Important Questions for CBSE Class 6 Maths Chapter 6 - Integers

1 Mark Questions

1. Integers are denoted using the alphabet ___?

Ans: Integers are denoted using the alphabet Z.

2. $-9$__$5$. Fill in the blanks.

Ans: $-9<5$ 

3. Compare \[-\mathbf{815}\] and \[-\mathbf{814}\].

Ans: $-815<-814$

4. Say true or false. The absolute value of an integer is always greater than the integer.

Ans: True 

5. The predecessor of\[~\mathbf{219}\] is \[\mathbf{218}\]. Say true or false.

Ans: Predecessor of a number is the one that comes before the number.

\[\begin{align} & \text{Predecessor of a number} \\  & =\text{Number}1 \\  & =\left( -219 \right)1 \\  & =220. \\  \end{align}\]

Hence the statement is false.

6. ___ is called the Additive identity.

Ans: 0 is called the additive identity. This is because addition of zero to any number bears the same number.

7. \[-\mathbf{3}\] is the ___ of \[\mathbf{3}\].

Ans: $-3$ is the additive inverse of $3$. This is because on adding the numbers, we get zero, i.e., $\left( -3 \right)+3=0$.

8. \[\_\_\_\div \mathbf{483}=\mathbf{0}\]

Ans: 0

9. \[-\mathbf{843}\div \_\_\_=\mathbf{1}\]

Ans: -843

2 Marks Questions

1. Write opposite of each of the following:

(a) A decrease of 9

(b) Spending Rs.500

Ans: (a) An increase of $9$.

(b) Saving Rs.$500$.

2. Indicate using ‘$+$‘ or ‘$-$‘ sign

(a) 10km before sea level

(b) loss of Rs.900

Ans: (a) $-10$km

(b)$-$Rs.$900$

3. Write in ascending order: \[\mathbf{365}\], \[\mathbf{515}\], \[\mathbf{102}\], \[\mathbf{413}\], \[\mathbf{7}\].

Ans: $-515$, $-365$, $7$, $102$, $413$.

4. Write in descending order: \[\mathbf{21}\], \[\mathbf{501}\], \[\mathbf{2}\], \[\mathbf{16}\], \[\mathbf{81}\], \[\mathbf{363}\].

Ans: $21$, $-2$, $-16$, $-81$, $-363$, $-501$.

5. Find the value of the following:

(a)$-\left| -4 \right|$

(b)$\left| 7-4 \right|$

(c)$8-\left| 7 \right|$

Ans: (a)$-\left| -4 \right|=-4$

(b)$\left| 7-4 \right|=\left| 3 \right|=3$

(c)$8-\left| 7 \right|=8-7=1$

6. Add \[-\mathbf{82}\] and \[+\mathbf{45}\].

Ans: Adding $-82$ and $45$,

$\begin{align} & -82 \\  & +\underline{45} \\  & -37 \\  \end{align}$

Hence, the answer is $-37$.

7. Add \[-\mathbf{9568}\] and \[-\mathbf{695}\].

Ans: Adding $-9568$ and $-695$,

\[\begin{align} & -\text{ }9568 \\  & -\underline{\text{   }695} \\  & -10263 \\ \end{align}\]

Hence, the answer is $-10,263$.

8. Add 

(a) \[-\mathbf{19}+\mathbf{36}\]

(b) \[-\mathbf{49}+\mathbf{27}\]

Ans: (a) Adding $-19$ and $36$,

$\begin{align} & -19 \\  & +\underline{36} \\  & \text{  17} \\  \end{align}$

Hence, the answer is $17$.

(b) Adding $-49$ and $27$,

$\begin{align} & -49 \\ & +\underline{27} \\  & -22 \\  \end{align}$

Hence, the answer is $-22$.

9. \[\left( -14+6 \right)\]___$\left( -38-\left( -9 \right) \right)$. Use >, <, =

Ans: Solving both sides, we get

$\left( -14+6 \right)$__$\left( -38-\left( -9 \right) \right)$

$-8>-29$ 

3 Marks Questions

1. Mark the following on the number line:

(a) \[\mathbf{4}\]

(b) \[\mathbf{0}\]

(c) \[\mathbf{10}\] 

(d) \[\mathbf{6}\]

Ans: 

2. Write all integers between

(a) \[\mathbf{4}\] and \[\mathbf{4}\]

(b) \[\mathbf{8}\] and \[\mathbf{3}\]

Ans: (a) $-3$,$-2$, $-1$, $0$, $1$, $2$. $3$

(b) $-7$, $-6$, $-5$, $-4$

3. Subtract the following:

(a) \[-\mathbf{842}\] from \[\mathbf{0}\]

(b) \[-\mathbf{2959}\] from \[\mathbf{8158}\]

Ans: (a) Subtracting $-842$ from $0$,

$\begin{align} & 0-\left( -842 \right) \\  & =0+842 \\  & =842 \\  \end{align}$

Hence, the answer is $842$.

