Which is the largest integer and the smallest integer among them? Solution : Integers between – 8 and – 2 are – 7 – 6 – 5 – 4 – 3 The
Practice more on Integers Page - 1 www embibe com CBSE NCERT Solutions for Class 6 Mathematics Chapter 6 Back of Chapter Questions Exercise 6 1
Integers Worksheet for Class 6 1 Write all integers between a) 0 and 6 b) -3 and 3 2 Using the number line write the integer which is 6 less than 2?
RS Aggarwal Solutions for Class 6 Chapter 4 Integers Exercise 4A PAGE NO: 63 1 Write the opposite of each of the following: (i) An increase of 8
When we subtract –6 from 14 we get 20 14 – (–6) = 14 + 6 = 20 5 Zero is an integer which is neither positive nor
SUBJECT-MATHEMATICS CLASS-VI Short answer type question-I (3×2=6) Using the number line represent the integer which is 2 less than -3 6
+ Step 1: Multiply the absolute values of the numbers + Step 2: The sign of the answer is negative Remember: “Minus times plus is minus ” Example: 6 · (?5) =
b) Zero is not an integer as it is neither positive nor negative Write two integers whose sum is 6 and difference is also 6 Q5 Write 5 integers which
CLASS 6 (MATHS) CHAPTER – 5 ( INTEGERS) EXERCISE - 5 A ( SOLUTION) Q No 1 a Negative b Integer c – 4 d – 1 Q No 2 a A - 2 b B 3 c C 6
Class 6 Mathematics integers excluding the decimals or fractions ? The positive whole numbers are called the positive integers and the negative
948_6G6_NCERT_BOC_Integers.pdf
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 1 www.embibe.com CBSE NCERT Solutions for Class 6 Mathematics Chapter 6
Back of Chapter Questions
Exercise 6.1
1.Write opposite of the following:
(A)Increase in weight (B)30 km north (C)ͺͲ East (D)Loss of ൟ700 (E)ͳͲͲ above sea level
Solution:
(A)Decrease in weight(B)30 km south (C)ͺͲ West (D)Profit of ൟ700 (E)ͳͲͲ below sea level 2.
Represent the following numbers as integers with appropriate signs.(A)An aeroplane is flying at a height two thousand meters above the ground.
(B)A submarine is moving at a depth eight hundred meters below the sea level. (C)A deposit of rupees two hundred. (D)Withdrawal of rupees seven hundred.
Solution:
(A)ሺሻʹͲͲͲ meters Since, the aeroplane is flying above the ground, the height is taken to be positive. (B)ሺെሻͺͲͲ metersSince, the submarine is below the sea level, the depth is taken to be negative. (C)ሺሻʹͲͲ Rupees
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 2 www.embibe.com Deposition of money is considered to be positive while expenditure is
considered negative. (D) ሺെሻͲͲ Rupees Deposition of money is considered to be positive while expenditure is considered negative.
3. Represent the following numbers on number line:
(A) ͷ (B) െͳͲ (C) ͺ (D) െͳ (E) െ
Solution:
(A) ͷ is greater than 0, hence it appears towards the right of zero. (B) െͳͲ is lesser than 0, hence it appears towards the left of zero. (C) ͺ is greater than 0, hence it appears towards the right of zero. (D) െͳ is lesser than 0, hence it appears towards the left of zero. (E) െ is lesser than 0, hence it appears towards the left of zero.
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 3 www.embibe.com
4. Adjacent figure is a vertical number line, representing integers. Observe it and
locate the following points: (A) If point D is ͺ then which point is െͺ? (B) Is point a negative integer or a positive integer? (C) Write integers for points and . (D) Which point marked on this number line has the least value? (E) Arrange all the points in decreasing order of values.
Solution:
Let us draw a rough number line and locate points according to the given figure. (A) From the above figure, If point is ͺ, then െͺ will appear at a point :
ͺ units (from ͺ to Ͳ) ͺ units (from Ͳ to െͺ) ൌͳ units from .
Hence, point represents െͺ.
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 4 www.embibe.com (B) From the above figure,
Point G represents a negative integer.
