Class 6

Students can practice TS 6th Class Maths Solutions Chapter 2 Whole Numbers InText Questions to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 2 Whole Numbers InText Questions

Do This

Question 1.
Which is the smallest whole number ?
Answer:
‘0’ is the smallest whole

Think, Discuss And Write

Question 1.
Are all natural numbers whole numbers ?
Answer:
Yes, all natural numbers are whole numbers.

Question 2.
Are all whole numbers natural numbers ?
Answer:
No, all whole numbers are not natural numbers. Since 0 ∉ N.

Do This

Question 1.
Show these on number line :
1) 5 + 3
Answer:

2) 5 – 3
Answer:

3) 5 + 3
Answer:

4) 10 + 1
Answer:

Try These
Find the following by using the number line.

Question 1.
What number should be deducted from 8 to get 5 ?

Answer:
3 should be deducted from 8 to get 5.

Question 2.
What number should be deducted from 6 to get 1 ?

5 should be deducted from 6 to get 1.

Question 3.
What number should be added to 6 to get 8 ?

Answer:
2 should be added to 6 to get 8.

Question 4.
How many 6 are needed to get 30 ?

Answer:
The first leap takes you to 6.
From there, the second leap takes you to 12.
From there, the third leap takes you to 18.
From there, the fourth leap takes you to 24.
From there, the fifth leap takes you to 30.
∴ Five 6 are needed to get 30.

Think, Discuss And Write

Question 1.
Are the whole numbers closed under subtraction ?
Answer:
7 – 5 = 2, is a whole number.
5 – 7 = – 2, is not a whole number.
10 – 4 = 6, is a whole number.
4 – 10 = – 6, is not a whole number.
∴ The whole numbers are not closed under subtraction.

Question 2.
Are the whole numbers closed under division ?
Answer:
6 + 3 = 2, is a whole number,
5 ÷ 2 = \(\frac{5}{2}\), is not a whole number
14 ÷ 2 = 7, is a whole number.
19 ÷ 2 = \(\frac{19}{2}\), is not a whole number.
∴ The whole numbers are not closed under division.

Do This

Question 1.
Find out 12 ÷ 3 and 42 ÷ 7.
Answer:
12 ÷ 3 = 4 and 42 ÷ 7 = 6

Question 2.
What would 6 ÷ 0 and 9 ÷ 0 be equal to?
Answer:
6 ÷ 0 is not defined
9 ÷ 0 is also not defined.

Try These

Take a few examples and check whether.

Question 1.
Subtraction is commutative for whole numbers or not ?
Answer:
Observe the following:
i) 4 – 3 = 1; 3 – 4 = – 1
ii) 5 – 2 = 3; 2 – 5 = -3
1 and – 1 are not equal. 3 and – 3 are also not equal.
∴ Subtraction is not commutative for whole numbers.

Question 2.
Division is commutative for whole numbers or not ?
Answer:
Observe the following:
i) 6 ÷ 2 = 3; 2 ÷ 6 = \(\frac{1}{3}\)
ii) 11 ÷ 3 = \(\frac{11}{3}\); 3 ÷ 11 = \(\frac{3}{11}\)
3 and \(\frac{1}{3}\) are not equal; \(\frac{11}{3}\) and \(\frac{3}{11}\) are not equal.
∴ Division is not commutative for whole numbers.

Do this

Question 1.
Verify the following.
(i) (5 × 6) × 2 = 5 × (6 × 2)
Answer:
(5 × 6) × 2 = 30 × 2 = 60 (∵ 5 × 6 = 30)
5 × (6 × 2) = 5 × 12 = 60 (∵ 6 × 2= 12)
(5 × 6) × 2 = 5 × (6 × 2)

(ii)(3 × 7) × 5 = 3 × (7 × 5)
Answer:
(3 × 7) × 5 = 21 × 5 = 105 (∵ 3 × 7 = 21)
3 × (7 × 5) = 3 × 35 = 105 (∵ 7 × 5 = 35)
(3 × 7) × 5 = 3 × (7 × 5)
We see that multiplication is associative over whole numbers.

