. When multiplying integers, the product of two integers with the same sign is positive, while the product of two integers with different signs is negative. For example, 3 × 4 = 12 (positive) and 3 × -4 = -12 (negative).
| 5. How do you compare integers? | |
Ans. To compare integers, you can use the number line. If an integer is to the right of another on the number line, it is greater. Conversely, if it is to the left, it is smaller. For instance, -2 is greater than -5 because -2 is positioned to the right of -5 on the number line.
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