Exercise 1.6 - Chapter 1 Number Systems Term 1 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question $1 .$
What should be added to $-1$ to get 10 ?
Solution:
$(-1)+$ a number $=10$
$\therefore$ The number $=10+1=11$

Question $2 .$

Question $3 .$
Substract 94860 from (-86945)
Solution:
$-86945-(94860)=-86945+($ Additive inverse of 94860$)$
$=-86945+(-94860)=-1,81,805$
 

Question $4 .$
Find the value of $(-25)+60+(-95)+(-385)$
Solution:
$(-25)+60+(-95)+(-385)=35+(-95)+(-385)=-60+(-385)=-445$

Question $5 .$
Find the sum of $(-9999)(-2001)$ and $(-5999)$.
Solution:
$(-9999)+(-2001)+(-5999)=-12,000+(-5999)=-17,999$

Question $6 .$
Find the product of $(-30) \times(-70) \times 15$
$(-30) \times(-70) \times 15=(+2100) \times 15=31,500$

Question $7 .$
Divide- 72 by $8 .$
Solution:
$\frac{-72}{8}=-9$

Question $8 .$
Find two pairs of integers whose product is $+15$.
Solution:
(i) $(+3) \times(+5)$
(ii) $(-3) \times(-5)$

Question $9 .$
Check the following for equality.
(i) $(11+7)+10$ and $11+(7+10)$
(ii) $(8-13) \times 7$ and $8-(13 \times 7)$
(iii) $[(-6)-(+8)] \times(-4)$ and $(-6)-[8 \times(-4)]$
(iv) $3 \times[(-4)+(-10)]$ and $[3 \times(-4)+3 \times(-10)]$

Solution:
(i) LHS $=(11+7)+10=18+10=28$
$\mathrm{RHS}=11+(7+10)$
$=11+(17)=28$
$\mathrm{LHS}=\mathrm{RHS}$
$\therefore(11+7)+10=11+(7+10)$
(ii) $\mathrm{LHS}=(8-13) \times 7=-5 \times 7=-35$
RHS $=8-(13 \times 7)=8-91=-83$
$\mathrm{LHS} \neq \mathrm{RHS}$
$\therefore(8-13) \times 7 \neq 8-(13 \times 7)$
(iii) $\mathrm{LHS}=[(-6)-(+8)] \times(-4)=[(-6)+(-8)] \times(-4)=(-14) \times(-4)=+56$
$\mathrm{RHS}=(-6)-[8 \times(-4)]=-6-(-32)$
$=-6+(+32)=+26$
$\therefore[(-6)-(+8)] \times(-4) \neq(-6)-[8 \times(-4)]$ $\mathrm{LHS} \neq \mathrm{RHS}$ $\therefore[(-6)-(1)$
(iv) $\mathrm{LHS}=3 \times[(-4)+(-10)]=3 \times(-14)=-42$
RHS $=[3 \times(-4)+3 \times(-10)]=(-12)+(-30)=-42$
$\mathrm{LHS}=\mathrm{RHS}$
$3 \times[(-4)+(-10)]=[3 \times(-4)+3 \times(-10)]$

Question 10 .
Kalaivani had ₹ 5000 in her bank account on $01.01 .2018$. She deposited ₹ 2000 in January and withdrew ₹ 700 in February. What was Kalaivani's bank balance on $01.04 .2018$, if she deposited ₹ 1000 and withdraw ₹ 500 in March.
Solution:
Initial bank balance $=₹ 5000$; Total deposits: January : $₹ 2000$; March : $₹ 1000$
Total deposits upto March $=₹ 5000+₹ 2000+₹ 1000=₹ 8000$
Amount withdrawn: February : ₹ $700(-)$
March: ₹ $500(-)$
$\therefore$ Total amount withdrawn $=(-700)+(-500) ₹-1200$
Net bank balance $=₹ 8000-₹ 1200=₹ 6800$

Question $11 .$
The price of an item $x$ increases by $₹ 10$ every year and an item y decreases by $₹ 15$ every year. If in 2018 , the price of $x$ is ₹ 50 andy is ₹ 90 , then which item will be costlier in the year $2020 ?$
Solution:
Amount increases for $\mathrm{x}$ every year $=₹ 10$.
Price ofx in $2018=₹ 50$; Price of $x$ in $2019=₹ 50+₹ 10=₹ 60$
Price of $x$ in $2020=₹ 60+₹ 10=₹ 70$ Amount decreases for y per year $=₹ 15$
Price of $\mathrm{y}$ in $2018=₹ 90$
Price of y in $2019=₹ 90-₹ 15=₹ 75$
Price of y in $2020=₹ 75-₹ 15=₹ 60$
Here $70>60$. Item $x$ will costlier in year 2020 .
 

