Category: Class 6

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 3 Bill, Profit and Loss Intext Questions

Try These (Textbook Page No.49)

Question 1.
Arrange in ascending order
(i) C.P, M.P, Discount
(ii) M.P., S.P., Discount
Solution:
(i) Discount < C.P < M.P.
(ii) Discount < S.P < M.P

Question 2.
Which is greater S.P or M.P?
Solution:
M.P is greater than S.P

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 3 Bill, Profit and Loss Additional Questions

Question 1.
______ is the difference between S.P and C.P., when S.P > C.P.
Solution:
Profit

Question 2.

(a) What is the total bill amount?
(b) Which item is the costliest one?
(c) Write the name of the shop?
Solution:
(a) ₹ 4,050
(b) Tables
(c) ABC Furnitures, Madurai

Question 3.
A vegetable vendor bought a dozen drum sticks for ₹ 42. Two of them become dry. If he has to get a profit of ₹ 8. Find the S.P of each drumstick.
Solution:
12 drumsticks cost price = ₹ 42
Profit = ₹ 8
Profit = S.P – C.P
⇒ 8 = S.P – 42
⇒ S.P = 8 + 42 = ₹ 50
S.P of 10 drumsticks = ₹ 50
S.P of each drumstick = \(\frac { 50 }{ 10 }\) = ₹ 5

Question 4.
Rice is being sold at ₹ 1800 per bag of 25kg at profit of ₹ 250. Find the Cost price of the rice bag.
Solution:
S.P = ₹ 1800
Profit = ₹ 250
Profit = S.P – C.P
⇒ 250 = 1800 – C.P
⇒ C.P = 1800 – 250 = ₹ 1550

Question 5.
Mangai buys a book for ₹ 300. She wants to sell it at a profit of ₹ 50 after making a discount of ₹ 30. What is the M.P of a book?
Solution:
Profit = S.P – C.P
⇒ 50 = S.P – 300
⇒ S.P = 50 + 300 = 350
S.P = M.P – Discount
⇒ 350 = M.P – 30
⇒ M.P = 350 + 30 = ₹ 380

Question 6.
Manila buys a dress for ₹ 750. She wants to sell it at a profit of ₹ 75 on sales and she marks ₹ 900. What is the discount that she will give to her customers?
Solution:
Profit = S.P – C.P
⇒ 75 = S.P – 750
⇒ S.P = 75 + 750 = ₹ 825
S.P = M.P – Discount
⇒ 825 = 900 – Discount
⇒ Discount = 900 – 825 = ₹ 75

Question 7.
Complete the following table:

Solution:
(i) Profit = S.P – C.P = 60 – 50 where CP < SP = ₹ 10
(ii) S.P = C.P – loss = 80 – 15 = ₹ 65

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 3 Perimeter and Area Intext Questions

Activity (Text book Page No. 39)

Question 1.
Observe the following shapes and answer the questions given below.

i) Mark the closed shapes as ‘✓’ and open shapes as ‘✗’
ii) Find the measure of the boundary of closed shapes by using a ruler.
iii) Which closed shape has the shortest boundary?
iv) Which closed shape has the longest boundary?
Activity to be done by the students themselves

Try this (Text book Page No. 40)

Question 1.

Is the perimeter of the given shape possible ? why ?
Solution:
Not possible. Because perimeter is the length of the boundaries of any closed shape. It is not a closed shape.

Try These (Text book Page No.41)

Question 1.
Draw a shape with perimeter 16 cm in a dot sheet.
Solution:

Question 2.
What is the perimeter of a rectangle if the length is twice its breadth?
Solution:
Perimeter of a rectangle = 2(l + b) units
= 2 × (2b + b) units
= 2 × 3b units = 6b units

Perimeter of a rectangle = 6b units.

Question 3.
What would be the perimeter of a square if its side is reduced to half?
Solution:
Let a side of a square = s units.

Question 4.
What is the perimeter of a triangle if all sides are equal in length?
Solution:
Perimeter of a triangle P = sum of its 3 sides.
If all sides are equal, it is an equilateral triangle with side say a.
Perimeter = a + a + a units = 3a units

Activity (Text book Page No. 41)

Question 1.
Choose any five items like Table, A4 sheet, Note-book, etc in the classroom. Guess the approximate length of each side by observation and write down the estimated perimeter of the item. Then, measure by using ruler and record the actual perimeter and find the difference in the following table (to the nearest cm)

Solution:
Activity to be done by the students themselves

Try this (Text book Page No. 42)

Question 1.

Can different shapes have the same perimeter
Solution:
Yes, different shapes can have the same perimeter.