Counting the integers from point D, we can observe that point O represents 0. Therefore, all the numbers below point O represent negative integers. (C) From the above figure, Point B lies 4 units below ሺሻͺ Therefore, the integer value of B is ሺሻͺȂͶൌሺሻͶ Now, point E lies ͳͺ units below ૡ. Until point , we have ͺ units. Therefore ͳͺെͺൌͳͲ will be the number of units below zero. ൌሺሻͶൌሺെሻͳͲ Hence, point E represents െͳͲ and point represents Ͷ (D) From the above figure, Since, down the line the value of integers decreases, point has the least value. (E) From the above figure, The point at the top of the number line has the highest value.
The value decreases down the number line.
Hence, the points arranged in the decreasing order of their values will be as follows: ǡǡǡǡǡǡǡǡ
5. Following is the list of temperatures of five places in India, on a particular day of
the year.
Place Temperature
Siachin ͳͲι below Ͳι ______________
Shimla ʹι below Ͳι ______________
Ahmedabad ͵Ͳι above Ͳι ______________
Delhi ʹͲι above Ͳι ______________
Srinagar ͷι below Ͳι ______________
(A) Write the temperature of these places in the form of integers in the blank column. (B) Following is the number line representing the temperature in degree
Celsius.
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 5 www.embibe.com Plot the name of the city against its temperature.
(C) Which is the coolest place? (D) Write the names of the place where temperatures are above ͳͲ୭.
Solution:
(A) In the below table, the temperature values are shown in integers form.
Place Temperature Temperature
Siachin ͳͲι below Ͳι ሺെሻͳͲι Shimla ʹι below Ͳι ሺെሻʹι Ahmedabad ͵Ͳι above Ͳι ሺሻ͵Ͳι Delhi ʹͲι above Ͳι ሺሻʹͲι Srinagar ͷι below Ͳι ሺെሻͷι (B) Number line represents name of the cities against its temperature. (C) From Siachin is the coldest place with the least temperature ofሺെሻͳͲι. Minimum number will be the smallest negative number. So,ሺെሻͳͲι is on the left of the line which is the smallest negative number. (E) From the table we can observe that, Ahmedabad with a temperature of ሺሻ͵Ͳι and Delhi with a temperature of ሺሻʹͲι have temperatures above ሺሻͳͲι.
6. In each of the following pairs, which number is to the right of the other on the
number line? (A) ʹǡͻ (B) െ͵ǡെͺ (C) Ͳǡെͳ (D) െͳͳǡͳͲ (E) െǡ
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 6 www.embibe.com (F) ͳǡെͳͲͲ
Solution:
(A) Since 9 is greater than 2, the integer 9 is to the right of 2.
(B) Since െ͵ is greater than െͺ, the integer െ͵ is to the right of െͺ.
(C) Since 0 is greater than െͳ, the integer Ͳ is to the right of െͳ (D) Since 10 is greater than െͳͳ, the integer ͳͲ is to the right of െͳͳ (E) Since 6 is greater than െ, the integer is to the right of െ
(F) Since 1 is greater than െͳͲͲ, the integer ͳ is to the right of െͳͲͲ
7. Write all the integers between the given pairs (write them in the increasing order):
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 7 www.embibe.com (A) Ͳ and െ (B) െͶ and Ͷ (C) െͺ and െͳͷ (D) െ͵Ͳ and െʹ͵
Solution:
The following are the integers between the given pairs, in the increasing order. (A) െǡെͷǡെͶǡെ͵ǡെʹǡെͳ (B) െ͵ǡെʹǡെͳǡͲǡͳǡʹǡ͵
(C) െͳͶǡെͳ͵ǡെͳʹǡെͳͳǡെͳͲǡെͻ
(D) െʹͻǡെʹͺǡെʹǡെʹǡെʹͷǡെʹͶ
8. (A) Write four negative integers greater than െʹͲ.
(B) Write four negative integers less than െͳͲ.