Question $12 .$
Match the statements in Column A and Column B.

Solution:
1. $-\mathrm{d}$
2. $-\mathrm{a}$
3. $-\mathrm{e}$
4. $-\mathrm{c}$
5. $-\mathrm{b}$

Challenge Problems
Question $13 .$
Say True or False.
(i) The sum of a positive integer and a negative integer is always a positive integer.
(ii) The sum of two integers can never be zero
(iii) The product of two negative integers is a positive integer.
(iv) The quotient of two integers having opposite sign is a negative integer.
(v) The smallest negative integer is $-1$.
Solution:
(i) False
(ii) False
(iii) True
(iv) True
(v) False
 

Question $14 .$
An integer divided by 7 gives a result $-3$. What is that integer?
Solution:
According to the problem $\frac{\text { An integer }}{7}=-3$
$\therefore$ The integer $=-3 \times 7$
The required integer $=-21$.

Question $15 .$

Question $16 .$
Can you give 10 pairs of single digit integers whose sum is zero?
Solution:
$1+(-1)+2+(-2)+3+(-3)+4+(-4)+5+(-5)=0$

Question $17 .$
If $\mathrm{P}=-15$ and $\mathrm{Q}=5$ find $(\mathrm{P}-\mathrm{Q})-(\mathrm{P}+\mathrm{Q})$.
Solution:
Given $\mathrm{P}=15 ; \mathrm{Q}=5$
$(P-Q) \div(P+Q)=\frac{(-15)-5}{(-15)+5}=\frac{(-15)+(-5)}{-10}=\frac{-20}{-10}=2$

Question 18 .
If the letters in the English alphabets A to M represent the number from 1 to 13 respectively and N represents 0 and the letters $\mathrm{O}$ to $\mathrm{Z}$ correspond from $-1$ to $-12$, find the sum of integers for the names given below. For example,
MATH $\rightarrow$ Sum $\rightarrow 13+1-6+8=16$
(i) YOUR NAME
(ii) SUCCESS
Solution:
Given

(i) My name LEENA $\rightarrow 12+5+5+0+1=23$
(ii) SUCCESS $\rightarrow(-5)+(-7)+3+3+5+(-5)+(-5)$
$=-12+6+5+(-10)=-6+5+(-10)=(-1)+(-10)$
$=-11$
 

Question $19 .$
From a water tank 100 litres of water is used every day. After 10 days there is 2000 litres of water in the tank. How much water was there in the tank before 10 days?
Solution:
Water used for one day $=100$ litres.
Water used for 10 days $=100 \times 10=1000$ litres.
After 10 days water left in the tank $=2000$ litres
Initially amount of water will be $=2000+1000=3000$ litres
 

Question $20 .$
A dog is climbing down into a well to drink water. In each jump it goes down 4 steps. The water level is in 20 th step. How many jumps does the dog take to reach the water level?
Solution:
The water in the well is at 200 th step.
For each jump the dog goes low 4 steps. 5
$\therefore$ Number of jumps the dog to reach the water $=\frac{20}{4}=5$ jumps
 

Question $21 .$
Kannan has a fruit shop. He sells 1 dozen banana at a loss of ? 2 each because it may get rotten next day. What is his loss?
Solution:
1 dozen $=12$ bananas
For 1 banana loss $=₹ 2$
For 12 bananas loss $=₹ 2 \times 12=₹ 24$

Question $22 .$
A submarine was situated at 650 feet below the sea level. If it descends 200 feet, what is its new position?
Solution:
Position of submarine $=650$ feet below sea level $=-650$ feet
Again the depth it descends $=200$ feet below $=-200$ feet
$\therefore$ Position of submarine $=(-650)+(-200)=-850$ feet
The submarine will be 850 feet below the sea level.
 

Question $23 .$
In a magic square given below each row, column and diagonal should have the same sum. Find the values of $\mathrm{x}, \mathrm{y}$, and $\mathrm{z}$.

Solution:
Column total $=$ Row total $=$ diagonal total $\therefore 1+\mathrm{y}+(-6)=(-10)+(-3)+4$
$y+(-5)=-13+4$
$y=-9+5$
$y=-4$
So $1+(-10)+x=y+(-3)+(-2)$
$-9+x=(-4)+(-3)+(-2)$
$-9+x=-9$
$x=-9+9$
$x=0$
Now $x+(-2)+z=(-10)+(-3)+4$
$0+(-2)+z=(-13)+4$
$-2+z=-9$
$z=-9+2=-7$
$z=-7$
$\therefore \mathrm{x}=0, \mathrm{y}=-4, \mathrm{z}=-7$