Try These (Text book Page No. 43)

Question 1.
Find the breadth of the rectangle with perimeter 14 m and length 4 m.
Solution:
Given perimeter of the rectangle P = 14 m
length l = 4 m

Question 2.
The perimeter of an isosceles triangle is 21 cm. Find the measure of equal sides given that the third side is 5 cm.
Solution:
Perimeter of the triangle P = (a + b + c) units.
21 = [(a + b) + 5] cm
21 – 5 = a + b
16 = a + b
Here a and b are equal sides and let a = b
16 = a + a
2a = 16
\(a=\frac{16}{2}\)
a = 8 cm.
∴ Equal sides measure 8 cm.

Try these (Text book Page No. 44)

Question 1.
Find the number of tiles required to fill the area of following figures

Solution:
i) Total number of tiles required = 16
Number of tiles already filled = 7
Remaining required tiles = 16 – 7 = 9
ii) Total number of tiles required = 12
Number of tiles already filled = 6
Remaining required tiles = 12 – 6 = 6
iii) Total number of tiles required = 12
Number of tiles already filled = 6
Remaining required tiles = 12 – 6 = 6
iv) Total number of tiles required = 16
Number of tiles already filled = 8
Remaining required tiles = 16 – 8 = 8

Activity (Text book Page No. 45)

Question 1.
Mark the base and height of the following right angled triangle.

Solution:
Activity to be done by the students themselves

Try These (Text book Page No. 45)

Question 1.
Draw the following in a graph sheet?
i) Two different rectangles whose areas are 16cm²
Solution:

Activity (Text book Page No. 46)

Question 1.
Find the area of the given ‘L’ shaped rectangular figure by dividing it into squares of equal sizes
Solution:
Activity to be done by the students themselves

Try this (Text book Page No.46)

Question 2.
Can you find the area of ‘L’ shaped figure as the difference between two areas.
Solution:
Here Area of L shape = (Area of the rectangle ABCD)
(Area of the rectangle GFHB) = (2 × 3) – (2 × 1) cm²
= 6 – 2 cm² = 4 cm²

Try these (Text book Page No. 46)

Question 1.
Measure using ruler and find the perimeter of each of the following diagram

Solution:
i) Perimeter = 2.5 + 0.5 + 1 + 1 + 0.5 + 1 + 0.5 + 1 + 0.5 + 1.5 = 10 cm
ii) Perimeter = 2.5 + 0.5 + 2.5 + 0.5 + 0.5 cm = 6.5 cm
iii) Perimeter = 0.5 + 1 + 0.5 + 0.5 + 1 + 1 + 0.5 + 1 + 1.5 + 0.5 + 1 + 0.5 cm = 9 cm
iv) Perimeter = 2 + 0.5 + 1.5 + 1.5 + 0.5 + 0.5 + 2 + 1 cm = 9.5 cm

Activity (Text book Page No 46)

Question 1.
Form all possible shapes of perimeter 80 cm with 9 identical squares, each of side 4 cm.
Solution:
Activity to be done by the students themselves

Activity

Question 2.
Cut a rectangular sheet along one of its diagonals. Two identical scalene right angled triangles are obtained. Join them along their sides of identical length in all possible ways. Six different shapes can be obtained. Four of them are given. Find the remaining two shapes. Find the perimeter of all the six shapes and fill in the table.



Based on the above activity answer the following questions:
i) Are the perimeters same for all the shapes?
ii) Which shape has the longest perimeter?
iii) Which shape has the shortest perimeter?
iv) Are the areas of all the shapes same? why?
Solution:
Activity to be done by the students themselves

Try These (Text book Page No. 49)

Question 1.
Find the approximate area of the following figures:

Solution:

Try these (Text book Page No. 50)

Question 2.
Fill in the blanks.
(i) 7 cm² = ____ mm²
Hint: 1 cm² = 100 m
Solution:
700

(ii) 10 m² = ___ cm²
Hint: 1 m² = 10000 cm²
Solution:
1,00,000

(iii) 3 km² = ____ m²
Hint: 1 km² = 1000000
Solution:
30,00,000

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 2 Measurements Intext Questions

Try These (Textbook Page No. 26)

Question 1.
Complete the following table:

Solution:

Question 2.
Determine which metric unit you would use to express the following:

1. The length of your middle finger.
2. The weight of an elephant.
3. The weight of the ring.
4. The weight of the tablet.
5. The length of the safety pin.
6. The height of the building.
7. The length of the seashore in Tamilnadu.
8. The volume of a cup of coffee.
9. The capacity of water in the tank.

