Edudel, Directorate of Education Govt. of NCT of Delhi Class 6 Mental Maths Chapter 6 Integers Questions Solution. In this chapter, there is total 50 math problems. We have given each questions solution step by step.
1.) Find the smallest positive integer.
Answer: 1
2.) Find the smallest integer greater than all the negative numbers.
Answer: 0
3.) Find the integer which is neither positive nor negative.
Answer: 0
4.) Find the opposite of the following and represent with signs: (i) 1320 metre above sea level (ii) Going 2 km towards West (iii) Temperature 7° C above 0° C
Find the integers for the following: (Q. No. 5 to Q. No. 80)
Answer:
(i) 1320 m below sea level that is ( -1320m )
(ii) Going 2 km towards East that is (+ 2 km )
(iii) Temperature 7°C below 0°C that is ( – 7°C )
5.) Add 5 to additive inverse of (– 12).
Answer:
Additive inverse of (-12) = 12
5 + 12 = 17
Add 5 to additive inverse of (– 12) is 17
6.) Subtract (– 123) from (– 456).
Answer:
= (- 456) – (- 123)
= (- 456) + 123
= ( -333)
When a positive integer and a negative integer are added, actually they will be subtracted like whole numbers and the difference will take the sign of the integer which is greater in magnitude.
7.) 9 less than (– 5).
Answer: -14
= (- 5) – 9
= -5 – 9
= (-14 )
When two negative integers are added, sum is also a negative integer.
8.) 5 more than (– 2).
Answer:
= (-2) + 5
= 3
When a positive integer and a negative integer are added, actually they will be subtracted like whole numbers and the difference will take the sign of the integer which is greater in magnitude.
9.) Find the integer which when divided by (– 2) gives (– 24).
Answer:
Let the integer be X
X÷(-2) = (-24) – – – – ( Given equation)
X = (-24) ×(- 2)
X = 48
Integer which when divided by (– 2) gives (– 24) is 48
10.) Find the integer which when divided by (– 3) gives 25.
Answer: -75
Let the integer be X
X÷(-3) = 25 – – – – ( Given equation)
X = 25 ×(- 3)
X = (- 75)
Integer which when divided by (– 3) gives 25 is ( – 75)
11.) On the number line, which number do we get if we move 5 numbers to the right of (– 2)?
Answer: 3
12.) On the number line, which number do we get if we move 9 steps to the left of 4?
Answer:(-5)
13.) Find the value of : 4 – {13 – (23 – 18)}
Answer :
= 4 –( 13 – 5)
= 4 – ( 8)
= (- 4)
Observe the given line and find the integers for the following: (Q. No. 14 to Q. No. 21)
14.) Find the integer for K
Answer: (-7)
15.) Find the integer for Y
Answer: 10
16.) Find the integer for M
Answer: 7
17.) Find the integer for R + P – W
Answer: (-3) + (-1) – 3
=(-3) – 1 – 3
= (-3) – 4
= ( -7)
18.) Find the integer for Y + P – M
Answer:
10 + (-1) – 7
=10 – 1 -7
= 10 -8
= 2
19.) Find the integer for W + T + Y
Answer: 3 + 5 + 10
= 8 + 10
= 18
20.) Find the integer for S + R + W
Answer:
= (-5) + (-3) + 3
= (-5) – 3 +3
= (-5)
21.) Find the integer for P – T – M
Answer: (-1) – 5 –7
= (-1) – 12
= (-13)
22.) Arrange in increasing order: 3, 0, – 3, 5, – 1
Answer:(– 3) < (– 1) < 0 < 3 < 5
23.) Arrange in decreasing order: 23, 15, – 5, 2, – 25
Answer: 23 > 15 > 2 > (– 5) > (–25)
24.) Arrange in increasing order: 5, –6, – 4, 0, 8, 6
Answer: (– 6) < (– 4) < 0 < 5 < 6 < 8
25.) Arrange in decreasing order: 13, – 21, 17, 15, – 15, 10
Answer:17 > 15 > 13 > 10 > (– 15) > (– 21)
26.) Find the value of 9999 – 999 – 100
Answer: = (9999 –999) – 100
= 9000 – 100
= 8900
27.) Find the integers that lie between (– 3) and 1.
Answer:(– 2), (– 1), 0
28.) If you are at (– 3) on the number line, in which direction should you move to reach (– 8)?
Answer: Left side
29.) If you are at (– 5) on the number line, in which direction should you move to reach at 2?
Answer: Right Side
30.) Subtract (– 104) from the sum of 38 and (– 27).
Answer: = 38 + (-27) – ( -104)
= 11 – (-104)
= 11 + 104
= 115
31.) Subtract the sum of (– 100) and 225 from 50.
