Ncert Solutions for Class 6 Maths Chapter 6 Integers
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NCERT SOLUTIONS FOR CLASS 6 MATH CHAPTER 6
Integers
6th standard maths Chapter 6
NCERT Solutions for Class 6 Maths Chapter 6
ncert class 6 maths Chapter 6
Ex . 6.1
1. Write opposites of the following :
(a) Increase in weight
Answer тАУ Decrease in weight
(b) 30 km north
Answer тАУ 30 km south
(c) 326 BC
Answer тАУ 326 A.D.
(d) Loss of Rs 700
Answer тАУ Gain of Rs 700
(e) 100 m above sea level
Answer тАУ Gain of Rs 700
2. Represent the following numbers as integers with appropriate signs.
(a) An aeroplane is flying at a height two thousand metre above the ground.
Answer тАУ + 2000
(b) A submarine is moving at a depth, eight hundred metre below the sea level.
Answer тАУ тАУ 800
(c) A deposit of rupees two hundred.
Answer тАУ + 200
(d) Withdrawal of rupees seven hundred.
Answer тАУ тАУ 700
(e) 100 m above sea level
Answer тАУ + 100
3. Represent the following numbers on a number line :
(a) + 5 | (b) тАУ 10 | (c) + 8 |
(d) тАУ 1 | (e) тАУ 6 | ┬а |
Answer тАУ┬а
(a) + 5
(b) тАУ 10
(c) + 8
(d) тАУ 1
(e) тАУ 6
4. Adjacent figure is a vertical number line, representing integers. Observe it and locate the following points :
(a) If point D is + 8, then which point is тАУ 8?
Answer тАУ F
(b) Is point G a negative integer or a positive integer?
Answer тАУ Negative Integer (тАУ 6)
(c) Write integers for points B and E.
Answer тАУ Point B represents 4 and point E represent тАУ 10.
(d) Which point marked on this number line has the least value?
Answer тАУ E has the least value as it represents тАУ 10
(e) Arrange all the points in decreasing order of value.
Answer тАУ D > C > B > A > O > H > G > F > E
5. Following is the list of temperatures of five places in India on a particular day of the year.
Place | Temperature | ┬а |
Siachin | 10┬░C below 0┬░C | ………. |
Shimla | 2┬░C below 0┬░C | ………. |
Ahmedabad | 30┬░C above 0┬░C | ………. |
Delhi | 20┬░C above 0┬░C | ………. |
Srinagar | 5┬░C below 0┬░C | ………. |
(a) Write the temperatures of these places in the form of integers in the blank column.
Answer тАУ
Place | Temperature | ┬а |
Siachin | 10┬░C below 0┬░C | тАУ 10┬░C |
Shimla | 2┬░C below 0┬░C | тАУ 2┬░C |
Ahmedabad | 30┬░C above 0┬░C | + 30┬░C |
Delhi | 20┬░C above 0┬░C | + 20┬░C |
Srinagar | 5┬░C below 0┬░C | + 5┬░C |
(b) Following is the number line representing the temperature in degree Celsius.
Plot the name of the city against its temperature.
Ans тАУ┬а
(c) Which is the coolest place?
Answer тАУ Siachin
(d) Write the names of the places where temperatures are above 10┬░C.
Answer тАУ Delhi and Ahmedabad
6. In each of the following pairs, which number is to the right of the other on the number line?
(a) 2, 9 | (b) тАУ 3, тАУ 8 | (c) 0, тАУ 1 |
(d) тАУ 11, 10 | (e) тАУ 6, 6 | (f) 1, тАУ 100 |
Answer тАУ┬а
(a) 2, 9
Ans тАУ 9 (because 9 is greater than 2)
(b) тАУ 3, тАУ 8
Ans тАУ тАУ 3 (because тАУ 3 is greater than тАУ 8)
(c) 0, тАУ 1
Ans тАУ 0 (because 0 is greater than тАУ 1)
(d) тАУ 11, 10
Ans тАУ 10 (because 10 is greater than тАУ 11)
(e) тАУ 6, 6
Ans тАУ (because 6 is greater than тАУ 6)
(f) 1, тАУ 100
Ans тАУ 1 (because 1 is greater than тАУ 100)
