NCERT Solutions for Class 7 Maths Chapter 1 Integers (EX 1.1) Exercise 1.1

Q.1

$\begin{array}{l}\mathrm{Following}\mathrm{number}\mathrm{line}\mathrm{shows}\mathrm{the}\mathrm{temperature}\mathrm{in}\mathrm{degree}\\ \mathrm{celsius}(°\mathrm{C})\mathrm{at}\mathrm{different}\mathrm{places}\mathrm{on}\mathrm{a}\mathrm{particular}\mathrm{day}\\ \left(\text{a}\right)\text{Observe this number line and write the}\\ \text{temperature of the places marked on it}.\\ \left(\text{b}\right)\text{What is the temperature difference between the}\\ \text{hottest and the coldest places among the above}?\\ \left(\text{c}\right)\text{What is the temperature difference between Lahulspiti}\\ \text{and Srinagar}?\\ \left(\text{d}\right)\text{Can we say temperature of Srinagar and Shimla taken}\\ \text{together is less than the temperature at Shimla}?\\ \text{Is it also less than the temperature at Srinagar}?\end{array}$

Ans.

\begin{array}{l}\text{(a)}\text{By observing the number line, the temprature of the}\\ \text{places marked are as follows:}\\ \text{Lahulspiti:}-8°C\\ \text{Srinagar:}-2°C\\ \text{Shimla:}5°C\\ \text{Ooty:}14°C\\ \text{Banglore:}22°C\\ \\ \text{(b)}\text{The hottest place is Banglore with temprature}22°C\\ \text{and coldest place is Lahulspiti}\text{with temprature}-8°C\text{.}\\ \text{So},\text{the temperature difference between the hottest}\\ \text{and the coldest places is}\\ \text{=22}°\text{C}-\left(-8°\text{C}\right)\\ =22°\text{C}+8°\text{C}\\ =\boxed{30°\text{C}}\\ \\ (c)\text{The temperature difference between Lahulspiti and}\\ \text{Srinagar}\\ =-2°\text{C}-\left(-8°\text{C}\right)\\ =-2°\text{C}+8°\text{C}\\ =\boxed{6°\text{C}}\\ \\ (d)\text{The temprature of Srinagar and Shimla are}-2°C\\ \text{and}5°C.\\ \text{So, together their temprature would be}\\ -2°C+5°C=3°C\text{, which is less than temprature of Shimla}\\ \text{Thus, temprature of Srinagar and Shimla taken together}\\ \text{is less than the temprature at Shimla}\text{.}\\ \text{But, it is not less than temprature at Srinagar}\text{.}\end{array}

Q.2

$\begin{array}{l}\mathrm{In}\mathrm{a}\mathrm{quiz},\mathrm{positive}\mathrm{marks}\mathrm{are}\mathrm{given}\mathrm{for}\mathrm{correct}\mathrm{answers}\\ \mathrm{and}\mathrm{negative}\mathrm{marks}\mathrm{are}\mathrm{given}\mathrm{for}\mathrm{in}\mathrm{correct}\mathrm{answers}.\\ \mathrm{If}\mathrm{Jack}’\mathrm{s}\mathrm{scores}\mathrm{in}\mathrm{five}\mathrm{successive}\mathrm{rounds}\mathrm{were}\\ 25,–5,–10,15\mathrm{and}10,\mathrm{what}\mathrm{was}\mathrm{his}\mathrm{total}\mathrm{at}\mathrm{the}\mathrm{end}?\end{array}$

Ans.

\begin{array}{l}\text{Jack’s scores in five successive rounds were 25,}-5,-10,\\ \text{15 and and 10}\text{.}\\ \text{His total at the end would be}\\ \text{=25+}\left(-5\right)+\left(-10\right)+15+10\\ =50-15\\ =\boxed{35}\end{array}

Q.3

$\begin{array}{l}\text{At Srinagar temperature was-5°C on Monday and then}\\ \text{it dropped by2°C on Tuesday. What was the temperature}\\ \text{of Srinagar on Tuesday? On Wednesday, it rose by 4°C.}\\ \text{What was the temperature on this day?}\end{array}$

Ans.

$\begin{array}{l}\text{Temprature on Monday=}-5°C\\ \text{Since, temperature dropped by}2°C\text{on Tuesday}\text{.}\\ \text{So, the temperature of Srinagar on Tuesday was}\\ =-5°C-2°C\\ =\boxed{-7°C}\\ \text{On Wednesday, temperature rose by}4°C,\text{so temperature of}\\ \text{Srinagar on Wednesday was}\\ =-7°C+4°C\\ =\boxed{-3°C}\\ \text{Thus, Temperature on Tuesday and Wednesday was}\\ \boxed{-7°C\text{and}-3°C}\text{respectively}\text{.}\end{array}$

Q.4

$\begin{array}{l}\text{A plane is flying at the height of 5000 m above the sea}\\ \text{level. At a particular point, it is exactly above a submarine}\\ \text{floating 1200 m below the sea level. What is the vertical}\\ \text{distance between them?}\end{array}$

Ans.