Solution:

1. Cm
2. Kilogram
3. gram
4. milligram
5. millimetre
6. metre
7. Kilometre
8. Millilitre
9. Litre

Try These (Textbook Page No. 28)

Question 1.
Convert the following.
(i) 23 km into m
(ii) 1.78 m into cm
(iii) 7814 m into km
(iv) 8.67 mm into cm
(v) 16 l into ml
(vi) 1500 ml into l
(vii) 2360 l into kl
(viii) 873 l into ml
(ix) 40 mg into g
(x) 1550 g into kg
(xi) 6.5 kg into g
(xii) 723 g into mg
Solution:

Try These (Textbook Page No. 30)

Question 1.
Five kilograms of compost is needed for a coconut tree for every six months. How many kilograms of compost is needed for 50 such coconut trees for one and a half years?
Solution:
Compost needed for a tree for 6 months = 5 kg
Compost needed for 50 trees for half a year = 5 × 50 = 250 kg.
Compost needed for 1\(\frac { 1 }{ 2 }\) years = 250 × 3 = 750 kg. [∴ 1\(\frac { 1 }{ 2 }\) years = 3 half years]

Question 2.
Say True or False and Justify.
(a) Is it correct: 4 m + 3 cm = 7 m
(b) Can we add the following?
(i) 6 litre + 7 kg
(ii) 3 m + 5 l
(iii) 400 ml + 300 g
Solution:
(a) False.
4 m + 3 cm = 400 cm + 3 cm = 403 cm.
(b) (i) No, we can’t add.
(ii) No. We can’t add.
(iii) No. We can’t add.

Recap (Textbook Page No. 33)

Question 1.
Read and write the time in the appropriate place.

Solution:

Try These (Textbook Page No. 33)

Question 1.
Say the following time in two ways.
(a) 9.20
(b) 4.50
(c) 5.15
(d) 6.45
(e) 11.30
Solution:
(a) 9.20
20 minutes past 9
40 minutes to 10
(b) 4.50
50 minutes past 4
10 minutes to 5
(c) 5.15
15 minutes past 5
45 minutes to 6
(d) 6.45
45 minutes past 6
15 minutes to 7
(e) 11.30
30 minutes past 11
30 minutes to 12

Try These (Textbook Page No. 34)

Question 1.
Convert the following:
(i) 4 hours = _____ minutes
(ii) 240 minutes = ____ hours
(iii) 30 minutes = _____ seconds
(iv) 3600 seconds = _____ hours
(v) 2 hours = _____ seconds
Solution:
(i) 4 hours = 240 minutes
4 hours = 4 × 60 minutes = 240 minutes
(ii) 240 minutes = 4 hrs
240 minutes = \(\frac{240}{60}\) = 4 hrs
(iii) 30 minutes = 1800 seconds
30 minutes = 30 × 60 seconds = 1800 seconds
(iv) 3600 seconds = 1 hrs
3600 seconds = \(\frac{3600}{60}\) minutes = 60 minutes = \(\frac{60}{60}\) hours = 1 hour
(v) 2 hrs = 7200 seconds
2 hrs = 2 × 60 minutes = 120 minutes = 120 × 60 seconds = 7200 seconds

Try These (Textbook Page No. 36)

Question 1.
Convert the 12-hour format into the 24-hour format and vice versa.

Solution:
10 : 40 a.m. = 10 : 40 hours
11 a.m. = 11 : 00 hours
1 : 15 a.m. = 01 : 15 hours
5 a.m. = 05 : 00 hours
16 : 20 hours = 4 : 20 p.m.
00 : 40 hours = 12 :40 a.m.
1 p.m. = 13 : 00 hours
11 : 15 p.m. = 23 : 15 hours
3 p.m. = 15 :00 hours
12 midnight = 00 : 00 hours
12 : 25 hrs = 00 : 25 p.m.
4 : 10hrs = 4 : 10 a.m.

Try These (Textbook Page No. 39)

Question 1.
Check whether the following years as Ordinary or Leap Year?
1994; 1985; 2000; 2007; 2010; 2100
Solution:
We know that a leap year is divisible by 4.
In the case of a century which is divisible by 400 is a leap year.
1994 – Not a leap year (Not divisible by 4)
1985 – Not a leap year (Not divisible by 4)
2000 – It is a leap year (divisible by 400)
2007 – Not a leap year (Not divisible by 4)
2010 – Not a leap year (Not divisible by 4)
2100 – Not a leap year (Not divisible by 400)

Question 2.
How many days are there from 1st April to 30th June?
Solution:
Months from April to June are:

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 2 Integers Intext Questions

(Try These Text Book Page No. 26)

Question 1.
Read the following numbers orally.
(i) + 24
(ii) -13
(iii) -9
(iv) 8
Solution:
(i) + 24 is read as ‘ plus 24’ or ‘positive 24’
(ii) -13 is read as ‘minus 13’ or ‘negative 13’
(iii) -9 is read as ‘minus 9’ or ‘ negative 9’
(iv) 8 is read as ‘plus 8’ or ‘positive 8’ or simply ‘8’

Question 2.
Draw a number line and mark the following integers.
(i) 0
(ii) -6
(iii) 5
(iv) -8
Solution:

Question 3.
Are all natural numbers integers?
Solution:
Yes, all natural numbers are positive integers

Question 4.
Which part of the integers are not whole numbers?
Solution:
The numbers 0, 1, 2, 3, are whole numbers. Therefore negative part of the integers are not whole numbers.

