Q1. Divide:
(i) 102 by 17
(ii) -85 by 5
(iii) -161 by -23
(iv) 76 by -19
(v) 17654 by -17654
(vi) (-729) by (-27)
(vii) 21590 by -10
(viii) 0 by -135
Sol. (i) Given 102 by 17
$$ = 102 \div 17 = \frac {|102 |}{| 17|}=\frac {102}{ 17} =6 $$(ii) Given -85 by 5
$$ = -85 \div 5 = – \frac {|-85 |}{| 5|}= – \frac {85}{ 5} =-17 $$(iii) Given -161 by -23
$$ = -161 \div -23 = \frac {|-161 |}{|-23|}= \frac {161}{23} =7 $$(iv) Given 76 by -19
$$ = 76 \div -19 = -\frac {|76 |}{|-19|}= -\frac {76}{19} = -4 $$(v) Given 17654 by -17654
$$ = 17654 \div (-17654) = – \frac {|17654 |}{| -17654|}= – \frac {17654}{17654} =-1 $$(vi) Given (-729) by (-27)
$$ = (-729) \div (-27) = \frac {|-729 |}{| -27|}=\frac {729}{27} =27 $$(vii) Given 21590 by -10
$$ = 21590 \div (-10) = – \frac {|21590 |}{|-10 |}= -\frac {21590}{10} =- 2159 $$(viii) Given 0 by -135
$$ = 0 \quad \quad [\because \text {0 divided by anything is 0}] $$Q2. Fill in the blanks:
$$ (i) \quad 296 \div \ldots=-148 $$ $$ (ii) \quad -88 \div \ldots=11 $$ $$ (iii) \quad 84 \div \ldots=12 $$ $$ (iv) \quad \cdots \ldots \ldots \div -5=25 $$ $$ (v) \quad \ldots \ldots \div 156=-2 $$ $$ (vi) \quad \ldots \ldots \ldots \div 567=-1 $$Sol. Lets assume x is the missing number.
$$ (i) Given \quad 296 \div \ldots=-148 $$ $$ \Rightarrow \quad 296 \div x=-148 $$ $$ \Rightarrow \quad x=296 \div -148 =- \frac {|296|}{|-148|} = – \frac {296}{148} = -2 $$$$ (ii) Given \quad -88 \div \ldots=11 $$ $$ \Rightarrow \quad -88 \div x =11 $$ $$ \Rightarrow \quad x=(-88) \div 11 =- \frac {|-88|}{|11|} = – \frac {88}{11} = -8 $$$$ (iii) Given \quad 84 \div \ldots=12 $$ $$ \Rightarrow \quad 84 \div x =12 $$ $$ \Rightarrow \quad x=(84) \div 12 = \frac {|84|}{|12|} = \frac {84}{12} = 7 $$$$ (iv) Given \quad \ldots \ldots \div -5=25 $$ $$ \Rightarrow \quad x \div (-5) = 25 $$ $$ \Rightarrow \quad x=(-5) \times 25 =- |-5| \times 25 = – (5 \times 25) =-125 $$$$ (v) Given \quad \ldots \ldots \div 156=-2 $$ $$ \Rightarrow \quad x \div 156=-2 $$ $$ \Rightarrow \quad x=(-2) \times 156 =- |-2| \times 156 = – (2 \times 156) =-312 $$$$ (vi) Given \quad \ldots \ldots \ldots \div 567=-1 $$ $$ \Rightarrow \quad x \div 567=-1 $$ $$ \Rightarrow \quad x=(-1) \times 567 =- |-1| \times 567 = – (1 \times 567) =-567 $$Q3. Which of the following statements are true?
