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Important Questions for CBSE Class 7 Maths Chapter 1 - Integers (Free PDF Download)

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Important Practice Problems for CBSE Class 7 Maths Chapter 1: Integers

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Study Important Questions for Class 7 Maths Chapter 1- Integers

A.Very short answer question – 1 marks

1. Define Integers.

Ans: The numbers range from negative infinity to positive infinity including zero. They are denoted by I i.e.  $ \text{I=}\left\{ \left. .....\text{-3,-2,-1,0,1,2,3}..... \right\} \right. $ .


2. We move to the left in the number line when we__________ or __________.

Ans: We move to the left in the number line when we add a negative integer or subtract a positive integer.


3. Additive inverse of  $ \text{-25} $  is ____.

Ans:  $ 25 $ .


4. Fill the blanks for  $ \text{-228+96+125} $  ___  $ \text{-451+197+76}\left( \text{use,,=} \right) $ 

Ans:  $  >  $ 


5. What would come in place of ? in  $ \text{-11+0=?} $ 

Ans:  $ \text{-11} $ 


6. Fill the blanks for  $ \text{-22 }\!\!\times\!\!\text{ -13 }\!\!\times\!\!\text{ 5=} $  _____

Ans:  $ \text{1430} $ 


7.Fill the blanks for  $ \text{-3 }\!\!\times\!\!\text{ 125=} $  ___

Ans: $ \text{-375} $ 


B. Short Answer Questions – 2 marks

8. Verify  $ \text{a-}\left( \text{-b} \right)\text{=a+b} $  for the following values of  $ \text{a} $  and  $ \text{b} $ 


a.  $ \text{a=25,b=12} $ 

Ans: Substituting value of  $ \text{a} $  and  $ \text{b} $  in given equation

$ \text{a-}\left( \text{-b} \right)\text{=a+b} $ 

 $ \text{25-}\left( \text{-12} \right)\text{=25+12} $ 

 $ \,\text{25+12=25+12} $ 

 $ \text{37=37} $ 

Hence, verified.


b. $ \text{a=113,b=16} $ 

Ans: Substituting value of  $ \text{a} $  and  $ \text{b} $  in given equation

 $ \text{a-}\left( \text{-b} \right)\text{=a+b} $ 

 $ \text{113-}\left( \text{-16} \right)\text{=113+16} $ 

 $ \text{113+16=113+16} $ 

 $ \text{129=129} $ 


9. Use  $ \text{,} $   or  $ \text{=} $  sign for the below statements to make it true 

a. $ \left( \text{-9} \right)\text{+}\left( \text{-28} \right) $ ____  $ \left( \text{-9} \right)\text{-}\left( \text{-28} \right) $ 

Ans: Solving both sides-

$ \left( \text{-9} \right)\text{+}\left( \text{-28} \right)=-37 $ 

$ \left( \text{-9} \right)\text{-}\left( \text{-28} \right)=19 $ 

Thus,  $ \left( \text{-9} \right)\text{+}\left( \text{-28} \right) < \left( \text{-9} \right)\text{-}\left( \text{-28} \right) $  


b. $ \text{25+}\left( \text{-14} \right)\text{-18} $  ____   $ \text{25+}\left( \text{-14} \right)\text{-}\left( \text{-18} \right) $ 

Ans: Solving both sides-

 $  \text{2}5+\left( -14 \right)-18=11-18  $ 

 $  =\text{-7} $ 

 $  \text{25+}\left( \text{-14} \right)\text{-}\left( \text{-18} \right)=11+18  $ 

 $  =29 $ 

Thus,  $ \text{2}5+\left( -14 \right)-18 < \text{25+}\left( \text{-14} \right)\text{-}\left( \text{-18} \right) $.


10. Write down a pair of integers for the following 

a. Sum gives  $ \text{-9} $ 

Ans:  A pair of integers that gives sum  $ \text{-9} $  is  $ \left( -6,-3 \right) $.


b. Difference gives  $ \text{-11} $ 

Ans:  A pair of integers that gives sum  $ \text{-11} $  is  $ \left( -14,3 \right) $.


11.  a. Write a positive and negative integer whose sum is  $ \text{-4} $ .

Ans: $ \left( 4,-8 \right) $  is a positive and negative integer whose sum is  $ \text{-4} $  .


b.Write a negative integer and a positive integer whose difference is  $ \text{-2} $ .

