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

• Class 7 Important Question
• Chapter 1: Integer

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} $ 

 $ \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) $ 

 $  \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 $ 

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 $  .

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

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} $ 

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} $ 

$ 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) $ 

 $ =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} $ 

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

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

 $ \text{=-5} $ 

 $ \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?

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} $  

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:

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.

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 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: 

Subtraction

Multiplication

The main properties of integers are as follows: 

Closure 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,

= (–5) + (– 8) = (– 8) + (x)

= – 5 – 8 = – 8 + x

= – 13 = – 8 + x

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

= – 13 + 8 = x

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:

Chapterwise Important Questions for CBSE Class 7 Maths

Ncert solutions for class 7 cbse.

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CBSE Worksheets for Class 7 Science

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Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 7 Science Number of Worksheets: 139

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Assignments For Class 7 Science

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NCERT Solutions for Class 7 Social Science

NCERT Solutions for Class 7 Social Science includes all the questions provided in NCERT Class 7 Social Science Text Book of Geography The Earth: Our Habitat, History Our Pasts, Civics Social and Political Life. Here CBSE Class 7 SST all questions are solved with the detailed explanation to score good marks in the exams. you can check Extra Questions for Class 7 Social Science

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• Chapter 1 Environment
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• Chapter 3 Our Changing Earth
• Chapter 4 Air
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• Chapter 1 Tracing Changes Through A Thousand Years
• Chapter 2 New Kings and Kingdoms
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Lesson Plan

June 17, 2024, 6:05 a.m.

Lesson plan: History of Juneteenth and why it became a national holiday

A Juneteenth celebration in Richmond, Virginia, 1905. Library of Congress

This lesson was originally published on June 16, 2021, and was updated on June 16, 2024.

For a Google version of this lesson plan, click here . (Note: you will need to make a copy of the document to edit it).

In this lesson, students will explore and discuss the history and context around the Juneteenth holiday in the United States. Topics explored will include the history of racial injustice in the U.S., the Civil War and the limitations of the Emancipation Proclamation. Additionally, students will be encouraged to explore the modern significance of Juneteenth and its long-term impact.

Estimated time

One 50-60 minute class period

Grade Level

Grades 6-12

On June 15, 2021, the Senate unanimously approved a bill approving June 19 as a federal holiday for “Juneteenth National Independence Day.” The House passed the bill one day later. Still, many Americans are still unaware of the history and significance of June 19.

On Jan. 1, 1863, President Abraham Lincoln issued the Emancipation Proclamation declaring “that all persons held as slaves” in the Confederacy “shall be free.” While this may have freed some enslaved people on paper, the reality was much more complicated.

Source: PBS NewsHour via Associated Press

For instance, the Emancipation Proclamation only freed those slaves held under the Confederacy, not in border states loyal to the Union, including Kentucky, West Virginia and Delaware, where slavery was still legal after the Emancipation Proclamation. In fact, slavery was still legal in Kentucky until Dec. 1865, when the 13th Amendment was passed, though Kentucky voted against ratifying the amendment.

Confederate states and slaveholders also resisted emancipation, and many people remained enslaved in Confederate states after the proclamation, even as many enslaved people fought for their freedom or escaped behind Union lines. On June 19, 1865, Major General Gordon Granger of the Union issued an order in Galveston, Texas, alerting all enslaved persons that they were legally free.

At this point in 1865, Texas was the westernmost state in America and one of the last Confederate states to be occupied by the Union. Many slaveholders had fled Union advances in other parts of the South to Texas, along with the people they had enslaved.

While it took time for the logistics of “freeing” enslaved people to come into effect, the importance of June 19, or “Juneteenth” lived on. Considering how complicated emancipation was, many dates were considered for holding celebrations of emancipation, but over 150 years later, June 19 remains.

What originally was a holiday mainly observed by Texans has grown to be recognized all over the country. Each year on “Juneteenth,” (or more formally Juneteenth National Freedom Day), communities all around the United States gather and celebrate and reflect on the history of slavery and struggle for civil rights and equality, including the work that still remains after conditional advances such as the Emancipation Proclamation.

Warm up activity

As a class, watch the BrainPop video (8 minutes) below found here introducing Juneteenth. While watching the video, answer the following discussion questions.

Source: BrainPop

Discussion questions:

• What is “Juneteenth”? What does it celebrate?
• Why did it take so long for enslaved peoples in Texas to finally be free? What obstacles existed?
• What were some of the forms of discrimination against newly freed people mentioned in the video?
• What is the Great Migration?
• How did Juneteenth become a national, not just regional, celebration?

After watching the video, separate into groups of 3-4 to discuss the focus questions (5 minutes).