(b) Subtracting $-2959$ from $8158$,

$\begin{align} & 8158-\left( -2959 \right) \\  & =8158+2959 \\  & =11117 \\ \end{align}$

Hence, the answer is $11,117$.

4. The sum of two integers is – 38. If one of them is 240. Find the other.

Ans: We know that, $\text{addend+addend=sum}$

From given,

$\begin{align} & 240+X=-38 \\  & X=-38-240 \\  & X=-278 \\  \end{align}$

Hence, the other number is $-278$.

5. Find the product of \[\left( -27 \right)\times 18\times 30\].

Ans: The product of \[\left( -27 \right)\times 18\times 30\] is

\[\begin{align} & \left( -27 \right)\times 30\times 18 \\  & =-810\times 18 \\  & =-14580 \\  \end{align}\]

Hence, the answer is \[-14,580\].

6. Simplify: $\left( -37 \right)\times \left( -16 \right)+\left( -37 \right)\times \left( -14 \right)$.

Ans: $\left( -37 \right)\times \left( -16 \right)+\left( -37 \right)\times \left( -14 \right)$…(1)

We know that by distributive property,

$a\times b+a\times c=a\times \left( b+c \right)$

Hence, by (1),

$a=-37$, $b=-16$, $c=-14$

We get,

$\begin{align} & \left( -37 \right)\left[ \left( -16 \right)+\left( -14 \right) \right] \\  & =\left( -37 \right)\left[ -30 \right] \\  & =-1110 \\ \end{align}$

The answer after simplification is $-1110$.

7. Divide \[\left( +\mathbf{3251} \right)\] by \[\left( -\mathbf{27} \right)\].

Ans: We know that, 

$\frac{\left( +3251 \right)}{\left( -27 \right)}=-\left( \frac{3251}{27} \right)$

By long division, we get,

Hence, we get,

$\begin{align} & \text{Quotient=-120} \\  & \text{Remainder=11} \\  \end{align}$

4 Marks Questions

1. Using number line, write the following

(a) \[\mathbf{4}\] more than \[\mathbf{6}\]

(b) \[\mathbf{5}\] more than \[\mathbf{2}\]

(c) \[\mathbf{6}\] less than \[\mathbf{4}\]

(d) \[\mathbf{3}\] less than \[\mathbf{2}\]

Ans: (a) $4\text{ more than 6}=6+4=10$

(b) \[\text{5 more than -2}=5+\left( -2 \right)=5-2=3\]

(c) $6\text{ less than 4=4-6=-2}$

(d)$3\text{ less than }-2=\left( -2 \right)-3=-2-3=-5$

2. A bus travelled 30km to south, then 40km to north and from 30km to west. How for did the bus travel?

Ans:

Distance travelled south = \[-30\]km

Distance travelled North = \[40\]km

Distance travelled West = $-30$km

Hence, Total distance travelled 

\[\begin{array}{*{35}{l}} =\left( -30 \right)+40+\left( 30 \right)  \\ \begin{align} & =60+40 \\  & =-20 \\  \end{align}  \\ \end{array}\]

Thus, the total distance travelled is $20$km towards the south.

5 Marks Questions

1. In a class test containing \[\mathbf{25}\] questions, \[\mathbf{4}\] marks are given for every correct answer and \[\left( \mathbf{2} \right)\] marks are given for every wrong answer. A student attempts all questions and \[\mathbf{20}\] of his answers are correct. What is the total score of a student?

Ans: Total questions in test \[=25\]

Marks are given for 1 correct answer \[=4\]

Marks are given for 1 incorrect answer \[=2\]

Marks given for 20 correct answers \[=20\times 4=80\]

Total incorrect answers \[=\left( 2520 \right)=5\]

Marks given for incorrect answers \[=5\times \left( 2 \right)=10\]

Total score in test 

\[\begin{align} & =80+\left( 10 \right) \\  & =70 \\  \end{align}\]

Hence, the total score in the test is $70$ marks.

CBSE Class 6 Maths Important Questions Chapter 6 - Free PDF Download

Let’s Revise

• Integers is a set of all natural numbers, 0 and negatives of natural numbers are called integers, i.e., we can represent the integers on the number line. 

• Integers range from { ………, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …….. }

• The absolute value of an integer is the numerical value of the integer in any case regardless of its sign.

• Successors and predecessor of an integer: Let abe an integer, then: 

(a + 1) is called the successor of a.

(a - 1) is called the predecessor of a.

• Properties of addition of integers:

(i) Closure property of addition: The total of two integers is always an integer.

(ii) Commutative law of addition: a + b = b + a

(iii) Associative law of addition: the sum remains the same even if the grouping of addends change.