Ans:  $ \left( -1,1 \right) $  is a positive and negative integer whose sum is  $ \text{-2} $  . 


12. Fill in the blanks

a.  $ \left( \text{-4} \right)\text{+}\left( \text{-11} \right)\text{=}\left( \text{-11} \right)\text{+ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ } $ 

Ans: $ \left( \text{-4} \right)\text{+}\left( \text{-11} \right)\text{=}\left( \text{-11} \right)\text{+ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ } $ 

\[\Rightarrow \left( \text{-4} \right)\text{+}\left( \text{-11} \right)\text{+11}\]

\[\Rightarrow -4\]

Thus,  $ \left( \text{-4} \right)\text{+}\left( \text{-11} \right)\text{=}\left( \text{-11} \right)\text{+-4} $ 


b.  $ \left[ \text{22+}\left( \text{-9} \right) \right]\text{+}\left( \text{-2} \right)\text{=22+}\left[ \text{ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ +}\left( \text{-2} \right) \right] $ 

Ans: \[\left[ \text{22+}\left( \text{-9} \right) \right]\text{+}\left( \text{-2} \right)\text{=22+}\left[ \text{ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ +}\left( \text{-2} \right) \right]\]

\[\Rightarrow \text{13-2=22+}\left[ \text{ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ +}\left( \text{-2} \right) \right]\]

\[\Rightarrow \text{11-22=}\left[ \text{ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ +}\left( \text{-2} \right) \right]\]

\[\Rightarrow \text{-11= }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ +}\left( \text{-2} \right)\]

\[\Rightarrow \text{-11+2}\]

\[\Rightarrow \text{-9}\]

Thus, \[\left[ \text{22+}\left( \text{-9} \right) \right]\text{+}\left( \text{-2} \right)\text{=22+}\left[ \text{-9+}\left( \text{-2} \right) \right]\]


13.  Verify  $ \text{7 }\!\!\times\!\!\text{ }\left[ \left( \text{22} \right)\text{+}\left( \text{-9} \right) \right]\text{=}\left[ \left( \text{7} \right)\text{ }\!\!\times\!\!\text{ 22} \right]\text{+}\left[ \text{7 }\!\!\times\!\!\text{ -9} \right] $ 

Ans:  On solving both sides

$ \text{7 }\!\!\times\!\!\text{ }\left[ \left( \text{22} \right)\text{+}\left( \text{-9} \right) \right]\text{=}\left[ \left( \text{7} \right)\text{ }\!\!\times\!\!\text{ 22} \right]\text{+}\left[ \text{7 }\!\!\times\!\!\text{ -9} \right] $ 

$ 7\times \left[ 13 \right]=154-63 $ 

$ 91=91 $ 

Hence, verified.


14.Find the product of

a.  $ \text{63 }\!\!\times\!\!\text{ 0 }\!\!\times\!\!\text{ -7} $ 

Ans: The product of  $ \text{63 }\!\!\times\!\!\text{ 0 }\!\!\times\!\!\text{ -7} $  is  $ 0 $  .


b. $ \text{5 }\!\!\times\!\!\text{ }\left( \text{-3} \right)\text{ }\!\!\times\!\!\text{ -2} $ 

Ans: So, $ 5\times \left( -3 \right)\times -2=5\times 6 $ 

$ =30 $ 

The product of  $ 5\times \left( -3 \right)\times -2 $  is  $ 30 $  .


15. 

a.  $ \text{-2 }\!\!\times\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ =14} $ 

Ans: So,  $ \text{-2 }\!\!\times\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{ =14} $ 

$ \Rightarrow \dfrac{\text{14}}{\text{-2}} $ 

$ \Rightarrow \text{-7} $ 

Hence,  $ \text{-2 }\!\!\times\!\!\text{ 7 =14} $  .


b. \[\text{ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\times\!\!\text{ -8=-32}\]

Ans:  So, \[\text{ }\!\!\_\!\!\text{  }\!\!\_\!\!\text{  }\!\!\_\!\!\text{   }\!\!\times\!\!\text{ -8=-32}\]

\[\Rightarrow \dfrac{-32}{-8}\]

\[\Rightarrow 4\]

Hence, \[\text{4 }\!\!\times\!\!\text{ -8=-32}\]


