Exercise 1.4
Question 1
(i) $(-36) \div(-9)$
$\begin{aligned}=+(36 \div 9) &=+4 \\ &=4 \end{aligned}$
(ii) $150 \div(-25)$
$=-(150+25)$
$=-6$
(iii) $(-270) \div 27$
$=-(270+27)$
=-10
(iv) $(-59)+(59)$
$=-(59 \div 59)$
=-1
(v) $0 \div(-17)$
$=0$
(vi) $(-784) \div(-56)$
$=+(784 \div 56)$
$=+14$
$=14$
Question 2
(i) $13 \div[(-2)+1]$
$=13 \div[-2+1]$
$=13 \div[-1]$
$=-[13 \div 1]$
=-13
(ii) $(-47) \div[(-45)+(-2)]$
$=(-47) \div[-45-2]$
$=(-47) \div(-47)$
$=+[47 \div 47]$
=1
(iii) $[(-6)+5] \div[(-2)+1]$
$=[-6+5] \div[-2+1]$
$=(-1) \div(-1)$
=1
(iv) $[(-48) \div(-6)] \div(-2)$
$=[+(48 \div 6)] \div(-2)$
$=[8] \div(-2)$
$=-[8+2]$
=-4
Question 3
$(a+b) \div c$
$=[(-225) \div 15] \div(-3)$
$=[-(225 \div 15)] \div(-3)$
$=(-15) \div(-3)$
$=+(15+3)$
$=5$
$a \div(b+c)$
$=(-225) \div(15 \div(-3))$
$=(-225) \div(-(15 \div 3))$
$=(-225) \div(-5)$
$=+(225 \div 5)$
=45
$5 \neq 45$
Verified
Question 4
(i)
$\begin{aligned} & a \div(b+c) \\=&(-10) \div(1+1) \\=&(-10) \div(2) \\=&-(10 \div 2) \\=&-5 \end{aligned}$
$(a \div b)+(a \div c)$
$=(-10+1)+(-10 \div 1)$
$\equiv-10+(-10)$
$=-10-10$
$=-20$
$-5 \neq-20$
$\therefore$ verified
(ii)
$\begin{aligned} & a \div(b+c) \\=& 12\div(1+(-2)) \\=& 12 \div(1-2) \\=& 12+(-1) \\=&-(12 \div 1) \quad ; \\=&-12 \end{aligned}$
$(a \div b)+(a \div c)$
$=(12 \div 1)+(12 \div(-2))$
$=12+[-(12 \div 2)]$
=$12+[-6]$
=$12-6$
=6
$-12 \neq 6$
verified.
Question 5
We know $a \div a=1 \quad-a \div a=-1$
i) $239 \div 239=1$
ii) $(-85) \div 85=-1$
iii) $(-213) \div(-213)=1$
iv) $(-43) \div(-1)=43$
v) $(-84) \div(-21)=4$
vi) $(-66) \div 22=-3$
Question 6
$a \div b=-3$
$\frac{a}{b}=-3 \Rightarrow a=-3 b$
$b=1 ; a=-3 \times 1=-3$
$b=2 ; a=-3 \times 2=-6$
$b=3 ; a=-3 \times 3=-9$
$b=4: a=-3 \times 4=-12$
$b=5 ; a=-3 \times 5=-15$
∴ Five p;airs are $(-3,1)(-6,2)(-9,3)(-12, 4)(-15,5)$
Question 7
(i) Marks Scored for 14 Correct answer = $14 \times 3=42$
Sachin's Score = 24
∴ Marks obtained for incorrect answer $=-42+24$
=-18
∴ The number of incorrect answer = $(-18) \div(-2)$
=9
(ii) Marks Scored for 9 correct answers $=9 \times 3$
$=27$
Nalini's Score = -7
Marks obtained for incorrect answers = $-7-27$
$-34$
Marks given for one incorrect answer = -2
∴ The number of incorrect answer = $(-34) \div(-2)$
$=3 4+2$
=17
Question 8
Elevator descends at a rate of $6 \mathrm{~m} / \mathrm{min}$.
Descend starts from 10m above ground level
It has to reach the shaft 350m below ground level
Total 360 m it has to reach
$\begin{aligned} \text { Time } &=\frac{\text { Distance }}{\text { speed }} \\ &=\frac{360}{6} \\ &=60 \mathrm{~min} \end{aligned}$
$\therefore$ Time $=1$ hour
$\therefore$ It will take 1hour to reach the shaft
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