$$ (i) \quad 0 \div 4=0 $$ $$ (ii) \quad 0 \div (-7)=0 $$ $$ (iii) \quad -15 \div 0=0 $$ $$ (iv) \quad 0 \div 0=0 $$ $$ (v) \quad (-8) \div (-1)=-8 $$ $$ (vi) \quad -8 \div (-2)=4 $$Sol. (i) True
(ii) True
$$ \text {(iii) False } \quad [\because \text {anything divided by 0 is meaningless or undefined}] $$ $$ \text {(iv) False } \quad [\because \text {anything divided by 0 is meaningless or undefined}] $$(v) False
(vi) True
(i) 102 by 17
(ii) -85 by 5
(iii) -161 by -23
(iv) 76 by -19
(v) 17654 by -17654
(vi) (-729) by (-27)
(vii) 21590 by -10
(viii) 0 by -135
Sol. (i) Given 102 by 17
$$ = 102 \div 17 = \frac {|102 |}{| 17|}=\frac {102}{ 17} =6 $$(ii) Given -85 by 5
$$ = -85 \div 5 = – \frac {|-85 |}{| 5|}= – \frac {85}{ 5} =-17 $$(iii) Given -161 by -23
$$ = -161 \div -23 = \frac {|-161 |}{|-23|}= \frac {161}{23} =7 $$(iv) Given 76 by -19
$$ = 76 \div -19 = -\frac {|76 |}{|-19|}= -\frac {76}{19} = -4 $$(v) Given 17654 by -17654
$$ = 17654 \div (-17654) = – \frac {|17654 |}{| -17654|}= – \frac {17654}{17654} =-1 $$(vi) Given (-729) by (-27)
$$ = (-729) \div (-27) = \frac {|-729 |}{| -27|}=\frac {729}{27} =27 $$(vii) Given 21590 by -10
$$ = 21590 \div (-10) = – \frac {|21590 |}{|-10 |}= -\frac {21590}{10} =- 2159 $$(viii) Given 0 by -135
$$ = 0 \quad \quad [\because \text {0 divided by anything is 0}] $$Q2. Fill in the blanks:
$$ (i) \quad 296 \div \ldots=-148 $$ $$ (ii) \quad -88 \div \ldots=11 $$ $$ (iii) \quad 84 \div \ldots=12 $$ $$ (iv) \quad \cdots \ldots \ldots \div -5=25 $$ $$ (v) \quad \ldots \ldots \div 156=-2 $$ $$ (vi) \quad \ldots \ldots \ldots \div 567=-1 $$Sol. Lets assume x is the missing number.
$$ (i) Given \quad 296 \div \ldots=-148 $$ $$ \Rightarrow \quad 296 \div x=-148 $$ $$ \Rightarrow \quad x=296 \div -148 =- \frac {|296|}{|-148|} = – \frac {296}{148} = -2 $$$$ (ii) Given \quad -88 \div \ldots=11 $$ $$ \Rightarrow \quad -88 \div x =11 $$ $$ \Rightarrow \quad x=(-88) \div 11 =- \frac {|-88|}{|11|} = – \frac {88}{11} = -8 $$$$ (iii) Given \quad 84 \div \ldots=12 $$ $$ \Rightarrow \quad 84 \div x =12 $$ $$ \Rightarrow \quad x=(84) \div 12 = \frac {|84|}{|12|} = \frac {84}{12} = 7 $$$$ (iv) Given \quad \ldots \ldots \div -5=25 $$ $$ \Rightarrow \quad x \div (-5) = 25 $$ $$ \Rightarrow \quad x=(-5) \times 25 =- |-5| \times 25 = – (5 \times 25) =-125 $$$$ (v) Given \quad \ldots \ldots \div 156=-2 $$ $$ \Rightarrow \quad x \div 156=-2 $$ $$ \Rightarrow \quad x=(-2) \times 156 =- |-2| \times 156 = – (2 \times 156) =-312 $$$$ (vi) Given \quad \ldots \ldots \ldots \div 567=-1 $$ $$ \Rightarrow \quad x \div 567=-1 $$ $$ \Rightarrow \quad x=(-1) \times 567 =- |-1| \times 567 = – (1 \times 567) =-567 $$Q3. Which of the following statements are true?
$$ (i) \quad 0 \div 4=0 $$ $$ (ii) \quad 0 \div (-7)=0 $$ $$ (iii) \quad -15 \div 0=0 $$ $$ (iv) \quad 0 \div 0=0 $$ $$ (v) \quad (-8) \div (-1)=-8 $$ $$ (vi) \quad -8 \div (-2)=4 $$Sol. (i) True
(ii) True
$$ \text {(iii) False } \quad [\because \text {anything divided by 0 is meaningless or undefined}] $$ $$ \text {(iv) False } \quad [\because \text {anything divided by 0 is meaningless or undefined}] $$(v) False
(vi) True