16. Evaluate 

a. $ \text{-39 }\!\!\div\!\!\text{ 13} $ 

Ans:  $ -39\div 13 $ 

$ \Rightarrow \dfrac{-39}{13} $ 

$ \Rightarrow -3 $ 

Hence,  $ -39\div 13=-3 $ 


b. $ \text{-64 }\!\!\div\!\!\text{ }\left[ \text{-8 }\!\!\times\!\!\text{ -8} \right] $ 

Ans:  $ -64\div \left[ -8\times -8 \right] $ 

$ \Rightarrow \dfrac{-64}{\left[ -8\times -8 \right]} $ 

$ \Rightarrow \dfrac{-64}{64} $ 

$ \Rightarrow -1 $ 

Hence,  $ -64\div \left[ -8\times -8 \right]=-1 $


17. Write two pairs of integers such that  $ \text{a }\!\!\div\!\!\text{ b=-5} $ 

Ans:The two pairs of integers such that  $ \text{a }\!\!\div\!\!\text{ b=-5} $  are:

> $ \left( 10,-2 \right) $ 

> $ \left( -70,14 \right) $ 


C. Short answer questions – 3 marks

18.  Manvita deposits Rs.  $ \text{5000} $   in her bank account after two days. She withdraws Rs.  $ \text{3748} $   from it. If the amount deposited is a positive integer. How will you represent the amount withdrawn and also find the balance amount in the account?

Ans: The amount withdrawn should always be represented as a negative integer.

Thus, it would be  $ -3748 $.

Since, Total balance  $ = $   Amount deposited  $ - $  Amount withdrawn

Therefore,

Total balance  $ =5000-3748 $ 

 $ \text{=Rs}\text{. 1252} $ .

Hence, the amount withdrawn would be negative integer i.e.,  $ -3748 $  and the balance amount in the account is  $ \text{Rs}\text{. 1252} $ .


19. In a game Mishala scored  $ \text{20,}\,\text{-40,}\,\text{10} $  and Meera scored  $ \text{-40,10,}\,\text{20} $ . Who scored more and can we add scores (integers) in any order?

Ans: Since, Mishala scored  $ \text{20,}\,\text{-40,}\,\text{10} $ .

Therefore, total score of Mishala is 

 $ \text{=20-40+}\,\text{10} $ 

 $ \text{=-20+10} $ 

 $ \text{=-10} $ 

And since, Meera scored  $ \text{-40,}\,1\text{0,}\,2\text{0} $ .

Therefore, total score of Meera is 

 $ \text{=-40+}\,\text{10+20} $ 

 $ \text{=-20+10} $ 

 $ \text{=-10} $ 

Hence, both scored the same points in a game but in a different order.

Yes, we can add integers in any order.


20. Find the product with suitable properties for the following-

a. $ \text{16 }\!\!\times\!\!\text{ }\left( \text{-34} \right)\text{+}\left( \text{-34} \right)\text{ }\!\!\times\!\!\text{ }\left( \text{-18} \right) $ 

Ans: Given 

$ \text{16 }\!\!\times\!\!\text{ }\left( \text{-34} \right)\text{+}\left( \text{-34} \right)\text{ }\!\!\times\!\!\text{ }\left( \text{-18} \right) $ 

By distributive property-

 $ \text{a }\!\!\times\!\!\text{ b+a }\!\!\times\!\!\text{ c=a}\left[ \text{b+c} \right] $ 

Thus, 

 $ \text{=-34}\left[ \text{16-18} \right] $ 

 $ \text{=-34 }\!\!\times\!\!\text{ -2} $ 

 $ \text{=68} $ 

Hence,  $ \text{16 }\!\!\times\!\!\text{ }\left( \text{-34} \right)\text{+}\left( \text{-34} \right)\text{ }\!\!\times\!\!\text{ }\left( \text{-18} \right)=68 $ .


b. $ \text{23 }\!\!\times\!\!\text{ -36 }\!\!\times\!\!\text{ 10} $ 

Ans: Given 

$ 23\times -36\times 10 $ 

By commutative property-

 $ \left( \text{a }\!\!\times\!\!\text{ b} \right)\text{ }\!\!\times\!\!\text{ c=a }\!\!\times\!\!\text{ }\left( \text{b }\!\!\times\!\!\text{ c} \right) $ 

Thus,

 $ =23\times \left[ -36\times 10 \right] $ 

 $ =23\times -360 $ 

 $ =-8280 $ 


21.  A fruit merchant earns a profit of Rs. $ \text{6} $  per bag of orange sold and a loss of Rs. $ \text{4} $  per bag of grapes sold.

a. Merchant sells  $ \text{1800} $  bags of orange and  $ \text{2500} $  bags of grapes. What is the profit or loss?