Main activities:

• Why was June 19th chosen as the date to celebrate the freedom of all Americans? What were some of the drawbacks to other dates? Can you make an argument for why you think a different date might have been better and/or worse?
• Gates describes several reasons why Juneteenth struggled to be remembered at times, and why it was able to endure. Compare and contrast what the BrainPop video included as reasons why Juneteenth struggled and endured with what Gate’s emphasizes. What do you think were the most important factors in Juneteenth’s momentum and remembrance continuing?
• “When did they start recognizing Juneteenth, if at all?”
• “What was the process of Juneteenth becoming a holiday in my state?”
• If Juneteenth isn’t recognized in your state, see if you can answer, “Why is Juneteenth not recognized?”
• This search engine for state and local government websites
• The Library of Congress

Additional activities

• Brainstorm or plan a Juneteenth celebration activity. This can be decorating a common area, bringing in a relevant local speaker or planning a refreshment break for your school. Juneteenth celebrations can be in the home, at school or in community locations. For more inspiration see these resources:
• “ How to Celebrate ” from Juneteenth.com
• See how others are celebrating Juneteenth on Twitter .
• Some activists feel ambivalent about Juneteenth becoming a national holiday, or reject the idea. To learn more about the nuances surrounding making Juneteenth a federal holiday, watch this NewsHour interview with Dr. Mark Anthony Neal recorded in 2020 amid the George Floyd protests.

• The day now known as Juneteenth was formally recognized as a national holiday in 2021, due in large part to the activism of retired teacher Opal Lee. Learn more about Lee's activism and the message of Juneteenth in this NewsHour interview with Opal Lee.

If classrooms finish and plan a celebratory activity, please share your ideas with us on social media @NewsHourEXTRA on Twitter.

This lesson was written by Cecilia Curran, NewsHour Classroom intern, while she was a rising sophomore at Amherst College. This lesson was edited by NewsHour Classroom's education producer and former history teacher Vic Pasquantonio.

Fill out this form to share your thoughts on Classroom’s resources. Sign up for NewsHour Classroom’s ready-to-go Daily News Lessons delivered to your inbox each morning.

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NCERT Exemplar Solutions Class 7 Science

Ncert exemplar solutions for class 7 science – free pdf download (updated for 2023-24).

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Top things to know about Copilot+ PCs from Microsoft Surface, available today at Microsoft.com

• Microsoft Store Team

Available today, the all-new Copilot+ PCs from Microsoft Surface – Surface Laptop and Surface Pro – are thin, light and beautiful devices that help you do more of what you love. Whether it’s starting a new creative project, connecting with friends and family or pursuing a new business venture, these devices are designed to support your journey.

The new Surface Laptop and Surface Pro are Copilot+ PCs, which are the fastest, most intelligent Windows PCs on the market. They are available in four color options at an incredible value, beginning at $999 Estimated Retail Price (ERP) USD on Microsoft.com or at a Microsoft Experience Center .

Exclusively on Microsoft.com, customers can purchase Copilot+ PCs from Microsoft Surface with 64GB memory (RAM) configurations which offer more performance and multi-tasking:

• Surface Laptop (7 th Edition) , starting at $2,399.99 ERP USD in Black with a 13.8-inch Display, Snapdragon® X Elite (12 Core) Processor and 1TB SSD Storage.
• Surface Laptop (7 th Edition) , starting at $2,499.99 ERP in Black with a 15-inch Display, Snapdragon® X Elite (12 Core) Processor and 1TB SSD Storage.
• Surface Pro Essentials Bundle , starting at $1,144 ERP, get the most out of your Surface Pro with this bundle, saving on a Microsoft 365 subscription and Microsoft Complete Protection Plan. Plus, when purchasing the Essential Bundle, customers can take advantage of 20% off accessories including the new Surface Pro Flex Keyboard.

Read on for everything you need to know about the new Copilot+ PCs from Microsoft Surface.

Our three favorite things about the new Copilot+ PCs from Microsoft Surface: 1 – Designed for your everyday work and play

• Power through your day without a worry. The new Surface Laptop and Surface Pro are more powerful than ever with Snapdragon X Series Processors, providing faster performance and all-day battery life with a powerful Neural Processing Unit (NPU) for all-new AI experiences.
• Sleek design and colors that match your aesthetic. Thoughtfully designed with your everyday in mind, the thin, lightweight and ultraportable devices feature premium finishes. They come in four stunning colors – perfect for any style: classic Black, timeless Platinum, bold Sapphire, and the new and refreshing Dune [i] .
• Brighter, more immersive displays for ultimate viewing. We’re introducing a new OLED with HDR [ii] display to the new Surface Pro for a cinematic experience, and the Surface Laptop has a new HDR touchscreen display with razor-thin bezels. No matter what you watch or view, your content is going to look stunning.
• Everyday AI companion with the Copilot key. The Copilot app is just a click away with the Copilot key – one of the newest additions to Windows 11 keyboards on Copilot+ PCs.