Question 5.
How many units should you move to the left of 3 to reach -4.
Solution:

From 3, we should move 7 units to the left to reach -4.

(Activity Textbook Page No. 27)

Question 1.
Ask your parents / grandparents about the depth at which the various types of vegetables (seeds) should be planted, for their better and efficient growth. For the same, draw a number line indicating the depth of various vegetable seeds. (Draw the planting chart!).
Solution:
Activity to be done by the students themselves

(Try These Text Book Page No. 29)

Question 1.
Find the opposite of the following numbers :
(i) 55
(ii) -300
(iii) +5080
(iv) -2500
(v) 0
Solution:
For every positive integer, there is a corresponding negative integer as its opposite number and vice versa

Question 2.
Represent the following situations as integers.
i) A loss of ₹ 2000
ii) 2018 CE (AD)
iii) Fishes found at 60 m below the sea level
iv) 18°C below 0°C
v) Gaining 13 points
vi) A jet plane at a height of 2500 m
Solution:
(i) Since loss is negative, a loss of t 2000 is denoted as – ₹ 2000
(ii) Here CE (AD) can be considered as a positive number. Hence CE (AD) 2018 can be represented as + 2018.
(iii) Below sea level is represented as -60 m.
(iv) 18°C below 0°C is represented as – 18°C
(v) Gaining 13 points can be represented as + 13
(vi) Height of 2500 m is represented as + 2500 m.

Question 3.
Suppose in a building, there are 2 basement floors. If the ground floor is denoted as zero, how can we represent the basement floors?
Solution:
If the ground floor is denoted as 0, basement floors are represented as -1 and -2.

(Try This Textbook Page No. 31)

Question 1.
For two numbers, say 3 and 5, we know that 5 > 3. Will there be a change in the inequality if both the numbers have negative sign before them?
Solution:
We know that 5 > 3
But when we change the sign of both the numbers we get – 5 and – 3.
Here -5 is 2 units to the left of-3 and so – 5 < 3.
∴ The inequality changes when the signs of both the numbers are changed.

(Activity Textbook Page No. 31)

Question 1.
Take two cards from a deck of playing cards and identify, which is greater between them, assuming that the Joker card represents zero, black cards represent positive integers, red cards represent negative integers and the cards A, J, Q and K represent 1,11,12 and 13 respectively.
Solution:
Activity to be done by the students themselves

(Try These Textbook Page No. 31)

Question 1.
Is -15 < -26? Why?
Solution:
Given statement is wrong.
We will draw the number line and plot the numbers on it.

So -26 < -15

Question 2.
Which is smaller -3 or -5? Why?
Solution:
Comparing the numbers from the number line.

– 5 is 2 units to the left of -3 and so -5 is smaller than -3. i.e. – 5 < – 3

Question 3.
Which is greater 7 or -4? Why?
Solution:
7 is a positive integer and lies to the right of 0.-4 is a negative integer and lies to the left of 0
∴ 7 > -4

Question 4.
Which is the greatest negative integer?
Solution:

– 1 is the greatest negative integer.

Question 5.
Which is the smallest positive integer?
Solution:

+ 1 is the smallest positive integer.

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 4 Geometry Intext Questions

Try this (Text book Page No. 56)

Question 1.

The diagonal of a rectangle divides it into two equal halves but it is not a line of symmetry. why?
Solution:
We get two equal halves. But one half of the figure does not coincide exactly with
the other half with the line of symmetry. Therefore it is not a line of symmetry.

Try These (Text book Page No. 57)

Question 1.
Is the dotted line shown in each figure a line of symmetry? If yes put ✓otherwise put ✗ Justify your answer.

Question 2.
Check the following figures for symmetry ? Write YES or NO.

Try these (Text Book Page No. 59)

Question 1.
Draw the following figures in a paper. Cut out each of them and fold so that the two parts of each figure exactly coincide.

i) Which of the above figures have one, two or more lines of symmetry?
ii) Which of the above figures do not have any line of symmetry?
Solution:

2) All have lines of symmetry

Question 2.
Write the numbers from 0 to 9.
(i) Which numbers have a line of symmetry?
(ii) List out the numbers which do not have a line of symmetry.
Solution:
i) Numbers 1 and 3 have one line of symmetry.
ii) Numbers 2, 4, 5, 6, 7 and 9 do not have a line of symmetry7.