Ans: Since, profit is denoted by a positive integer and a loss is denoted by a positive integer.

Therefore, profit earned by selling  $ \text{1} $  bag of orange is Rs.  $ 6 $ 

Profit earned by selling  $ \text{1800} $  bags or orange is 

 $ \text{6 }\!\!\times\!\!\text{ 1800} $  

 $ \text{=Rs}\text{. 10,800} $  

Loss incurred by selling  $ 1 $  bag of grapes is Rs.  $ -4 $  

Loss incurred by selling  $ 2500 $  bags of grapes is

 $ =-4\times 2500 $ 

 $ =10,000 $  

Total profit or loss earned  $ = $  Profit  $ + $ Loss

 $  =10,800+10,000  $ 

 $  =800 $  

Hence, a profit of Rs. $ 800 $   will be earned by a merchant.


b. What is the number of bags of oranges to be sold to have neither profit nor loss if the number of grapes bags are sold is  $ \text{900} $  bags?

Ans: Since profit is denoted by a positive integer and a loss is denoted by a positive integer.

Therefore, Loss incurred while selling  $ 1 $   bag of grapes  $ \text{=-Rs}\text{.4} $  

Loss incurred while selling 900 bags of grapes be 

 $ =-4\times 900 $ 

 $ =-3600 $  

Let the number of bags of oranges to be sold  $ \text{=x} $  

Profit earned when  $ 1 $  bag of orange is sold  $ \text{=Rs}\text{.6} $  

Profit earned while selling x bags of orange  $ \text{=6x} $  

Condition for no profit, no loss

Profit earned  $ + $   Loss incurred  $ =0 $  

 $ \text{6x-3600=0} $ 

 $ \text{6x=3600} $ 

 $ \text{x=}\dfrac{\text{3600}}{\text{6}} $ 

\[\text{x=600}\]

Hence, to have neither profit nor loss \[\text{600}\] number of bags of oranges to be sold.


22.  Verify that \[\text{a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\ne \left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\] for each of the following values of  $ \text{a,b} $  and  $ \text{c} $ .

a. $ \text{a=8,}\,\text{b=4,}\,\text{c=2} $ 

Ans:For equation \[\text{a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\ne \left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\].

L.H.S  \[\text{=a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\]

\[\text{=8 }\!\!\div\!\!\text{ }\left( \text{-4+2} \right)\]

\[\text{=8 }\!\!\div\!\!\text{ }\left( \text{-2} \right)\]

\[\text{=-4}\]

R.H.S  \[=\left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\]

 $ \text{=}\left( \text{8 }\!\!\div\!\!\text{ -4} \right)\text{+}\left( \text{8 }\!\!\div\!\!\text{ 2} \right) $ 

 $ \text{=-2+4} $ 

 $ \text{=2} $ 

Hence,  $ \text{L}\text{.H}\text{.S}\ne \text{R}\text{.H}\text{.S} $  .

Thus, \[\text{a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\ne \left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\] for  $ \text{a=8,}\,\text{b=4,}\,\text{c=2} $ .


b. $ \text{a=-15,}\,\text{b=2,}\,\text{c=1} $ 

Ans: For equation \[\text{a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\ne \left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\].

L.H.S  \[\text{=a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\]

 $ \text{=-15 }\!\!\div\!\!\text{ }\left( \text{2+1} \right) $ 

 $ \text{=-15 }\!\!\div\!\!\text{ 3} $ 

 $ \text{=-5} $ 

R.H.S  \[=\left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\]

 $ \text{=}\left( \text{-15 }\!\!\div\!\!\text{ 2} \right)\text{+}\left( \text{-15 }\!\!\div\!\!\text{ 1} \right) $ 

 $ \text{=-7}\text{.5+}\left( \text{-15} \right) $ 

 $ \text{=-22}\text{.5} $ 

Hence,  $ \text{L}\text{.H}\text{.S}\ne \text{R}\text{.H}\text{.S} $ 

Thus, \[\text{a }\!\!\div\!\!\text{ }\left( \text{b+c} \right)\ne \left( \text{a }\!\!\div\!\!\text{ b} \right)\text{+}\left( \text{a }\!\!\div\!\!\text{ c} \right)\] for  $ \text{a=-15,}\,\text{b=2,}\,\text{c=1} $  .


