KnowledgeBoat Logo
|
OPEN IN APP

Chapter 1

Integers - Exercise 1(D)

Class - 7 RS Aggarwal Mathematics Solutions

Exercise 1(D)

Question 1

Simplify:

5 {(-6) + (12 ÷ 4)}

Answer

Given expression:

5 {(-6) + (12 ÷ 4)}
= 5 {(-6) + 3} \quad [Simplifying ( )]
= 5 x -3 \quad [Simplifying { }]
= -15

The answer is -15

Question 2

Simplify:

10 - {56 ÷ (-16 + 9)}

Answer

Given expression:

10 - {56 ÷ (-16 + 9)}
= 10 - {56 ÷ (-7)} \quad [Simplifying ( )]
= 10 - (-8) \quad [Simplifying { }]
= 10 + 8 \quad [Removing ( )]
= 18

The answer is 18

Question 3

Simplify:

(-6) - {(-28) ÷ (-7)}

Answer

Given expression:

(-6) - {(-28) ÷ (-7)}
= (-6) - {4} \quad [Simplifying ÷]
= (-6) - 4 \quad [Removing { }]
= -6 - 4 \quad [Removing ( )]
= -10

The answer is -10

Question 4

Simplify:

8−{12−(9−7−4‾)}8 - \text{\textbraceleft}12 - (9 - \overline{7 - 4})\text{\textbraceright}

Answer

Given expression:

8−{12−(9−7−4‾)}8 - \text{\textbraceleft}12 - (9 - \overline{7 - 4})\text{\textbraceright}

=8−{12−(9−3)}[Removing bar]=8−{12−6}[Removing ( )]=8−6=2[Removing { }]= 8 - \text{\textbraceleft}12 - (9 - 3)\text{\textbraceright} \quad \text{[Removing bar]} \\[1em] = 8 - \text{\textbraceleft}12 - 6\text{\textbraceright} \quad \text{[Removing ( )]} \\[1em] = 8 - 6 = 2 \quad \text{[Removing \text{\textbraceleft} \text{\textbraceright}]}

The answer is 2

Question 5

Simplify:

11−[(−8)−{10−(9−7−4‾)}]11 - [(-8) - \text{\textbraceleft}10 - (9 - \overline{7 - 4})\text{\textbraceright}]

Answer

Given expression:

11−[(−8)−{10−(9−7−4‾)}]11 - [(-8) - \text{\textbraceleft}10 - (9 - \overline{7 - 4})\text{\textbraceright}]

=11−[(−8)−{10−(9−3)}][Removing bar]=11−[(−8)−{10−6}][Simplifying ( )]=11−[(−8)−4][Simplifying { }]=11−[−12][Removing ( )]=11+12=23[Removing [ ]]= 11 - [(-8) - \text{\textbraceleft}10 - (9 - 3)\text{\textbraceright}] \quad \text{[Removing bar]} \\[1em] = 11 - [(-8) - \text{\textbraceleft}10 - 6\text{\textbraceright}] \quad \text{[Simplifying ( )]} \\[1em] = 11 - [(-8) - 4] \quad \text{[Simplifying \text{\textbraceleft} \text{\textbraceright}]} \\[1em] = 11 - [-12] \quad\text{[Removing ( )]} \\[1em] = 11 + 12 = 23 \quad \text{[Removing [ ]]}

The answer is 23

Question 6

Simplify:

(−9)−[(−5)−{11−(8−5−2‾)}](-9) - [(-5) - \text{\textbraceleft}11 - (8 - \overline{5 - 2})\text{\textbraceright}]

Answer

Given expression:

(−9)−[(−5)−{11−(8−5−2‾)}](-9) - [(-5) - \text{\textbraceleft}11 - (8 - \overline{5 - 2})\text{\textbraceright}]

=(−9)−[(−5)−{11−(8−3)}][Removing bar]=(−9)−[(−5)−{11−5}][Simplifying ( )]=(−9)−[(−5)−6][Simplifying { }]=(−9)−[−11][Removing ( )]=−9+11=2[Removing [ ]]= (-9) - [(-5) - \text{\textbraceleft}11 - (8 - 3)\text{\textbraceright}] \quad\text{[Removing bar]} \\[1em] = (-9) - [(-5) - \text{\textbraceleft}11 - 5\text{\textbraceright}] \quad\text{[Simplifying ( )]} \\[1em] = (-9) - [(-5) - 6] \quad\text{[Simplifying \text{\textbraceleft} \text{\textbraceright}]} \\[1em] = (-9) - [-11] \quad\text{[Removing ( )]} \\[1em] = -9 + 11 = 2 \quad\text{[Removing [ ]]}

The answer is 2

Question 7

Simplify:

10−[8−{11+30÷(4−5−7‾)}]10 - [8 - \text{\textbraceleft}11 + 30 ÷ (4 - \overline{5 - 7})\text{\textbraceright}]

Answer

Given expression:

10−[8−{11+30÷(4−5−7‾)}]10 - [8 - \text{\textbraceleft}11 + 30 ÷ (4 - \overline{5 - 7})\text{\textbraceright}]

=10−[8−{11+30÷(4−(−2))}][Removing bar]=10−[8−{11+30÷(6)}][Simplifying ( )]=10−[8−{11+5}][Simplifying ÷]=10−[8−16][Simplifying { }]=10−[−8][Simplifying [ ]]=10+8=18[Removing [ ]]= 10 - [8 - \text{\textbraceleft}11 + 30 ÷ (4 - (-2))\text{\textbraceright}] \quad\text{[Removing bar]} \\[1em] = 10 - [8 - \text{\textbraceleft}11 + 30 ÷ (6)\text{\textbraceright}] \quad\text{[Simplifying ( )]} \\[1em] = 10 - [8 - \text{\textbraceleft}11 + 5\text{\textbraceright}] \quad\text{[Simplifying ÷]} \\[1em] = 10 - [8 - 16] \quad\text{[Simplifying \text{\textbraceleft} \text{\textbraceright}]} \\[1em] = 10 - [-8] \quad\text{[Simplifying [ ]]} \\[1em] = 10 + 8 = 18 \quad\text{[Removing [ ]]}

The answer is 18

PrevNext