\begin{array}{l}\text{Height of the plane = 5000 m}\\ \text{Depth of the submarine}=-1200\text{m}\\ \text{So, the distance between plane and submarine}\\ \text{=5000 m}-\left(-1200\text{m}\right)\\ =5000\text{m+1200 m}\\ \text{=}\boxed{\text{6200 m}}\\ \text{Thus, the vertical distance between them is 6200 m}\text{.}\end{array}

Q.5

$\begin{array}{l}\text{Mohan deposits Rs 2,000 in his bank account and}\\ \text{withdraws Rs 1,642 from it, the next day. If withdrawal}\\ \text{of amount from the account is represented by a negative}\\ \text{integer, then how will you represent the amount deposited?}\\ \text{Find the balance in Mohan’s account after the withdraw.}\end{array}$

Ans.

\begin{array}{l}\text{Since, withdrawal of amount from the account is represented}\\ \text{by a negative integer, so we take amount deposited as a positive}\\ \text{integer}\\ \text{Amount deposited = Rs 2000}\\ \text{Amount withdrawn}=-\text{Rs 1642}\\ \text{Balance left in Mohan’s account}\\ \text{= Rs 2000}-\text{Rs 1642}\\ \text{=}\boxed{\text{Rs 358}}\\ \text{Thus, the balance in Mohan’s account after withdrawal}\\ \text{is Rs 358}\text{.}\end{array}

Q.6

$\begin{array}{l}\text{Rita goes 20 km towards east from a point A to the point B.}\\ \text{From B, she moves 30 km towards west along the same road.}\\ \text{If the distance towards east is represented by a positive}\\ \text{integer then, how will you represent the distance travelled}\\ \text{towards west? By which integer will you represent her final}\\ \text{position from A?}\end{array}$

Ans.

\begin{array}{l}\text{Here, the distance towards east is represented by a positive}\\ \text{integer and the distance travelled towards west will be}\\ \text{represented by a negative integer}\text{.}\\ \text{So, distance travelled in east direction = 20 km}\\ \text{distance travelled in west direction =}-\text{30 km}\\ \text{Distance travelled from A = 20 km+}\left(-30\text{km}\right)\\ =-10\text{km}\\ \text{Thus, Rita’s distance travelled from point A}\text{​}\text{will be represented}\\ \text{by a negative integer}\left(-10\text{km}\right)\text{.}\\ \text{Rita is in west direction}\text{.}\end{array}

Q.7

$\begin{array}{l}\text{In a magic square each row, column and diagonal have the}\\ \text{same sum. Check which of the following is a magic square.}\end{array}$

Ans.

\begin{array}{l}\text{In a magic square, each row, column and diagonal have}\\ \text{the same sum}\text{.}\\ \text{So, in square (i), every row and column sum up to 0}\text{.}\\ \text{However sum of one of its diagonal is not zero}\text{.}\\ -4-2=-6\ne \text{0}\\ \text{So, (i) is not a magic square}\text{.}\\ \text{Similarly, in square (ii) every row, column and diagonal}\\ \text{sum up to}-\text{9}\text{.}\\ \text{Thus, (ii) is a magic square}\text{.}\end{array}

Q.8

$\begin{array}{l}\text{Verifya}-\left(-\text{b}\right)\text{=a+b for the following values of a and b.}\\ \left(\text{i}\right)\text{\hspace{0.17em}a=21,b=18}\left(\text{ii}\right)\text{\hspace{0.17em}a=118,b=125}\\ \left(\text{iii}\right)\text{a=75,b=84}\left(\text{iv}\right)\text{a=28,b=11}\end{array}$

Ans.

$\begin{array}{l}\left(\mathrm{i}\right)\text{\hspace{0.17em}a=21, b=18}\\ \mathrm{a}-(-\mathrm{b})=21-(-18)=21+18=39\\ \mathrm{a}+\mathrm{b}=21+18=39\\ \mathrm{Thus},\mathrm{a}-(-\mathrm{b})=\mathrm{a}+\mathrm{b}\\ \left(\mathrm{ii}\right)\text{\hspace{0.17em}a=118, b=125}\\ \mathrm{a}-(-\mathrm{b})=118-(-125)=118+125=243\\ \mathrm{a}+\mathrm{b}=118+125=243\\ \mathrm{Thus},\mathrm{a}-(-\mathrm{b})=\mathrm{a}+\mathrm{b}\\ \left(\mathrm{iii}\right)\text{\hspace{0.17em}a=75, b=84}\\ \mathrm{a}-(-\mathrm{b})=75-(-84)=75+84=159\\ \mathrm{a}+\mathrm{b}=75+84=39\\ \mathrm{Thus},\mathrm{a}-(-\mathrm{b})=\mathrm{a}+\mathrm{b}\\ \left(\mathrm{iv}\right)\text{\hspace{0.17em}a=28, b=11}\\ \mathrm{a}-(-\mathrm{b})=28-(-11)=28+11=39\\ \mathrm{a}+\mathrm{b}=28+11=39\\ \mathrm{Thus},\mathrm{a}-(-\mathrm{b})=\mathrm{a}+\mathrm{b}\end{array}$