Do This

Question 1.
Use the commutative and associative properties to simplify the following.
(i) 319 + 69 + 81
(ii) 431 + 37 + 69 + 63
(iii) 2 × (71 × 5)
(iv) 50 × 17 × 2
Answer:

Think, Discuss And Write

Question 1.
Is (16 ÷ 4) + 2 = 16 ÷ (4 ÷ 2) ?
Does the associative property for division hold for the set of whole numbers? Check if the property holds for subtraction of whole numbers too.Give 5 examples each for substantiate your answer.
Answer:
(16 ÷ 4) ÷ 2 = 16 ÷ (4 ÷ 2)
⇒ 4 ÷ 2 = 16 ÷ (4 ÷ 2)
⇒ 4 ÷ 2 = 16 ÷ 2
⇒ 2 = 8 (False)
For division associative property doesn’t applicable.
Examples for Associative property for division
1) (54 ÷ 9) ÷ 3 = 18 ÷ (9 ÷ 3)
6 ÷ 3 = 18 ÷ 3
2 = 6 (false)

2) (64 ÷ 8) ÷ 4 = 64 ÷ (8 ÷ 4)
8 ÷ 4 = 64 ÷ 2
2 = 32(false)

3) (24 ÷ 6) ÷ 2 = 24 ÷ (6 ÷ 2)
4 ÷ 2 = 24 ÷ 3
2 = 8 (false)

4) (32 ÷ 8) ÷ 4 = 32 ÷ (8 ÷ 4)
4 ÷ 4 = 32 ÷ 2
1 = 16 (false)

5) (49 ÷ 7) ÷ 7 = 49 ÷ (7 ÷ 7)
7 ÷ 7 = 49 ÷ 1
1 = 49 (false)

Similarly, 3 – (2 – 1) = (3 – 2) – 1 ⇒ 3 – 1 = 1 – 1 ⇒ 2 = 0 (False)
∴ For subtraction also associative property doesn’t applicable.
Examples for associative property for subtraction :

1) 4 – (3 – 1) = (4 – 3) – 1
4 – 2 = 1 – 1
2 = 0 (false)

2) 8 – (4 – 3) = (8 – 4) – 3
8 – 1 = 4 – 3
7 = 1 (false)

3) 12 – (4 – 1) = (12 – 4) – 1
12 – 3 = 8 – 1
9 = 7 (false)

4) 13 – (8 – 7) = (13 – 8) – 7
13 – 1 = 5 – 7
12 = -2(false)

5) 15 – (12 – 3) = (15 – 12) – 3
15 – 9 = 3 – 3
6 = 0 (false)

Do This

Question 1.
Find the values of 25 × 78; 17 × 26; 49 × 68 + 32 × 49 using distributive property.
Answer:
(i) 25 × 78; a × (b + c) = a × b + a × c =>.25x 78 = 25 × (80 – 2) = 25 × 80 – 25 × 2 = 2000 – 50 = 1950
(ii) 17 × 26 = 17 × (30 – 4) = 17 × 30 – 17 × 4 = 510 – 68 = 442
(iii) 49 × 68 + 32 × 49 = 49 [68 + 32] = 49 × 100 = 4900

(Try These)

Question 1.
Which numbers can be shown as a line only ?
Answer:
Every number can be shown as a line.
But out of these numbers some numbers can be shown as triangles, some as squares and some as rectangles.
∴ The numbers that can be shown only as lines are 2, 5, 7, 11, 13, ……………..

Question 2.
Which numbers can be shown as rectangles ?
Answer:
The numbers that can be expressed as the product of two numbers can be shown as rectangles.
6 = 2 × 3
8 = 2 × 4
10 = 2 × 5
12 = 2 × 6 (or) 3 × 4
…………….

Question 3.
Which numbers can be shown as squares ?
Answer:
The perfect square numbers such as 4, 9, 16, 25, 36, 49, 64, 81, ………. can be shown as squares.

