Ex.1.1 Q1 Integers - NCERT Maths Class 7

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Question

Following number line shows the temperature in degree Celsius (\(^\circ \rm C\)) at different places on a particular day.

(a) Observe this number line and write the temperature of the places marked on it.

(b) What is the temperature difference between the hottest and the coldest places among the above?

(c) What is the temperature difference between Lahulspiti and Srinagar?

(d) Can we say temperature of Srinagar and Shimla taken together is less than the temperature at Shimla? Is it also less than the temperature at Srinagar?

Text Solution

(a)

What is known?

Temperature in degree Celsius (\(^\circ \rm C\)) at different places on a particular day marked on the number line.

What is unknown?

Temperature at different places marked on the number line.

Reasoning:

Identify the integer on the given number line and match it with the place which is written on the top (and connected to the point by an arrow). That integer is the temperature of the place in degree Celsius (\(^\circ \rm C\)).

Steps:

Place

Temperature

Lahulspiti

\(-8\) \(^\circ \rm C\)

Srinagar

\(–2\) \(^\circ \rm C\)

Shimla

\(5\) \(^\circ \rm C\)

Ooty

\(14\) \(^\circ \rm C\)

Bengaluru

\(22\) \(^\circ \rm C\)

 

(b) 

What is known?

Different places and their respective temperatures.

What is unknown?

The temperature difference between the hottest and the coldest places.

Reasoning:

Identify the hottest place – highest temperature (or the highest positive value of the integer) and the coldest place – lowest temperature (or the lowest negative value of the integer). Find the difference between the two values.

Steps:

Hottest place is Bengaluru at \(22 ^\circ \rm C\).

Coldest place is Lahulspiti at  \(-8 ^\circ \rm C\)

The difference between the temperature of the two cities:

\[\begin{align} &= {22^{\rm{o}}}{\rm{C}} - \left( { - {8^{\rm{o}}}{\rm{C}}} \right) = {22^{\rm{o}}}{\rm{C}} +{8^{\rm{o}}}{\rm{C}}\\&= {30^{\rm{o}}}{\rm{C}}\end{align}\]

Remember that for subtraction, we add the additive inverse of the integer that is being subtracted, to the other integer. The additive inverse of \(-8\) is \(8\) and therefore, we added \(22\) and \(8\) to get the answer.

(c) 

What is known?

Different places and their respective temperatures.

What is unknown?

The temperature difference between Lahulspiti and Srinagar.

Reasoning:

Use the table and find the temperature of Lahulspiti and Srinagar. Then subtract the two values. But remember one thing – subtract the er value from the higher one.

Steps:

Temperature of Srinagar: \(–2^\circ \rm C\)

Temperature of Lahulspiti: \(-8\)\(^\circ \rm C\)

Although the absolute value of the temperature of Lahulspiti is higher than that of Srinagar, it is a negative integer and thus, it is lower. Therefore, the difference between the temperature is:

\[\begin{align}  {-2^{\rm{o}}}{\rm{C}} - \left( { - {8^{\rm{o}}}{\rm{C}}} \right) &= {-2^{\rm{o}}}{\rm{C}} +{8^{\rm{o}}}{\rm{C}}\\&= {8^{\rm{o}}-2^{\rm{o}}}{\rm{C}}\\ &= 6^\rm {o} C \end{align}\]

(d) 

What is known?

Different places and their respective temperatures.

What is unknown?

The temperature difference between Lahulspiti and Srinagar.

Reasoning:

Use the table and find the temperature values for Lahulspiti and Srinagar. Subtract the lower value from the higher values.

Steps:

Temperature of Srinagar: \(–2\)\(^\circ \rm C\)

Temperature of Shimla: \(5\)\(^\circ \rm C\)

Temperature of Srinagar and Shimla together

\[\begin{align}&=  - 2^\circ {\rm{C}} + {\rm{ }}5^\circ {\rm{C}}\\&= {\rm{ }}3^\circ {C}\end{align}\]

So, we can say that temperature of Srinagar and Shimla, taken together is less than the temperature of Shimla.

\[\begin{align}3^\circ {\rm{C}} < 5^\circ {\rm{C}}\end{align}\]

But the temperature of Srinagar and Shimla taken together is not less than the temperature of Srinagar.

\[\begin{align}-2^\circ {\rm{C}} < 3^\circ {\rm{C}}\end{align}\]

  
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