Activity (Text Book Page No. 59)

Question 1.
Complete the other half of the following figures such that the dotted line is the line of symmetry.

Activity to be done by the students themselves

Try this (Text Book Page No. 60)

Question 1.
Which other capital letters of English alphabets look like the same in the mirror?
Solution:
A, H, I, M, O, T, U, V, W, X and Z.

Activity (Text book Page No. 62)

Symmetrical figures by ink blots
Step 1 : Take a sheet of paper and fold it into half to make the crease.
Step 2 : Put some ink blots on one side of the crease of the paper.
Step 3 : Fold the paper along the crease and press it.
Step 4 : Open the paper, you will find an imprint of the ink blots on the other part also which is symmetrical about the crease.

Activity to be done by the students themselves

Try These (Text book Page No. 62)

Question 1.
Find the password :
“Kannukkiniyal has a new game app in her laptop protected with a password. She has decided to challenge her friends with this paragraph which contains that password”.
If you follow the steps given below, you will find it.
Steps :
i) Write the above paragraph in capita! letters.
ii) Turn the paper upside down and look at it in the mirror.
iii) The word which remains unchanged in the mirror is the password.
Solution:
i) KANNUKK IN IYAL HAS ANEW GAME APP IN HER LAPTOP PROTECTED WITH A PASSWORD SHE HAS DECIDED TO CHALLENGE HER FRIENDS WITH THIS PARAGRAPH WHICH CONTAINS THAT PASSWORD

iii) “DECIDED” is the password.

Question 2.
Form words using the Setters B, C, D, E,H, I, K, O and X. Write those words in paper in capital letters. Turn it upside down and look at them in the mirror.
Solution:
i) List the letters which have horizontal and vertical line of symmetry
ii) Do the words HIKE, DICE, COOK remain unchanged in the mirror?
iii) The words which you have found that remain unchanged in the mirror are ______, ______, ______
Solution:
B, C, D, E, H, I, K, O, X
i) Vertical lines of symmetry A, H, I, M, O, T, U, V, W, X, Y
Horizontal lines of symmetry B, C, D, E, H, I, K, O, X
ii) Yes
iii) HOOK, KICK, ICE

Try this (Text book Page No. 64)

Question 1.
Can you identify the object which does not have rotational symmetry in the above situations? Why?
Solution:
1) Computer mouse
2) Trapezium
3) Chair
4) School bags etc.

Question 2.
Suppose, the man hole cover of the water sump is in circular shape
i) The number of ways to dose that circular lid is ___
ii) What is its order of rotational symmetry?

Solution:
i) many
ii) Infinite

Activity (Text book Page No. 64)

Question 1.
Find the order of rotational symmetry by fixing the relevant shape in different ways.

Activity to be done by the students themselves

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 2 Integers Additional Questions

Additional Questions and Problems

Question 1.
Write all the integers between – 5 and 10.
Solution:
On the number line, the number increases as we move to right and decreases as we move to the left
∴ -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

Question 2.
Write the opposite of each of the following
a) Profit of ₹ 500
b) Deposit of ₹ 2000
c) 50 km towards south
Solution:
The opposite of each are
a) loss of ₹ 500
b) withdrawal of ₹ 2000
c) 50 km towards North.

Question 3.
Write the succeeding number of the following

Solution:
We know that one more than the given number is its successor.

Question 4.
Write the preceding number of the following

Solution:
We know that one more than the given number is its successor

Question 5.
Write the following numbers with appropriate signs.
a) 100 m below sea level
b) 25°C above 0°C
c) Any 3 numbers less than 0
Solution:
a) -100 m
b) + 25°C
c) -1, -2, -3

Question 6.
Mark -4, -6, -2 and 3 on the number line
Solution:

Question 7.
Draw a number line and answer the following.
a) Which number will we reach, if we move 4 numbers to the right of-2?
b) Which number will we reach, if we move 5 numbers to the left of 1?
c) If we are at -8 on the number line, in which direction should we move to reach -13?
d) If we are at -6 on the number line in which direction should we move to reach -1 ?
Solution:

(a) 2
(b) -4
(c) left
(d) right

Question 8.
a) Write four negative integers greater than -15?
b) Write four negative integers less than -5?
Solution:
a) -11, -10, -5, -1,
b) -7, -15, -18, -20.

Question 9.
Compare the following using < or >

Solution:

Question 10.
Represent the following as integers
a) A deposit of rupees two thousand
b) An aeroplane is flying at a height of three thousand metres above the ground.
Solution:
a) + ₹ 2000
b) + 3000 m

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 2 Integers Ex 2.2

Miscellaneous Practice Problems

Question 1.
Write two different real life situations that represent the integer -3.
Solution:
(i) A sapling planted at a depth of 3m
(ii) Sheela lost ₹ 3 on selling an apple.