Q.9

$\begin{array}{l}\text{Use the sign of>,<or=in the box to make the statement}\\ \text{true.}\\ \left(\text{a}\right)\left(-\text{8}\right)\text{+}\left(-\text{4}\right)\boxed{}\left(-\text{8}\right)-\left(-\text{4}\right)\\ \left(b\right)(–3)+7–\left(19\right)\boxed{}15–8+(–9)\\ \left(c\right)23–41+11\boxed{}23–41–11\\ \left(d\right)39+(–24)–\left(15\right)\boxed{}36+(–52)–(–36)\\ \left(e\right)–231+79+51\boxed{}–399+159+81\end{array}$

Ans.

\begin{array}{l}\text{(a) (}-\text{8) + (}-\text{4)}\boxed{<}\text{(}-\text{8)}-\text{(}-\text{4)}\\ \text{(b) (}-\text{3) +7}-\text{(19)}\boxed{<}\text{15}-\text{8+(}-\text{9)}\\ \text{(c) 23}-\text{41+11}\boxed{>}23-41-11\\ \text{(d) 39+(}-\text{24)}-\text{(15)}\boxed{<}36+\text{(}-\text{52)}-\text{(}-\text{36)}\\ \text{(e)}-\text{231+79+51}\boxed{>}-\text{399 + 159 + 81}\end{array}

Q.10

$\begin{array}{l}\text{Awater tank has steps inside it. A monkey is sitting on}\\ \text{the topmost step}\left(\text{i.e., the first step}\right)\text{. The water level is}\\ \text{at the ninth step.}\\ \left(\text{i}\right)\text{He jumps 3 steps down and then jumps back 2 steps}\\ \text{up.In how many jumps will he reach the water level?}\\ \left(\text{ii}\right)\text{After drinking water, he wants to go back. For this,}\\ \text{he jumps 4 steps up and then jumps back 2}\\ \text{steps down in every move. In how many jumps will he}\\ \text{reach back the top step?}\\ \left(\text{iii}\right)\text{If the number of steps moved down is represented}\\ \text{by negative integers and the number of steps moved up}\\ \text{by positive integers, represent his moves in part}\left(\text{i}\right)\text{and}\\ \left(\text{ii}\right)\text{by completing the following;}\\ \left(\text{a}\right)\text{– 3 + 2 –}\mathrm{\dots }\text{=- 8}\\ \left(\text{b}\right)\text{4 – 2 +}\mathrm{\dots }\text{= 8.}\\ \text{In}\left(\text{a}\right)\text{the sum}\left(\text{– 8}\right)\text{represents going down by eight}\\ \text{steps. So, what will the sum 8 in}\left(\text{b}\right)\text{represent?}\end{array}$

Ans.

\begin{array}{l}\text{Consider the steps moved down be represented by positive}\\ \text{integers and steps moved up be represented by negative}\\ \text{integers}\text{.}\\ (i)\text{Initially, the monkey was at step = 1}\\ \text{After 1st jump, monkey will be at step = 1+3=4}\\ \text{After 2nd jump, monkey will be at step = 4+}\left(-2\right)\text{=2}\\ \text{After 3rd jump, monkey will be at step = 2+3=5}\\ \text{After 4th jump, monkey will be at step = 5+}\left(-2\right)\text{=3}\\ \text{After 5th jump, monkey will be at step = 3+3=6}\\ \text{After 6th jump, monkey will be at step = 6+}\left(-2\right)\text{=4}\\ \text{After 7th jump, monkey will be at step = 4+3=7}\\ \text{After 8th jump, monkey will be at step = 7+}\left(-2\right)\text{=5}\\ \text{After 9th jump, monkey will be at step = 5+3=8}\\ \text{After 10th jump, monkey will be at step = 8+}\left(-2\right)\text{=6}\\ \text{After 11th jump, monkey will be at step = 6+3=9}\\ \text{Clearly, the monkey will be at water level (i}\text{.e}\text{., 9th step)}\\ \text{after 11 jumps}\text{.}\\ \\ \text{(ii)}\\ \text{Initiall, the monkey was at step = 9}\\ \text{After 1st jump, monkey will be at step = 9+}\left(-4\right)\text{=5}\\ \text{After 2nd jump, monkey will be at step = 5+2=7}\\ \text{After 3rd jump, monkey will be at step = 7+}\left(-4\right)\text{=3}\\ \text{After 4th jump, monkey will be at step = 3+2=5}\\ \text{After 5th jump, monkey will be at step = 5+}\left(-4\right)\text{=1}\\ \text{Clearly,}\text{the will reach back at the top step after 5 jumps}\text{.}\\ \text{(iii) If steps moved down are represented by a negative}\\ \text{integers and steps moved up are represented bya positive}\\ \text{integers, then his moves will be as follows:}\\ \text{Moves in part (i):}\\ -\text{3+2}-\text{3+2}-\text{3+2}-\text{3+2}-\text{3+2}-\text{3=}-\text{8}\\ \text{Moves in part (ii):}\\ \text{4}-\text{2+4}-\text{2+4=8}\\ \text{Moves in part (ii) represent goin up 8 steps}\text{.}\end{array}