Question 4.
Which numbers can be shown as triangles ? eg. 3, 6, ……..
Answer:
The numbers that can be shown as triangles are 3, 6, 10, 15, 21, etc.

Students can practice TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Ex 1.3 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Exercise 1.3

Question 1.
Write the numbers using commas according to place values.
(i) 11245670
Answer:
1,12,45,670

(ii) 22402151
Answer:
2,24,02,151

(iii) 30608712
Answer:
3,06,08,712

(iv) 190308020
Answer:
19,03,08,020

Question 2.
Write the numbers in words.
(i) 34,025
Answer:
34,025

(ii) 7,09,115
Answer:
7,09,115

(iii) 47,60,00,317
Answer:
47,60,00,317

(iv) 6,18,07,000
Answer:
6,18,07,000

Question 3.
Write the numbers in figures.
(i) Four lakh fifty seven thousand four hundred.
Answer:
4,57,400

(ii) Sixty lakh two thousand seven hundred seventy five.
Answer:
60,02,775

(iii) Two crore fifty lakh forty thousand three hundred and three.
Answer:
2,50,40,303

(iv) Sixty crore sixty lakh sixty thou-sand six hundred.
Answer:
60,60,60,600

Question 4.
Write the numbers in the expanded form.
(i) 6,40,156
Answer:
6,40,156 = (6 × 1,00,000) + (4 × 10,000) + (0 × 1,000) + (1 × 100) + (5 × 10) + (6 × 1)
= 60,00,000 + 40,000 + 100 + 50 + 6

(ii) 63,20,500
Answer:
63,20,500 = (6 × 10,00,000) +(3 × 1,00,000) + (2 × 10,000)+ (0 × 1,000) + (5 × 100) + (0 × 10) + (0 × 1)
= 60,00,000 + 3,00,000 + 20,000 + 500

(iii) 1,25,30,275
Answer:
1,25,30,275 = (1 × 1,00,00,000) + (2 × 10,00,000) + (5 × 1,00,000) + (3 × 10,000) + (0 × 1,000) + (2 × 100) + (7 × 10) + (5 × 1)
= 1,00,00,000 + 20,00,000 + 5,00,000 + 30,000 + 200 + 70 + 5

(iv) 75,80,19,202
Answer:
75,80,19,202 = (7 × 10,00,00,000) +(5 × 1,00,00,000) + (8 × 10,00,000) + (0 × 1,00,000) + (1 × 10,000) + (9 × 1,000) + (2 × 100) + (0 × 10) + (2 × 1)
= 70,00,00,000 + 5,00,00,000 + 80,00,000 + 10,000 + 9,000 + 200 + 2

Question 5.
Write the following numbers in short form (standard notation).
(i) 50,00,000 + 4,00,000 + 20,000 + 8,000 + 500 + 20 + 4
Answer:
54,28,524

(ii) 6,00,00,000 + 40,00,000 + 3,00,000 + 20,000 + 500 + 1
Answer:
6,43,20,501

(iii) 3,00,00,000 + 3,00,000 + 7,000 + 800 + 80 + 1
Answer:
3,03,07,881

(iv) 7,00,00,000 + 70,00,000 + 7,000 + 70
Answer:
7,70,07,070

Question 6.
Which is larger between each of these two? Use greater than symbol (>) and write.
(i) 4,67,612 or 18,71,964
Answer:
18,71,964 > 4,67,612
(∵ The number on the left side of the symbol has 7 digits while the number on the right side has only 6 digits)

(ii) 14,35,10,300 or 14,25,10,300
Answer:
14,35,10,300 > 14,25,10,300
(∵ The digits in ten lakhs place of left side number is greater than that of right side number (i.e.) 3 > 2)

Question 7.
Which is smaller between each of these two ? Use less than symbol (<) and write.
(i) 2,00,015 or 99,999
Answer:
99,999 < 2,00,015
(∵ The number on the left side of the symbol has 5 digits while the number on the right side has 6 digits).