7. Write all the integers between the given pairs (write them in the increasing order.)
(a) 0 and тАУ 7 | (b) тАУ 4 and 4 |
(c) тАУ 8 and тАУ 15 | (d) тАУ 30 and тАУ 23 |
Answer тАУ┬а
(a) 0 and тАУ 7
Ans тАУ тАУ 6, тАУ 5, тАУ 4, тАУ 3, тАУ 2 and тАУ 1
(b) тАУ 4 and 4
Ans тАУ тАУ 3, тАУ 2, тАУ 1, 0, 1, 2 and 3
(c) тАУ 8 and тАУ 15
Ans тАУ тАУ 14, тАУ 13, тАУ 12, тАУ 11, тАУ 10 and тАУ 9
(d) тАУ 30 and тАУ 23
Ans тАУ тАУ 29, тАУ 28, тАУ 27, тАУ 26, тАУ 25, тАУ 24
8. (a) Write four negative integers greater than тАУ 20.
(b) Write four integers less than тАУ 10.
Answer тАУ
(a) four negative integers greater than тАУ 20 are тАУ 19, тАУ 18, тАУ 17, тАУ 16
(b) four integers less than тАУ 10 are тАУ 11, тАУ 12, тАУ 13, тАУ 14
9. For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
(a) тАУ 8 is to the right of тАУ 10 on a number line.
(b) тАУ 100 is to the right of тАУ 50 on a number line.
(c) Smallest negative integer is тАУ 1.
(d) тАУ 26 is greater than тАУ 25.
Answer тАУ┬а
(a) тАУ 8 is to the right of тАУ 10 on a number line.
Ans тАУ T
(b) тАУ 100 is to the right of тАУ 50 on a number line.
Ans тАУ F (because тАУ 100 is to the left of тАУ 50 on number line)
(c) Smallest negative integer is тАУ 1.
Ans тАУ F (because greatest negative integer is тАУ 1)
(d) тАУ 26 is greater than тАУ 25.
Ans тАУ F (because тАУ 26 is smaller than тАУ 25)
10. Draw a number line and answer the following :
(a) Which number will we reach if we move 4 numbers to the right of тАУ 2.
(b) Which number will we reach if we move 5 numbers to the left of 1.
(c) If we are at тАУ 8 on the number line, in which direction should we move to reach тАУ 13?
(d) If we are at тАУ 6 on the number line, in which direction should we move to reach тАУ 1?
Answer тАУ┬а
(a) Which number will we reach if we move 4 numbers to the right of тАУ 2.
Ans тАУ we reach at 2 if we move 4 numbers to the right of тАУ 2.
(b) Which number will we reach if we move 5 numbers to the left of 1.
Ans тАУ we reach at тАУ 4 if we move 5 numbers to the left of 1.
(c) If we are at тАУ 8 on the number line, in which direction should we move to reach тАУ 13?
Ans тАУ we are at тАУ 8 on the number line, in left direction should we move to reach тАУ 13.
(d) If we are at тАУ 6 on the number line, in which direction should we move to reach тАУ 1?
Ans тАУ we are at тАУ 6 on the number line, in right direction should we move to reach тАУ 1.