23. In a CET Examination  $ \left( \text{+2} \right) $  marks are given for every current answer and  $ \left( \text{-0}\text{.5} \right) $   marks are given for every wrong answer and  $ 0 $  for non-attempting any question.

a. Likitha scores  $ \text{30} $  marks. If she got  $ \text{20} $ correct answers, how many questions she has attempted incorrectly?

Ans: Marks obtained for  $ 1 $  correct answer  $ \text{=+2} $  

Marks obtained for  $ 1 $  wrong answer  $ \text{=-0}\text{.5} $  

So, Marks scored by Likitha =  $ 30 $  

Marks obtained by  $ 20 $  correct answers $ =20\times 2=40 $  

Marks obtained for incorrect answer  $ = $  Total score  $ - $  Marks obtained by  $ 20 $  correct answer

 $ =30-40 $  

 $ =-10 $ 

Marks obtained for  $ 1 $  wrong answer $ =-0.5 $  

 $ \therefore  $ The number of incorrect answers $ =\dfrac{-10}{-0.5} $  

 $ =20 $  

Hence, she attempted  $ 20 $  questions wrongly.


b. Saara scores  $ \text{-4} $  marks if she got  $ \text{3} $  correct answers. How many were incorrect?

Ans: Marks obtained for  $ 1 $  correct answer  $ \text{=+2} $  

Marks obtained for  $ 1 $  wrong answer  $ \text{=-0}\text{.5} $  

So, Marks scored by Saara  $ =-4 $  

Marks obtained for 3 correct answers $ =3\times 2=6 $  

Marks obtained for incorrect answers  $ = $  Total score  $ - $  Marks obtained for  $ 3 $  correct answer

 $ =-4-6=-10 $  

Marks obtained for 1 wrong answer $ =-0.5 $  

 $ \therefore  $ The number of incorrect questions  $ =\dfrac{-10}{-0.5} $  

 $ =20 $  

Hence,  $ 20 $  questions were incorrect. 

Important Questions for CBSE Class 7 Maths Chapter 1 - Integers

Students who have not developed a solid base feel that Maths is hard to excel in and may perceive the subject as a burden. As they have not worked on the subject or failed to grasp its theories and logic, they must start well in class 7 to lead a strong foundation in Mathematics, to conquer good marks in the examination. The magic wand of a good Mathematician is practice. Therefore, to secure a good score in the examination, the students must practice questions based on every theory and formula of Maths.

 

They may begin with class 7 Maths Chapter 1 important questions to start their practice from the first chapter. If the students find the topics challenging or cannot deal with complex issues, they may use efficient study material to dismantle diplomatic problems into manageable solutions. The critical questions for Class 7 Maths Chapter 1 are available in text and PDF formats online, which is accessible to them for free.

 

Details of Class 7 Maths Chapter 1 Integers

In the first chapter of class 7 Maths, the students get a sneak peek into the integer number system. The students must ensure a deep understanding of the topic to proceed with the upcoming chapters. To grasp the topic’s in-depth knowledge, they must practice the important questions for Class 7 Maths Chapter 1. Now, we will highlight some of the important concepts that are included in chapter 1:

 

Integer

An integer is one of the fundamental parts of Mathematics. It can be quoted as a number that can be depicted without any fractional components. For instance, 3, 61, 70, 5 all are integers, while 6.54, 5.89 are non-integer numbers.

 

We can easily blend out an integer from a series of counting numbers. Let's make it clear with an example, suppose if a counting number is subtracted from itself, the result will be zero. If a larger counting number is removed from a smaller whole number, the output becomes a negative integer. When we subtract the smaller number from the larger whole number, it results in a positive integer. Applying this methodology, we can derive many integers ranging from negative to positive. A set of integers are depicted by 'Z.'

 

Z = {….., -4,-3,-2,-1,0,1,2,3,4,…..n}.

 

Properties of Integers

Some of the properties of an integer are as follows:

 

Commutative Property

The commutative properties of an integer depict that if we perform any operation like multiplication or some numbers, the numbers’ position can be swapped without differing in the output.

 

Let's make the property clear with an example:

  • Suppose X and Y are two non-zero integers,

  • Therefore, the commutative property of addition is X + Y = Y + X.

  • And, the commutative property of multiplication is X x Y = Y x X.