2 – Exclusive AI experiences designed to empower creativity and productivity  

• Express your creativity with Cocreator [iii] . Whether a seasoned artist or new to design, Cocreator simplifies image creation and photo editing with easy text prompts and natural inking using a Slim Pen [iv] on Surface Pro or touch on Surface Laptop. Exclusive to Copilot+ PCs, Cocreator lets you bring your ideas to life, and it works alongside you to iteratively update the image in real time. Cocreator is available in Paint – the app you’ve grown to know and love.
• No matter where you are, Live Captions keeps you better connected [v] . Available on Windows, Live Captions can quickly translate any live or prerecorded audio into English – and in real time. Connecting with friends, family and colleagues just got easier, and you’ll never miss a beat when watching your favorite international movies or TV shows.
• New and enhanced audio and video effects bring new meaning to ”camera ready.” Both device cameras are powered by new features to Windows Studio Effects. Powered by an industry-leading NPU, they help improve lighting, ensure you appear clear and crisp on video, reduce background noise and offer creative filters so you can express yourself on camera. Built to automatically improve video calls, it’s like having a studio ring light and microphone right on your Windows PC! And the Surface Pro’s ultrawide field-of-view camera keeps you, or the whole family, in focus, even as you move around your space.
• Recall (preview) coming soon: For the solo-preneur who has too many working files and emails to maintain organization, Recall helps you quickly find things you have seen on your PC, keeping all documents, images, websites, instant messages, emails and apps right at your fingertips. This experience comes with built-in privacy and security controls.

Learn how to unlock the best of the new AI-powered features on your Copilot+ PC .

3 – The all-new Surface Pro Flex Keyboard [vi] unlocks new levels of flexibility  

Alongside the new Surface Pro, we are introducing the Surface Pro Flex Keyboard , unlocking powerful new levels of flexibility to effortlessly adapt to your work and play routines. Ready to attach to your Pro for the ultimate laptop set-up or detach for more flexibility and to support your creative workflows. It is built with extra carbon fiber layers for stability and has a larger, customizable haptic touchpad. With integrated pen storage, your Slim Pen is secure, charged and ready to go. Accessibility remains core to our approach, so we designed the new Surface Pro Flex Keyboard with a bold keyset option to reduce eye strain and assist people with low vision.

Discover, learn and buy with Microsoft Store

Shopping at Microsoft Store is all about ease and convenience. Whether the new Copilot+ PCs from Microsoft Surface, Copilot Pro, Xbox consoles and games, apps, movies and TV shows, we’ve got you covered. Don’t miss our top deals on your favorite TV shows like Rick & Morty: Seasons 1-7, Buffy The Vampire Slayer Complete Series, Sons of Anarchy: The Complete Box Set and so much more – available for up to 50% off for a limited time .

• Flexible payment options : Find a payment plan that works for you with options like PayPal Pay Later and Citizens Pay Line of Credit [vii] . It’s budgeting made easy.
• Online Trade-in Program : For a limited time, buy a new Copilot+ PC from Microsoft Surface and get extra cash back when you trade in an eligible device.
• Free and fast shipping with 60-day returns : Get your items quickly with 2–3-day shipping at no extra cost or minimum purchase required and enjoy the flexibility of 60-day returns on almost any physical product.
• 60-day price protection : Shop with confidence knowing you have 60 days of price protection from your delivery date. If the price drops or you find a lower price elsewhere, we’ll honor a one-time price adjustment.

You can also bet on Microsoft Store offering lots of great deals throughout the upcoming back-to-school season. Be sure to keep an eye on the deals page !

Available alongside Microsoft Surface today, are brand new Copilot+ PCs from the biggest brands: Acer , ASUS , Dell , HP , Lenovo and Samsung . Learn more from major PC manufacturers or visit leading retailers, including Best Buy .

[i] Colors available on selected models only. Available colors, sizes, finishes and processors may vary by store, market and configuration. 

[ii] HDR requires HDR content and enabling HDR in device settings.

[iii] Microsoft account required.

[iv] Surface Slim Pen sold separately.

[v] Currently supports translation for video and audio subtitles into English from 40+ languages. See  https://aka.ms/copilotpluspcs . 

[vi] Surface Pro Flex Keyboard sold separately.

[vii] With approval of Citizens Pay Line of Credit at 0% APR and 12- or 18-month term. Subject to individual credit approval. See the Citizens Pay Line of Credit Agreement  for full terms and conditions. Citizens Pay Line of Credit Account offered by Citizens Bank, N.A. ​