Answer:
= 50 –(-100 + 225)
= 50 –125
= (- 75)
32.) Find: (– 5) – (6) – (– 16)
Answer:
= (-5) –(6) – (-16)
= (-11) – (-16)
= (-11) + 16
= 5
33.) Find: (– 10) + (18) + (– 28) + (– 6)
Answer:
= (– 10) + (18) + (– 28) + (– 6)
= (- 10 + 18 ) + (-28) + (-6)
= 8 – 28 + (-6)
= (-20) – 6
= ( – 26 )
34.) Find: (– 7) + (– 9) + (4) + (16)
Represent the following integers with appropriate sign: (Q. No. 35 to Q. No. 40)
Answer:
= (– 7) + (– 9) + (4) + (16)
= ((-7) -9 + 4) +16
= (-16 + 4)+ 16
= (-12) + 16
= 4
35.) A withdrawal of Rs 2300 from the bank.
Answer: withdrawal means decrease in money so the number can be written as Rs(– 2300 )
36.) A submarine is moving at a depth of five hundred metre below sea level.
Answer: depth means distance downwards so the the number can be written as (-500) m
37.) Gaining a weight of 2 kg.
Answer:- Gaining means receive or add on which is shown positively
Number can be written as + 2 kg
38.) Going 600 metre above sea level.
Answer: Going above is shown in positive
Number is written as + 600 m
39.) Temperature six degree Celsius above 0 degree Celsius.
Answer: + 6°C
40.) An aeroplane is flying at a height three thousand five hundred metre above the ground.
Answer: + 3500 m
41.) Sachin scores 35 runs more than his previous score,
Answer: + 35
42.) The sum of two integers is (– 26). If one of them is 43, then find the other integer.
Answer: Let one integer be X
43 + X = (-26) – – – – – ( Given Equation)
X = (-26) – 43
X = (– 69)
43.) If a = (– 8), b = (– 6) and c = 6, then find the value of a + b – c.
Answer: a = (– 8), b = (– 6) and c = 6
Substituting the values of a , b and c
We get
a + b – c = (-8) + (-6) – 6
= ((-8) – 6 ) – 6
= (-14) – 6
= ( – 20 )
44.) The difference of an integer P and (– 5) is 4. Find the value of P.
Answer: Given equation is
P – (-5) = 4
P +5 = 4
P = 4 -5
P= (- 1 )
45.) What must be subtracted from (– 3) to get (– 8)?
Answer: Let the number to be subtracted be X
Given equation is
(-3) –X = (-8)
X = (-3) + 8
X = 5
46.) A bucket contains 35 litres of water. Due to a small hole in the bucket, the quantity of water is decreasing at the rate of 2 litres every hour. Find the quantity of water in the bucket after 10 hours.
Answer:
Water in 1 bucket = 35 litres
Water decreasing per hour = 2 litres
Water decreasing after 10 hours =20 litres
Water left in the bucket after 10 hours = Total water in 1 bucket – water decreasing after 10 hours
Water left in the bucket after 10 hours = 35 – 20
Water left in the bucket after 10 hours = 15 litres
Quantity of water in the bucket after 10 hours is 15 litres
47.) An insect crawls 10 cm every second on a 90 cm vertical rod and then falls down 4 cm over the next second. How many seconds will it take to climb the rod?
Answer:
48.) In a class test containing 20 questions. 5 marks are given for every correct answer, (– 2) marks is given for every incorrect answer. Heena attempts all questions and 14 of her answers are correct. What is her total score?
Answer:
A test containing no. Of questions = 20
Every correct answer = 5 marks
Every wrong answer = (- 2) marks
No. Of questions heena attempts = 20
No. Of correct answer = 14
No. Of wrong answer = 20 – 14 = 6
Total marks for 20 questions = 20 × 5 = 100 marks
Total Score of heena can be calculated as Score of correct answer + Score of wrong answer
= (No. of correct answer × 5) + (No. of wrong answer × (-2))
= ( 14 ×5) + ( 6 × (-2))
= 70 + (-12)
= 58 marks
Total score of Heena is 58 marks
49.) In a class test containing 20 questions, 5 marks are given for every correct answer, (– 1) mark is given for every incorrect answer and 0 mark for each unattempted question. Ravi gets 4 correct and 4 incorrect answers. Find his score.
Answer:
A test containing no. of questions = 20
Every correct answer = 5 marks
Every incorrect answer = (- 1) marks
Every unattempted question = 0 marks
No. of correct answer score by Ravi = 4
No. of incorrect answer score by Ravi = 4
Total Score of Ravi can be calculated as Score of correct answer + Score of incorrect answer
= (No. of correct answer × 5) + (No. of wrong answer × (-1))
= ( 4×5) + ((4 × (-1))
= 20 + (-4)
= 16 marks
Total Score of Ravi is 16 marks
50.) A certain freezing process requires that room temperature be lowered from 40°C at the rate of 6°C per hour. What will be room temperature 10 hours after the process begins?
Answer:
Initial temperature = 40⁰ C
Rate of change in temperature = 6⁰ C/ hr
Total decrease in temperature after 10 hours = 6 X 10
= 60⁰ C
Final temperature will be
= (initial temperature) –(decrease in temperature after 10 hours)
= 40⁰ – 60⁰
= ( – 20⁰ C )
Final temperature will be (-20⁰C)
Other Chapter’s Solution:
Chapter 2 |
Whole Numbers |
Chapter 3 |
|
Chapter 4 |
Basic Geometrical ideas |
Chapter 5 |