 

Associative Property

The associative property of integers depicts that if we perform an addition or multiplication operation on any set of numbers, the result will be identical, irrespective of the grouping of the multiplicands or addends. Some of the traits of associative properties are mentioned below:

  • The associative property of integers involves a minimum of 3 numbers.

  • Generally, the integers are grouped using parenthesis.

  • The numbers defined within the parenthesis are depicted by one unit.

  • The associative property can only be implemented for addition and multiplication operations and not for division or subtraction.

Let's take an example to make the associative property clear. According to the property, 7 + (8 + 2) = 2 + (7 + 8).

 

Distributive Property

The distributive property depicts that if two or more numbers are added and multiplied with another number, it will be identical to the current output if each addend is individually multiplied and then added together.

 

Here's an example to clear the distributive property of integers:

  • (7 + 1 + 2) x 5

  • This equation can be simplified to 10 x 5 = 50,

  • While if we dismantle the equation as 7 x 5 + 1 x 5 + 2 x 5, the result will be equal, i.e., 50.

 

Arithmetical Operations Using Integers

Addition of Integers

There are a set of rules to add integer with same and different signs:

  • During the addition of two integer numbers with the same sign, the output generated also depicts the same sign. Example: 7 + 8 = 15.

  • For the addition of two integers, one with positive and one with negative signs, the result must retain the largest integer sign. The operation must be performed by subtracting the two integers. Example: 8 + (-14) = -6.

 

Subtraction of Integers

The rules to perform subtraction of integers are as follows:

  • If the subtraction is to be performed between two integers with different signs, i.e., one negative and one positive, the output will retain the largest integer's sign. Example: 9 - 5 = 4.

  • If the subtraction is performed between two negative integers, the result can be obtained by adding the same number with the opposite sign. Example: -7 - (-9) = -7 + 9 = 2.

 

Multiplication of Integers

Multiplication of a positive and a negative integer - The result of the multiplication of a positive and a negative integer can be generated simply by multiplying both the numbers and denoting the output with a minus(-) sign. For example: -7 x 6 = -42.

  • Multiplication of Two Negative Integers - The product of two negative integers is always a positive integer. For example: -2 x -7 = 14.

  • Multiplication of Three or More Negative Integers - If the total integers to be multiplied is even, then the output will carry plus (+) sign. The total number of integers to be multiplied is odd. The result will carry the minus(+) sign.

 

Division of Integers

  • Division of a Negative Integer by a Positive Integer - When a negative number is divided by a positive number, the quotient comes with a negative sign.

  • Division of a Negative Integer by Another Negative Integer - when a negative number is divided by another negative number, the quotient comes with a positive sign.

To get in-depth details about the topics, students can practice the important questions in class 7 Maths chapter 1.

 

Important Questions for Class 7 Maths Chapter 1 Integers

Thorough practicing of the important questions for Class 7 Maths integers may help the students grip the topics efficiently. Here we present you the vital questions on the chapter: 

  • What is an Integer? Explain with examples.

  • What are the dissimilarities between Integers and Real numbers?

  • What is the commutative property of integers? Explain with examples.

  • Define the additive identity of an integer.

  • What is the distributive property of an integer?

  • Explain the multiplication properties of integers.

  • What are the division properties of the integers?

  • A lift is moving towards a mine craft at a rate of 8m/min. How much time will it take to reach -300m if the descent began from 15m above the ground level?

  • Explain the associative property of integers with an example.

  • What are the five integer operations?

 

Benefits of Important Questions for Class 7 Maths Chapter 1

Students deserve the best study material to guide them on the topics. Therefore, they can unleash the actual benefits of the Class 7 Maths Chapter 1 important questions by thoroughly practicing to secure good marks in the examination. Here are some of the fruitfulness that the students can enjoy from the questions:

  • The questions are carefully designed under the strict guidelines of CBSE and are reviewed by top-notch professionals.

  • The students must practise these important questions to understand every concept and theory of the chapter.

In case the students find any difficulty to solve problems or understand any concept, they may refer to the in-detailed solutions. Vedantu, with its team of expert educators, has framed every important question of Class 7 Maths Integers after efficient analysis of the past year’s question papers.

 

Conclusion

Students who find it challenging to study Mathematics can build their logic to score well in the examination. To kick start the class 7 academic journey, the students must efficiently practice the Important Questions of Class 7 Maths Chapter 1 Integers, which they can access for free on Vedantu’s website. Students just have to download the PDF and then they can solve the extra questions from the comfort of their homes anytime.