Question 2.
Mark the following numbers on a number line
(i) All integers which are greater than -7 but less than 7.
(ii) The opposite of 3.
(iii) 5 units to the left of -1
Solution:
(i) All integers which are greater than -7 but less than 7.

-6 is placed 5 units to the left of-1.

Question 3.
Construct a number line that shows the depth of 10 feet from the ground level and its opposite.
Solution:

Question 4.
Identify the integers and mark on the number line that are at a distance of 8 units from -6.
Solution:

Question 5.
Answer the following questions from the number line given below

(i) Which integer is greater : G or K ? Why?
(ii) Find the integer that represents C.
(iii) How many integers are there between G and H?
(iv) Find the pairs of letters which are opposite of a number.
(v) Say True or False: 6 units to the left of D is -6. ‘
Solution:
(i) K is greater. K represents -1 and G represents -3. Because it is to the right of G in the negative side of the number line.
(ii) C represents -4
(iii) G represents -3 and H represents 4.
∴ -2, -1, 0, 1, 2, 3 are the 6 numbers between G and H.
(iv) (C, H) and (E, J) are opposite pairs.
(v) False. 6 units to the left of D is 0. Because D represents +6 on the number line

Question 6.
If G is 3 and C is -1, what numbers are A and K on the number line?

Solution:
Given G is 3 and C is -1,
∴ The number line becomes

A represents -3 and K represents 7

Question 7.
Find the integers that are 4 units to the left of 0 and 2 units to the right of -3
Solution:

4 units to the left of 0 is -4.2 units to the right of -3 is -1.

Challenge Problems

Question 8.
Is there the smallest and the largest number in the set of integers? Give reason.
Solution:
No, we cannot find the smallest (-) and largest (+) number in the set of integers, as the numbers on the number line extends on both the sides without end.

Question 9.
Look at the Celsius Thermometer and answer the following questions:
i) What is the temperature that is shown in the thermometer?
ii) Where will you mark the temperature 5°C below 0° C in the Thermometer?
iii) What will be the temperature, if 10°C is reduced from the temperature shown in the thermometer.
iv) Mark the opposite of 15°C in the Thermometer.

Solution:
(i) Temperature shown in the Thermometer is -10°
(ii) 5°C below 0°C is at -5°C.
(iii) Thermometer shows – 10°C if 10QC is reduced that means -10°C – (10°C) gives ^20°C.
(iv) Opposite of 15°C is -15°C

Question 10.
P, Q, R and S are four different integers on a number line. From the following clues, find these integers and write them in ascending order.
i) S is the least of the given integers.
ii) R is the smallest positive integer.
iii) The integers P and S are at the same distance from 0.
iv) Q is 2 units to the left of integer R.
Solution:
According to the clues, plotting the points on a number line, we get

As S is the least of the given integers, it is placed at the left most end.
Since R is the smallest positive integer, it is placed next to the right of 0.
As Q is 2 units to the left of R it is placed as the left next number of 0.
P and S are at the some distance from 0. P is placed opposite to S.
∴ Ascending order : S < Q < 0 < R < P.

Question 11.
Assuming that the home to be the starting point, mark the following places in order on the number line as per instructions given below and write their corresponding integers.

Places : Home, School, Library, Playground, Park, Departmental Store, Bus Stand, Railway station, Post office, Electricity Board.
Instructions:
i) Bus Stand is 3 units to the right of Home.
ii) Library is 2 units to the left of Home.
iii) Departmental Store is 6 unit to the left of Home
iv) Post office is 1 unit to the right of the library.
v) Park is 1 unit right of Departmental Store.
vi) Railway Station is 3 units left of Post Office.
vii) Bus Stand is 8 units to the right of Railway Station.
viii) School is next to the right hf Bus Stand.
ix) Playground and Library are opposite to each other.
x) Electricity Board and Departmental Store are at equal distance from Home.
Solution:

Question 12.
Complete the table using the following hints:

C1 : the first non-negative integer.
C3 : the opposite to the second negative integer.
C5 : the additive identity in whole numbers.
C6 : the successor of the integer in C2.
C8 : the predecessor of the integer in C7
C9 : the opposite to the integer in C5.
Solution:
C1 : First non negative integer is 0
C3 : Second negative integer is -2 its opposite is 2
C5 : 0 is the additive identity in whole numbers
C6 : C2 has -5. Its successor is -A
C8 : Integer in C7 is -7. Predecessor of-7 is -8
C9 : C5 has 0. Opposite of 0 is 0.