• Properties of subtraction of integers: 

(i) If two integers a and b are given then (a - b) is also an integer.

(ii) If a is considered an integer, then a - 0 = a.

(iii) if a, b, c are integers and a＞b, then (a - c)＞(b - c)

• Properties of multiplication of integers:

(i) Closure property: The result of two integers is always an integer after multiplication.

(ii) Commutative law: a x b = b x a.

(iii) Associative law: a x (b x c) = (a x b) x c.

(iv) Distributive law: a x (b + c) = a x b + a x c.

• Properties of division of integers:

(i) If two integers are a and b, then a ÷ b is not necessarily an integer.

(ii) If a ≠ 0, then a ÷ a = 1 

(iii) a ÷ 1 = a.

(iv) If a is a non-zero integer, then 0 ÷ a = 0, but  a ÷ 0 is not meaningful.

(v) (a ÷ b) ÷ c ≠ a ÷ (b ÷ c) unless c = 1.

• Representation of Integers on Number line: To represent integers on a number line, draw a line and mark some points at equal distances on it. Mark a point as 0 on it. Points to the right of 0 are positive integers and are marked as +1, +2, +3, etc. or simply 1, 2, 3, etc. Points to the left of are negative integers and are marked as -1, -2, -3, etc. 

• Ordering of Integers: On the number line, integers are grouped in such a way that when we move to the right the numbers increase and when we move to the left, the numbers decrease.

• We add the corresponding positive integers and retain the negative sign with the sum when adding two negative integers, Ex: Find the sum of -3 and -3. 

-3 + (-3) = - (3+ 3) = -6.

To add a positive integer and a negative integer, we ignore the signs and subtract integers with smaller numerical value from the integer with a larger numerical value and take the sign of the larger one. 

Ex: (a) Consider -6 and + 4

As 6 -4 = 2, therefore -6 + (+4) = -2

(b) Consider + 5 and -2

5 + (-2) = 5 - 2 = 3

Two integers whose sum is 0 are called additive inverse of each other. 

In order to subtract an integer from a given integer, we add an additive opposite of the integer to the given integer.

Ex: (a) Subtract 3 from -4

The additive inverse of 3 is -3

So, -4, -3 = -4 + (-3) = (4 + 3) = -7

(b) -2 from -4

The additive inverse of -3 is 3

So, -4 - (-2) = -4 + 2 = -2

• Addition/ Subtraction of Integers on Number line: Firstly draw the number line and represent the first number on it. Then to add/ subtract the second number in first, we move left/ right to the first number according to the second integer (either -ve or +ve)

Chapter 6 Integers for Class 6 teaches the concepts of Integers that you have learnt the basics of in your previous grade. The chapter Integers is the foundation of mathematics. Revising the chapter of Integers along with important questions will help you with other topics in mathematics. The important questions are prepared based on the topics that are discussed in this chapter. The reference notes for the chapter given above will benefit you in solving the Important Questions Of Chapter 6 of Maths for Class 6 Integers. The important questions of the chapter and the reference notes related to the chapter provided by Vedantu will not only help you to understand the concept better but also solve the questions successfully. If you still have any doubts then you can get answers to all your queries by reaching out to our experienced teachers. You can register on www.vedantu.com and master the topic. 

Why Should You Opt for Vedantu?

Vedantu is one of the foremost eLearning education forums of the country, where our team has worked very hard to create an awesome technology platform that enables learning in a very interactive and engaging manner. It is an online tutoring platform that connects teachers and students. Vedantu focuses on the quality of teachers because we believe a teacher can shape up the overall personality of a child. So our main priority is having good, qualified and experienced teachers on board. With the help of new technology, Vedantu has brought a revolution in all the traditional methods of teachings. Our experienced teachers have designed the courses with the latest technology called WAVE in which the teachers can teach while writing on the whiteboard. This will give a feeling of offline classes to the students. 

Students can avail abundant solutions and study materials affiliated to all the Boards of the country. These solutions for each subject, notes and study materials not only give you enough practice for the exams but also magnify your confidence and strengthen your conceptual understanding of the subject. You can also learn the shortcuts and tricks to solve the difficult questions from our master teachers. Our subject matter experts have done extensive research and have developed the NCERT Solution for all subjects. 

The solutions to the exercises in the course books are 100% verified and developed as per the latest edition CBSE textbooks. The online sessions are designed with in-class quizzes which enables master teachers to get real-time feedback on students' understanding. To prepare for advanced exams like IIT-JEE, KVPY and NEET examinations, you can count on Vedantu’s experienced teachers who are from some reputed institutions of the country. The USP of Vedantu is the live interactive sessions and innumerable students have been benefited from the courses that Vedantu provides. Take the right decision today to register with Vedantu and shape your career through us. 

Important Related Links for CBSE Class 6 Maths