Solution:
Farther a number from zero on the left, smaller is its value. Hence,
(A) െͳͻǡെͳͺǡെͳǡെͳ are the examples of the numbers that are greater than
െʹͲ
(B) െͳͳǡെͳʹǡെͳ͵ǡെͳͶ are the examples of the numbers that are lesser than
െͳͲǤ
9. For the following statements write True (T) or False (F). If the statement is false,
correct the statement: (A) െͺ is to the right of െͳͲ on a number line. (B) െͳͲͲ is to the right of െͷͲ on a number line. (C) Smallest negative integer is െͳ. (D) െʹ is larger than െʹͷ.
Solution:
(A) True Since െͺ is greater than െͳͲ, the integer െͺ lies towards the right of
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 8 www.embibe.com െͳͲ. (B) False
Since െͷͲ is greater than െͳͲͲ, the integer െͷͲ lies towards the right of
െͳͲͲ. (C) False Farther the number from zero on the left, smaller is its value. Therefore, െͳ is the greatest negative integer. (D) False Farther the number from zero on the left, smaller is its value.
So, െʹ൏െʹͷ
Since െʹͷ lies closer to zero than െʹ, the integer െʹͷ is larger than
െʹ.
10. Draw a number line and answer the following:
(A) Which number will we reach if we move Ͷ numbers to the right of െʹ. (B) Which number will we reach if we move ͷ numbers to the left of ͳ. (C) If we are at െͺ on the number line, in which direction should we move to reach െͳ͵? (D) If we are at െ on the number line, in which direction should we move to reach െͳ?
Solution:
(A) L
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 9 www.embibe.com We will reach 2 if we move 4 numbers to the right of െʹ.
(B) We will reach െͶ if we move ͷ numbers to the left of ͳ. (C)
Since െͺ is greater than െͳ͵, the integer െͺ will lie to the right of െͳ͵.
Hence, we need to move towards the left on the number line from െͺ to reach െͳ͵. (D) Since െͳ is greater than െ, the integer െͳ will lie on the right side of െ. Hence, we need to move towards the right on the number line from െ to reach െͳ.
Exercise 6.2
1. Using the number line write the integer which is:
(A) 3 more than ͷ (B) 5 more than െͷ (C) 6 less than ʹ (D) 3 less than െʹ
Solution:
Farther a number from zero on the right, larger is its value. Farther a number from zero on the left, smaller is its value.
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 10 www.embibe.com (A) Let us consider any number line to plot integers,
Since, we need to arrive at a number that is 3 more than 5, we move towards the right of 5 by three units. The number obtained is 8. (B) Let us consider the number line to plot integers, Since, we need to arrive at a number that is ͷ more than െͷ, we move towards the right of െͷ by ͷ units. The number obtained is Ͳ. (C) Let us consider the number line to plot integers, Since, we need to arrive at a number that is less than ʹ, we move towards the left of ʹ by units. The number obtained will be െͶ. (E) Let us consider the number line to plot integers, Since, we need to arrive at a number that is three less than െʹ, we move towards the left of െʹ by ͵ units. The number obtained will be െͷ.
2. Use number line and add the following integers:
(A) ͻሺെሻ (B) ͷሺെͳͳሻ (C) ሺെͳሻሺെሻ (D) ሺെͷሻͳͲ (E) ሺെͳሻሺെʹሻሺെ͵ሻ (F) ሺെʹሻͺሺെͶሻ
Solution:
(A) Let us consider the number line, First, we move to 9 steps to right on the number line from 0 and retreat by
6 units towards left, hence obtaining 3.