Question 13.
The following bar graph shows the profit (+) and loss (-) of a small scale company (in crores) between the years 2011 to 2017.

i) Write the integer that represents a profit or a loss for the company in 2014?
ii) Denote by an integer on the profit or loss in 2016.
iii) Denote by integers on the loss for the company in 2011 and 2012
iv) Say True or False: The loss is minimum in 2012.
v) Fill in: The amount of loss in 2011 is _____ as profit in 2013.
Solution:
(i) Profit ₹ 45 crores. ∴ Ans : + 45
(ii) In 2016 neither profit nor loss happened. ∴ Ans : 0
(iii) In 2011 loss is 10 crores and in 2012 loss is 20 crores. ∴ Ans : -10 and-20.
(iv) False. In 2011 the company’s loss is minimum.
(v) The same. Because in 2013 the profit is 10 crores and in 2011 the loss is 10 crores.

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 4 Geometry Additional Questions

Question 1.
List any three letters having same mirror image as the object or letters?
Solution:
A, O and T

Question 2.
In the word SYMMETRY which letters do not have identical mirror images?
Solution:
S, E and R

Question 3.
Is Indian National flag symmetrical ?
Solution:
Yes, Horizontal

Question 4.
In the word ‘FIGURE’ mention the symmetrical letters.
Solution:
I, U and E

Question 5.
Are the number of symmetrical lines equal in rectangle and square?
Solution:
No, not equal.

Question 6.
Find the number of lines of symmetry in

i) The number of lines of symmetry
ii) The number of lines of symmetry
Solution:
i) The number of lines of symmetry for this figure are 2.

ii) The number of lines of symmetry for this figure are 2.

Question 7.
Give the reflection of the letter M as shown in the figure.

Solution:

Question 8.
Find the number of lines of symmetry of the following.

Solution:

Question 9.
Are human faces symmetrical ?
Solution:
Yes

Question 10.
List some symmetrical objects from your home?
Solution:
Wall clock, dining table top, bucket, photo frame etc.

You can Download Samacheer Kalvi 6th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 2 Measurements Additional Questions

Question 1.
Convert into indicated units: 200 mg into g.
Solution:
200 mg = \(200.0 \times \frac{1}{1000}\) = 0.2 g

Question 2.
(a) What are the universally accepted basic metric units?
(b) A cow gives 10 litres of milk in the morning and 8 litres in the evening. Find the total milk it gives for a week in ml?
Solution:
(a) Universally accepted basic metric units are:
Length in metre, Weight in gram and Capacity (Volume) in litre.
(b) Litres of milk the cow gives in the morning = 10 l.
Litres of milk the cow gives in the evening = 8 l.
Total milk per day = 10 + 8 = 18 l
Total milk for a week = 18 × 7 l = 126 l = 126 × 1000 ml = 126000 ml.
Total milk the cow gives for a week = 1,26,000 ml.

Question 3.
A box contains 20 kg 280 g of sugar. After transferring into a smaller box of 2 kg 720 g 7 times find the remaining sugar left in the big box in cg.
Solution:
Total sugar in the box = 20 kg 280 g.
Measurement of smaller box = 2 kg 720 g.
7 times the smaller box = 2 kg 720 g × 7 = 19 kg 040 g.
Remaining sugar = 20 kg 280 g – 19 kg 40 g = 1 kg 240 g = 1240 g. = 1240 × 100 cg = 124000 eg.
Sugar left in the box = 1,24,000 eg.

Question 4.
Sneha needs 1 m 20 cm of cloth for her blouse. If she bought 20 such cloths find the total cloth she bought in cm?
Solution:
For one blouse the cloth needed = 1 m 20 cm
Cloth needed for 20 blouse = 1 m 20 cm × 20
= 20 m 400 cm
= 20 × 100 + 400 cm
= 2000 + 400 cm
= 2400 cm.
Total cloth bought = 2400 cm.

Question 5.
Can you add 2 m 20 cm and 4 kg 80 g? Why?
Solution:
No, we can’t. To add or subtract, the measures should be in the same unit.

Question 6.
If you serve a cup of coffee measuring 150 ml each for 200 people find the volume of coffee needed in litres?
Solution:
For one cup of coffee it needs 150 ml.
For 200 people it needs 150 × 200 ml = 30000 ml = 30000 × \(\frac{1}{1000}\) l = 30 l
Coffee needed = 30 l.

Question 7.
A lorry full of fertiliser is bought to the garden having 120 coconut trees. If the lorry contain 1920 kg, then find the measure of fertiliser each coconut tree can have?
Solution:
Total measure of fertiliser = 1920 kg.
Number of coconut tress = 120
For one tree = \(\frac{1920}{120}\) kg = 16 kg.
One tree can have 16 kg of fertiliser

Question 8.
Convert 7 kg 250 g in to mg, g and cg?
Solution:
7 kg 250 g.
(i) 7 kg 250 g = 7 × 1000 + 250 g. = 7000 + 250 = 7250 g.
(ii) 7 kg 250 g = 7250 g. = 7250 × 1000 mg = 72,50,000 mg.
(iii) 7 kg 250 g = 7250 g. = 7250 × 100 cg = 7,25,000 cg.