6th standard maths Chapter 6
NCERT Solutions for Class 6 Maths Chapter 6
ncert class 6 maths Chapter 6
Ex . 6.2
1. Using the number line write the integer which is :
(a) 3 more than 5
(b) 5 more than тАУ 5
(c) 6 less than 2
(d) 3 less than тАУ 2
Answer –┬а
(a) 3 more than 5
Sol – 8
(b) 5 more than тАУ 5
Sol – 0
(c) 6 less than 2
Sol – тАУ 4
(d) 3 less than тАУ 2
Sol – тАУ 5
2. Use number line and add the following integers :
(a) 9 + (тАУ 6)
(b) 5 + (тАУ 11)
(c) (тАУ 1) + (тАУ 7)
(d) (тАУ 5) + 10
(e) (тАУ 1) + (тАУ 2) + (тАУ 3)
(f) (тАУ 2) + 8 + (тАУ 4)
Answer –┬а
(a) 9 + (тАУ 6)
Sol – 3
(b) 5 + (тАУ 11)
Sol – тАУ 6
(c) (тАУ 1) + (тАУ 7)
Sol – тАУ 8
(d) (тАУ 5) + 10
Sol – 5
(e) (тАУ 1) + (тАУ 2) + (тАУ 3)
Sol – тАУ 6
(f) (тАУ 2) + 8 + (тАУ 4)
Sol – 2
3. Add without using number line :
(a) 11 + (тАУ 7) | (b) (тАУ 13) + (+ 18) |
(c) (тАУ 10) + (+ 19) | (d) (тАУ 250) + (+ 150) |
(e) (тАУ 380) + (тАУ 270) | (f) (тАУ 217) + (тАУ 100) |
Answer –┬а
(a) 11 + (тАУ 7)
Ans – 11 тАУ 7
= 4
(b) (тАУ 13) + (+ 18)
Ans – тАУ 13 + 18
= 5
(c) (тАУ 10) + (+ 19)
Ans – тАУ 10 + 19
= 9
(d) (тАУ 250) + (+ 150)
Ans – тАУ 250 + 150
= тАУ 100
(e) (тАУ 380) + (тАУ 270)
Ans – тАУ 380 тАУ 270
= тАУ 650
(f) (тАУ 217) + (тАУ 100)
Ans – тАУ 217 тАУ 100
= тАУ 317
4. Find the sum of :
(a) 137 and тАУ 354 | (b) тАУ 52 and 52 |
(c) тАУ 312, 39 and 192 | (d) тАУ 50, тАУ 200 and 300 |
Answer –
(a) 137 and тАУ 354
Sol – 137 + (тАУ 354)
= 137 тАУ 354
= тАУ 217
(b) тАУ 52 and 52
Sol – тАУ 52 + 52
= 0
(c) тАУ 312, 39 and 192
Sol – тАУ 312 + 39 + 192
= тАУ 312 + 231
= тАУ 81
(d) тАУ 50, тАУ 200 and 300
Sol –┬атАУ 50 + (тАУ 200) + 300
= тАУ 50 тАУ 200 + 300
= тАУ 250 + 300
= 50
5. Find the sum :
(a) (тАУ 7) + (тАУ 9) + 4 + 16
(b) (37) + (тАУ 2) + (тАУ 65) + (тАУ 8)
Answer –┬а
(a) (тАУ 7) + (тАУ 9) + 4 + 16
Sol – тАУ 7 тАУ 9 + 4 + 16
= тАУ 16 + 20
= 4
(b) (37) + (тАУ 2) + (тАУ 65) + (тАУ 8)
Ans – 37 тАУ 2 тАУ 65 тАУ 8
= 37 тАУ 75
= тАУ 38
6th standard maths Chapter 6
NCERT Solutions for Class 6 Maths Chapter 6
ncert class 6 maths Chapter 6
Ex . 6.3
1. Find
(a) 35 тАУ (20) | (b) 72 тАУ (90) |
(c) (тАУ 15) тАУ (тАУ 18) | (d) (тАУ 20) тАУ (13) |
(e) 23 тАУ (тАУ 12) | (f) (тАУ 32) тАУ (тАУ 40) |
Answer –
(a) 35 тАУ (20)
Sol – 35 тАУ 20
= 15
(b) 72 тАУ (90)
Ans – 72 тАУ 90
= тАУ 18
(c) (тАУ 15) тАУ (тАУ 18)
Sol – тАУ 15 + 18
= 3
(d) (тАУ 20) тАУ (13)
Sol – тАУ 20 тАУ 13
= тАУ 33
(e) 23 тАУ (тАУ 12)
Sol –┬а23 + 12
= 35
(f) (тАУ 32) тАУ (тАУ 40)