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 11 www.embibe.com ͻሺെሻൌ͵ (B) Let us consider the number line, Now first we move to 5 steps right from 0 on the number line and retreat by 11 units, hence obtaining െ. ͷሺെͳͳሻൌെ (C) Let us consider the number line, First, we move to 1 step left from 0 on the number line and then move units from െͳ towards left, hence obtaining െͺ. ሺെͳሻሺെሻൌെͺ (D) Let us consider the number line, Now first we move 5 units to the left of 0 to obtain െͷ and then move 10 units forward from െͷ, hence obtaining 5. ሺെͷሻͳͲൌͷ (E) We first move one unit to the left of 0 to obtain െͳ and then move 2 and 3 steps subsequently, hence obtaining െ. ሺെͳሻሺെʹሻሺെ͵ሻൌെ
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 12 www.embibe.com (F) We first move ʹ units to the left of zero, to obtain െʹ. Then we move ͺ units forward from െʹ, thereby reaching 6. From retreat by 4 units to obtain ʹ. ሺെʹሻͺሺെͶሻൌʹ
3. Add without using number line:
(A) ͳͳሺെሻ (B) ሺെͳ͵ሻሺͳͺሻ (C) ሺെͳͲሻሺͳͻሻ (D) ሺെʹͷͲሻሺͳͷͲሻ (E) ሺെ͵ͺͲሻሺെʹͲሻ (F) ሺെʹͳሻሺെͳͲͲሻ
Solution:
(A) ͳͳሺെሻ ൌͳͳെ ൌͶ (B) ሺെͳ͵ሻͳͺ ൌͳͺെͳ͵ ൌͷ (C) ሺെͳͲሻሺͳͻሻ ൌെͳͲͳͻ ൌͻ (D) ሺെʹͷͲሻሺͳͷͲሻ ൌെʹͷͲͳͷͲ ൌെͳͲͲ
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 13 www.embibe.com (E) ሺെ͵ͺͲሻሺെʹͲሻ
ൌെ͵ͺͲെʹͲ ൌെͷͲ (F) ሺെʹͳሻሺെͳͲͲሻ ൌെʹͳെͳͲͲ ൌെ͵ͳ
4. Find the sum of:
(A) ͳ͵ and െ͵ͷͶ (B) െͷʹ and ͷʹ (C) െʹͳ͵ǡ͵ͻ and ͳͻʹ (D) െͷͲǡെʹͲͲ and ͵ͲͲ
Solution:
(A) ͳ͵ሺെ͵ͷͶሻ ൌͳ͵െ͵ͷͶ ൌെʹͳ (E) ሺെͷʹሻͷʹൌͲ [Additive inverses] (C) ሺെ͵ͳʹሻ͵ͻͳͻʹ ൌെ͵ͳʹʹ͵ͳ ൌെͺͳ (D) ሺെͷͲሻሺെʹͲͲሻ͵ͲͲ ൌെͷͲെʹͲͲ͵ͲͲ ൌെʹͷͲ͵ͲͲ ൌͷͲ
5. Find the value of:
(A) ሺെሻሺെͻሻͶͳ
(B) ͵ሺെʹሻሺെͷሻሺെͺሻ
Solution:
(A) ሺെሻሺെͻሻͶͳ
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 14 www.embibe.com ൌെെͻͶͳ
ൌെͳʹͲ ൌͶ
(B) ͵ሺെʹሻሺെͷሻሺെͺሻ
ൌ͵െʹെͷെͺ ൌ͵െͷ ൌെ͵ͺ
Exercise 6.3
1. Find:
(A) ͵ͷെሺʹͲሻ (B) ʹെሺͻͲሻ (C) ሺെͳͷሻെሺെͳͺሻ (D) ሺെʹͲሻെሺͳ͵ሻ (E) ʹ͵െሺെͳʹሻ (F) ሺെ͵ʹሻെሺെͶͲሻ