 

For more study materials related to different chapters of Class 7 Mathematics, students can visit Vedantu’s website and explore the huge collection of free resources available with us.

FAQs on Important Questions for CBSE Class 7 Maths Chapter 1 - Integers (Free PDF Download)

1. What are the various types of integers?

The various types of Integers are as follows:

  • Positive Numbers - are those numbers which have a plus sign (+). They are always found on the right side of zero on the number line. Most of the time positive numbers are represented simply as a whole number without the plus sign (+). Every positive number is greater than zero as well as negative numbers.

Example: 1,2, 234, 5667,99999999, etc.

  • Negative Numbers

Negative numbers are numbers symbolized with a minus sign (-). Negative numbers are represented to the left of zero on a number line.

Example: …., -99, -158, -110, -1.

  • Zero

Zero is neither a positive nor a negative integer. It is a neutral number i.e. zero has no sign (+ or -).

2: What are the operations that can be done on Integers? What are its main properties?

The various operations that are performed on Integers are as follows: 

  • Addition

  • Subtraction

  • Multiplication

  • Division

The main properties of integers are as follows: 

  • Closure Property

  • Associative Property

  • Commutative Property

  • Distributive Property

  • Identity Property

3: What do you mean by commutative property?

The commutative property of addition and multiplication states that irrespective of the order of terms the result will not change. Swapping of terms will have no effect on the sum or product.

Ex:  x and y are any two integers, then

⇒ x + y = y + x

⇒ x × y = y × x

14 + (−6) = 8 = (−6) +1 4;

10 × (−3) = −30 = (−3) × 10

 

Note: Subtraction (x − y ≠ y − x) and division (x ÷ y ≠ y ÷ x) are not commutative for integers and whole numbers.

4: Fill in the blanks to make the following statements true:

(–5) + (– 8) = (– 8) + (…………)

 

A4: Let us assume the missing integer be x,

Then,

= (–5) + (– 8) = (– 8) + (x)

= – 5 – 8 = – 8 + x

= – 13 = – 8 + x

By sending – 8 from RHS to LHS it becomes 8,

= – 13 + 8 = x

= x = – 5

Now substitute the x value in the blank place,

(–5) + (– 8) = (– 8) + (- 5) … (This equation is in the form of Commutative law of Addition)

5. What is Chapter 1 of Class 7 Maths about?

The first Chapter of Class 7 Maths begins with a review of the fundamentals of integers that were covered in the previous classes. These recollected ideas are used in the first exercise in the Class 7 Mathematics Chapter 1 answers. You will learn more about integers, their characteristics, and operations in Chapter 1 of Class 7 Mathematics. Expert teachers prepare the important questions to assist students. For a student, the Important Questions of Chapter 1 of Class 7 Mathematics provided by Vedantu are very useful.

6. How many questions are there in Chapter 1 -Integer of Class 7 Maths?

There are four exercises in Chapter 1 “Integers” of Class 7 Maths. These four exercises contain a total of 30 questions. For more practice of Chapter 1 of Class 7 Maths, students can refer to the Important Questions of Chapter 1 of Class 7 Maths, prepared by experts at Vedantu for the benefit of the students.

7. Do I need to practice all questions provided in Important Questions for Chapter 1 of Class 7 Maths?

Yes, you need to practise all the questions. All the questions in this chapter deal with a unique concept and in order to get clarity on all the concepts, you must practice every sum. A short review of integers and their representation on the number line, operations such as addition, subtraction, and others that may be done on them, additive inverse, and negative integers are just a few of the subjects covered at the beginning. For important questions of Chapter 1 of Class 7 Maths, visit Vedantu website or mobile app and download the PDF free of cost.

8. What is the associative property of integers?

The associative property of integers states that no matter how the multiplicands or addends are grouped, the result of an addition or multiplication operation on any set of numbers will be the same. The following are some of the characteristics of associative properties:

  • In general, parentheses are used to arrange the numbers.

  • One unit represents the numbers defined within the parentheses.

  • Integers have an associative characteristic that requires a minimum of three numbers.

Q9. What is Associative Property?


Ans: The associative property of integers states that no matter how the multiplicands or addends are grouped, the result of an addition or multiplication operation on any set of numbers will be the same. The following are some of the characteristics of associative properties:

  • In general, parentheses are used to arrange the numbers.

  • One unit represents the numbers defined within the parentheses.

  • Integers have an associative characteristic that requires a minimum of three numbers.