NCERT Solution class 7 Mathematics Exercise 1.1
Exercise – 1.1
Q1. Following number line shows the temperature in degree Celsius (0C) at different places on a particular day .
SOLUTION:-
(A) Observe this number line and write the temperature of the places marked on it .
SOLUTION:-
By observing the number line we can find the temperature of the cities as follows,
Temperature at the lahulspiti is -80C
Temperature at the Srinagar is -2oC
Temperature at the shimla is 50C
Temperature at the bengaluru is 22oC
(B) What is the temperature difference between hottest and coldest places among the above?
SOLUTION:-
From the number line we observe that ,
The temperature at the hottest places bengaluru is 220C
The temperature at the coldest places lahulspiti -80C
Temperature difference between hottest and coldest place is = 22oC – (-8oC)
= 22OC + 8OC
= 300C
(C) What is the temperature difference between lahulspiti and Srinagar ?
SOLUTION:-
From the given number line
The temperature at the Srinagar is -20C
The temperature at the lahulspiti -80C
The temperature difference between lahulspiti and Srinagar is = -20C – (-80C)
= -2OC + 8OC
= 6OC
(D) Can we say temperature of Srinagar taken together is less than the the temperature at shimla ? Is it also less than the temperature at Srinagar ?
SOLUTION:-
From the given number line
The temperature at Srinagar = -20C
The temperature at shimla = 50C
The temperature of srinagar and shimla taken together is = – 2oC + 5OC
= 30C
50C > 30C
So the temperature of Srinagar and shimla taken together is less than the temperature at shimla.
Then,
30C > -20C
No , the temperature of Srinagar and shimla taken together is not less than the temperature of Srinagar .
Q2. In a quiz positive marks are given for correct answers and negative marks given for the wrong answers . If JACK scores in five successive rounds were 25,-5,-10,15 and 10 ,what was his total at the end ?
ANS – FROM THE QUESTION
JACK SCORED IN FIVE SUCCESSIVE ROUNDS 25,-5,-10,15 and 10
2+(-5) +(-10)+15+10 = 35
Jack score a total at the end is 35
Q3. At Srinagar temperature was -5 degree Celsius on Monday and then it dropped by 2 degree Celsius on Tuesday .What was the temperature of Srinagar on Tuesday ? On Wednesday ,it rose by 4 degree Celsius . What was the temperature on this day ?
Ans- From the question
The temperature on Monday at Srinagar -5degree Celsius
Temperature on Tuesday at Srinagar dropped by 2 degree Celsius =Temperature on Monday -2 degree Celsius
= -5 degree Celsius – 2 degree Celsius
= -7 degree Celsius
Temperature on Wednesday at Srinagar is rose by 4 degree Celsius = Temperature on Tuesday + 4 degree Celsius
=-7 degree Celsius + 4 degree Celsius
=-3 degree celsius
Thus the temperature on Tuesday and wednesday was -7 degree Celsius and -3 degree celsius respectively
Q4. A plane is flying at the height of 5000m above the sea level . At a particular point, it is exactly above a submarine floating 1200m below the sea level . What is the vertical distance between them ?
Ans – From the question ,
Plane is flying at the height =5000m
Depth of submarine = -1200m
The vertical height between plane and submarine =5000m-(-1200)m
=5000m+1200m
=6200m
Q5. Mohan deposit Rs 2000 in his bank account and withdraws Rs 1642 from it ,the next day . If withdrawl of amount from the account is represented by the negative integer ,then how will you represent the amount deposited? Find the balance in mohan account after the withdrawal .
Ans – Withdrawl of amount is represented by a negative integer .
Then, deposits of amount to the account is represented by a positive integer.
From the questions ,
Total amount deposited in bank account by the mohan = Rs= 2000
Total Amount withdrawn from the bank account by the mohan =-1642
Balance in mohan account after the withdrawl =amount deposited +amount withdrawn =Rs2000 +(-Rs 1642)
=Rs 2000 –Rs 1642
=Rs 358
Hence, the balance in Mohan account after the withdrawal is Rs 358
Q6. Rita goes 20 km towards east from a point A to the point B. From B ,she moves 30km towards west along the same road .If the distance towards east is represented by the positive integers then, how will you represent the distance travelled towards west ? By which integer will you represents her final position from A?
Ans – From the questions , it is given that
Then , distance travelled towards the west will be represented by a negative integer.
Rita travels a distance in east direction =20km
Rita travels a distance in west direction =-30km
Distance travelled from A
= 20 + (-30)
=20-30
= -10Km
Hence ,we will represents the distance travelled by rita from point A by a negative integer , i.e. -10km
Q7. In a magic square each row , column and diagonal have the same sum. Check which of the following is a magic square.
| 5 | -1 | -4 |
| -5 | -2 | 7 |
| 0 | 3 | -3 |
|
Ans – First we consider the square .
(i)By adding the numbers in each rows we get ,
=5 +(-1)+(-4)= 5-1-4
=5-5=0
= -5 +(-2)+7 = -5-2+7
=-7+7 =0
= 0+3+(-3)=3-3 =0
By adding the numbers in each columns we get ,
= 5+(-2)+(-3)=5-2-3
=5-5=0
=-4+(-2)+0=-4-2=-6
Because sum of one diagonal is not equal to zero,
So,(i) is not a magic square
Now , we consider the square (ii)
By adding the numbers in each row we get ,
=1+(-10)+0 =1-10+0=-9
= (-4) +(-3)+(-2)=-4-3-2=-9
By adding the numbers in each column we get,
= 1+(-4)+(-6)=1-4-6
=1-10=-9
=(-10)+(-3)+4=-10-3+4=-13+4
=0+(-2)+(-7)=0-2-7
=-9
By adding the numbers in diagonals we get ,
=1+(-3)+(-7)=1-3-7
=1-10=-9
=0+(-3)+(-6)=0-3-6
=-9
This (iii) square is a magic square ,because sum of each row each column and diagonal is equal to -9.
Q8.Verify a-(-b)=a+b for the following values of a and b.
(i) a=21 , b=18
Solution :
From the questions ,
A = 21 b=18
To verify a-(-b)=a+b
Let us take left hand side (LHS) = a-(-b)
=21-(-18)
=21+18
=39
Now right hand side (RHS)
=A+B
=21+18
=39
By comparing LHS and RHS
LHS=RHS
39=39
Hence, the value of a and b is verified.
(ii) a=118 , b=125
Solution :- From the question ,
A=118 and b = 125
To verify a-(-b)=a+b
Let us take left hand side (LHS)=a-(-b)
=118-(-125)
=118+125
=243
Now , right hand side (RHS)=a+b
=118+125
=243
By comparing LHS and RHS
LHS=RHS
243=243
Hence , the value of a and b is verified