Solution:
(A) ͵ͷെሺʹͲሻ ൌ͵ͷെʹͲ ൌͳͷ (B) ʹെሺͻͲሻ ൌʹെͻͲ ൌെͳͺ (C) ሺെͳͷሻെሺെͳͺሻ ൌെͳͷͳͺ ൌ͵ (D) ሺെʹͲሻെሺͳ͵ሻ ൌെʹͲെͳ͵ ൌെ͵͵ (E) ʹ͵െͳʹ
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 15 www.embibe.com ൌʹ͵ͳʹ ൌ͵ͷ (F) ሺെ͵ʹሻെሺെͶͲሻ ൌെ͵ʹͶͲ ൌͺ
2. Fill in the blanks with ǡ൏ or = sign:
(A) ሺെ͵ሻሺെሻ ____________ ሺെ͵ሻെሺെሻ
(B) ሺെʹͳሻെሺെͳͲሻǤ__________ ሺെ͵ͳሻሺെͳͳሻ
(C) Ͷͷെሺെͳͳሻ ___________ ͷሺെͶሻ
(D) ሺെʹͷሻെሺെͶʹሻǤ___________ ሺെͶʹሻെሺെʹͷሻ
Solution:
(A) Given, LHS: ሺെ͵ሻሺെሻൌሺെͻሻ RHS: ሺെ͵ሻെሺെሻൌ͵
Clearly, RHSLHS
So, ͵ሺെͻሻ
Therefore,ሺെ͵ሻሺെሻ൏ሺെ͵ሻെሺെሻ
(B) Given, LHS: ሺെʹͳሻെሺെͳͲሻൌሺെͳͳሻ RHS: ሺെ͵ͳሻሺെͳͳሻൌሺെͶʹሻ
Clearly, LHSRHS
So,ሺെͳͳሻሺെͶʹሻ
Therefore, ሺെʹͳሻെሺെͳͲሻሺെ͵ͳሻሺെͳͳሻ
(C) Given,
LHS: Ͷͷെͳͳൌͷ
RHS: ͷሺെͶሻൌͷ͵
Clearly, RHS൏LHS
So, ͷͷ͵
Hence, ͶͷെሺെͳͳሻͷሺെͶሻ
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 16 www.embibe.com (D) Given, LHS: ሺെʹͷሻെሺെͶʹሻൌͳ RHS: ሺെͶʹሻെሺെʹͷሻൌሺെͳሻ
Clearly, RHS൏LHS
So, ͳሺെͳሻ
Therefore, ሺെʹͷሻെሺെͶʹሻሺെͶʹሻെሺെʹͷሻ
3. Fill in the blanks:
(A) ሺെͺሻ __________ ൌͲ (B) ͳ͵ ___________ ൌͲ (C) ͳʹሺെͳʹሻൌ _________ (D) ሺെͶሻ _________ ൌെͳʹ (E) ___________ െͳͷൌെͳͲ
Solution:
(A) Additive inverse of ሺെͺሻ is 8.
So, ሺെͺሻͺൌͲ
Hence, 8 is the required answer.
(B) Additive inverse of ͳ͵ is ሺെͳ͵ሻ. So, ͳ͵ሺെͳ͵ሻൌͲ Hence, ሺെͳ͵ሻ is the required answer. (C) ͳʹ and ሺെͳʹሻ are additive inverses of each other. Hence, upon adding its sum will be equal to zero. ͳʹሺെͳʹሻൌͲ Therefore, ሺെͳʹሻ is the required answer. (D) Since, ሺെͳʹሻͶൌሺെͺሻ. So, ሺെͶሻሺെͺሻൌെͳʹ Hence, ሺെͺሻ is the required answer. (E) Since, ሺെͳͲሻͳͷൌͷ,
So, ͷെͳͷൌെͳͲ
Therefore, 5 is the required answer.
Class- VI-CBSE-Mathematics Integers
Practice more on Integers Page - 17 www.embibe.com 4. Find: (A) ሺെሻെͺെሺെʹͷሻ (B) ሺെͳ͵ሻ͵ʹെͺെͳ (C) ሺെሻሺെͺሻሺെͻͲሻ (D) ͷͲെሺെͶͲሻെሺെʹሻ
Solution:
(A) ሺെሻെͺെሺെʹͷሻ ൌെെͺʹͷ ൌെͳͷʹͷ ൌͳͲ (B) ሺെͳ͵ሻ͵ʹെͺെͳ ൌെͳ͵͵ʹെͺെͳ ൌ͵ʹെʹʹ ൌͳͲ (C) ሺെሻሺെͺሻሺെͻͲሻ ൌെെͺെͻͲ ൌെͳͲͷ (D) ͷͲሺെͶͲሻെሺെʹሻ ൌͷͲͶͲʹ ൌͻʹ