Sol – тАУ 32 + 40
= 8
2. Fill in the blanks with >, < or = sign.
(a) (тИТ 3) + (тАУ 6) ______ (тАУ 3) тАУ (тАУ 6)
(b) (тАУ 21) тАУ (тАУ 10) _____ (тАУ 31) + (тАУ 11)
(c) 45 тАУ (тАУ 11) ______ 57 + (тАУ 4)
(d) (тАУ 25) тАУ (тАУ 42) _____ (тАУ 42) тАУ (тАУ 25)
Answer –┬а
(a) (тИТ 3) + (тАУ 6) ______ (тАУ 3) тАУ (тАУ 6)
Sol – L.H.S тИТ 3 тИТ 6 = тИТ 9
R.H.S тИТ 3 + 6 = 3
So, (тИТ 3) + (тАУ 6) ┬а< ┬а(тАУ 3) тАУ (тАУ 6)
(b) (тАУ 21) тАУ (тАУ 10) _____ (тАУ 31) + (тАУ 11)
Sol – L.H.S тАУ 21 + 10 = тАУ 11
R.H.S тАУ 31 тАУ 11 = тАУ 42
So, (тАУ 21) тАУ (тАУ 10) ┬а>┬а (тАУ 31) + (тАУ 11)
(c) 45 тАУ (тАУ 11) ______ 57 + (тАУ 4)
Sol – L.H.S 45 + 11 = 56
R.H.S 57 тАУ 4 = 53
So, 45 тАУ (тАУ 11) ┬а>┬а 57 + (тАУ 4)
(d) (тАУ 25) тАУ (тАУ 42) _____ (тАУ 42) тАУ (тАУ 25)
Sol – L.H.S тАУ 25 тАУ (тАУ 42) = тАУ 25 + 42 = 17
R.H.S тАУ 42 + 25 = тАУ 17
So, (тАУ 25) тАУ (тАУ 42) ┬а>┬а (тАУ 42) тАУ (тАУ 25)
3. Fill in the blanks.
(a) (тАУ 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (тАУ 12) = ____
(d) (тАУ 4) + ____ = тАУ 12
(e) ____ тАУ 15 = тАУ 10
Answer –┬а
(a) (тАУ 8) + 8 = 0
(b) 13 + тАУ 13 = 0
(c) 12 + (тАУ 12) = 0
(d) (тАУ 4) + тАУ 8 = тАУ 12
(e) 5 тАУ 15 = тАУ 10
4. Find
(a) (тАУ 7) тАУ 8 тАУ (тАУ 25)
(b) (тАУ 13) + 32 тАУ 8 тАУ 1
(c) (тАУ 7) + (тАУ 8) + (тАУ 90)
(d) 50 тАУ (тАУ 40) тАУ (тАУ 2)
Answer –┬а
(a) (тАУ 7) тАУ 8 тАУ (тАУ 25)
Sol – тАУ 7 тАУ 8 + 25
= тАУ 15 + 25
= 10
(b) (тАУ 13) + 32 тАУ 8 тАУ 1
Sol – тАУ 13 + 32 тАУ 8 тАУ 1
= тАУ 22 + 32
= 10
(c) (тАУ 7) + (тАУ 8) + (тАУ 90)
Sol – тАУ 7 тАУ 8 тАУ 90
= тАУ 105
(d) 50 тАУ (тАУ 40) тАУ (тАУ 2)
Sol – 50 + 40 + 2
= 92