Question 9.
Convert 20 m 20 cm into cm, m and km.
Solution:
20 m 20 cm.
(i) 20 m 20 cm = 20 × 100 + 20 cm = 2000 + 20 cm = 2020 cm
(ii) 20 m 20 cm = 2020 cm = 2020 × \(\frac{1}{100}\) m = 20.20 m
(iii) 20 m 20 cm = 20.20 m = 20.20 × \(\frac{1}{1000}\) km = 0.02020 km

Question 10.
Convert 85 l 720 ml into ml, l and kl?
Solution:
85 l 720 ml
(i) 85 l 720 ml = 85 × 1000 + 720 ml = 85000 + 720 ml = 85,720
(ii) 85 l 720 ml = 85 l + 720 × \(\frac{1}{1000}\) l = 85 l + 0.720 l = 85.72 l.
(iii) 85 l 720 ml = 85.72 l = 85.72 × \(\frac{1}{1000}\) kl = 0.08572 kl.

Question 11.
Which is greater 0.007 g, 0.7 kg or 70 mg?
Solution:
0.007 g = 0.007 × 1000 mg = 7 mg
0.7 kg = 0.7 × 10,00,000 mg = 7,00,000 mg
70 mg = 70 mg
∴ 0.7 kg is greater.

Question 12.
A bus leaves for Kanchipuram from Chennai at 4.30 p.m. It takes 1 hr 25 min. to reach there. At what time will it reach at Kanchipuram?
Solution:
Starting time from Chennai = 4 : 30 pm.
Duration of travel = 01 hr : 25 min
Arrival at Kanchipuram = 5 : 55 pm
The bus will reach Kanchipuram at 5 : 55 pm.

Question 13.
The duration of a film show is 3 hrs 15 min. It starts at 6 : 30 p.m. When will it end?
Solution:
The film starts at = 6 : 30 pm.
Duration of the film show = 3 hr : 15 min
The show end at = 9 : 45 p.m.

Question 14.
A train arrive Chennai Central at 11 : 55 am. It reached Chennai 1 hr 25 min late. What is the scheduled arrival time of the train at Chennai?
Solution:
The train arrived Chennai at 11 : 55 am = 11 : 55 hours
The train is late by = 1 hour 25 min
Scheduled Time = 10 : 30 hours
The scheduled arrival time = 10.30 a.m

Question 15.
Raju visited a fashion show. He stayed there for 2 hr 30 min and came back to home. If he reached in the fashion show at 8 : 45 pm. When did he leave for his home?
Solution:
Raju reached the fashion show at 8 : 45 p.m
He stayed there for 2 hr : 30 min
He will leave the show at 10 : 75 min
= 10 hr 75 min
= 10 hrs (60 + 15) min
= 10 hrs + 1 hr 15 min
= 11 hrs 15 min
Raju will leave the show at 11 : 15 p.m

Question 16.
Mammalia travelled 4 hrs 45 min by bus and 4 hrs 45 min by train. Calculate the time she spent in travelling?
Solution:
Time travelled by bus = 4 hrs 45 min
Time travelled by train = 4 hrs 45 min
Total time she travelled = 8 hrs 90 min
= 8 hrs (60 + 30) min 8 hrs + 1 hr 30 min
Total time she travelled = 9 hr 30 min

Question 17.
David left home at 4 : 30 p.m to meet his friend. He came back after 3 hr 25 min At what time did he came back?
Solution:
Time at which David left home = 4 : 30 p.m.
Time he spent outside = 3 hr : 25 min
Time at which he came back = 7 : 55 p.m

Question 18.
Malar reached her school at 7 : 30 a.m. and left for home at 12 : 45 p.m. How long did she stay in school?
Solution:
Malar left for home at 12 : 45 p.m. = 12 : 45 hrs
She reached school at = 7 : 30 hrs
She stayed at school for = 5 : 15 hrs

Question 19.
Mathi’s date of birth was 25.07.2000. What is her age on 29.08.2017?
Solution:
Convert the given date in YY MM DD format
Age = 2017.08.29
Date of birth = 2000 .07 .25
Age = 17. 01. 04
She is 17 years one month 04 days old.

Question 20.
Find whether 2000,2018 and 2012 are leap years or not.
Solution:
2000 is a leap year (divisible by 400)
2018 is a not leap year (not divisible by 4)
2012 is a leap year (divisible by 4)

Question 21.
Find the railway time for 12 : 05 a.m, 4 : 20 pm
Solution:
12 : 05 am is 00 : 05 hrs
4 : 20 p.m. is (12 + 4) : 20 hrs = 16 : 20 hrs