(ii) 13,50,050 or 13,49,785
Answer:
13,49,785 < 13,50,050
(∵ The digit In ten thousands place of left side number is less than that of right side number (i.e.) 4 < 5).

Question 8.
Write any ten numbers with digits 5 in crores place, 2 in lakhs place, 1 in ten thousands place, 6 in tens place and 3 in ones place, (keep any digits in the remaining places)
Answer:
5 … 2 1 .. … 6 3 .
The required numbers are
(1) 5,92,18,563
(2) 5,82,17,463
(3) 5,72,16,363
(4) 5,62,15,263
(5) 5,52,14,163
(6) 5,42,13,063
(7) 5,32,11,963
(8) 5,22,10,863
(9) 5,12,09,763
(10) 5,02,08,663

Students can practice TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Ex 4.2 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.2

Question 1.
Tick the figures which are simple curves.

Answer:

Question 2.
State which curves are open and which are closed.

Answer:
Figure (i) and (v) are open
Figure (ii), (iii) & (iv) are closed

Question 3.
Name the points that lie in the interior, on the boundary and in the exterior of the figure.

Answer:
The points that lie in the interior of the figure are A, B, E, G and I.
The points that lie on the boundary of the figure are C, F and K.
The points that lie in the exterior of the figure are D and J.

Question 4.
Draw three simple closed figures :
i) by straight lines only
ii) by straight lines and curved lines both
Answer:
i) Simple closed figures drawn by straight lines only

ii) Simple closed figures drawn by straight lines and curved lines both

Students can practice TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Ex 1.5 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Exercise 1.5

Question 1.
The number of people who visited during common wealth games in New Delhi for the first four days was re-corded as 15,290, 14,181, 14,235 and 10,578. Find the total number of people visited in these four days ?
Answer:
Number of people visited common wealth games on the first day = 15,290
Number of people visited common wealth games on the second day = 14,181
Number of people visited common wealth games on the third day = 14,235
Number of people visited common wealth games on the fourth day = 10,578
Total number of people who visited in these four days = 15,290
= 15,290 + 14,181 + 14,235 + 10,578 = 54,284

Question 2.
In Lok Sabha election, the elected candidate got 5,87,500 votes and defeated candidate got 3,52,768. By how many votes did the winner win the election ?
Answer:
Number of votes the winner got = 5,87,500
Number of votes the defeated candidate got = 3,52,768
Number of votes that the winner got more than the defeated candidate
= 5,87,500 – 3,52,768 = 2,34,732
By 2,34,732 votes did the winner win the election.

Question 3.
Write the greatest and smallest 5- digit number formed by the digits 5, 3, 4, 0 and 7 and find their difference.
Answer:
The digits given are 5, 3, 4, 0, 7. The greatest 5-digit number formed with the given digits = 75430
The smallest number formed with the given digits = 30457
The difference between these numbers = 75430 – 30457 = 44973

Question 4.
A bicycle industry makes 3,125 bicycles each day. Find the total number of bicycles manufactured in the month of July ?
Answer:
Number of days in month of July = 31
Number of bicycles made in one day = 3,125
Number of bicycles made in 31 days = 31 × 3,125 = 96,875

Question 5.
A helicopter covers 600 km in 1 hour. How much distance will it cover in 4 hours ? Express your answer in metres.
Answer:
Distance covered by helicopter in 1 hour = 600 km
Distance covered in 4 hours = 4 × 600 km = 2400 km
We know that 1km = 1000 metres
∴ Distance covered by helicopter in 4 hours = 2400 km
= 2400 × 1000 metres
= 24,00,000 metres

Question 6.
The total weight of 5 biscuit packets of same size is 8 kg 400 grams. What is the weight of each packet ?
Answer:
The total weight of 5 biscuit packets (of same size) = 8 kg 400 grams
∴ The weight of each packet
= 8 kg 400 gms ÷ 5
= 1 kg 680 gms

Question 7.
Everyday Gayatri walks both the ways to attend the school. The distance between the school and her house is 1 km 875 m. Find the total distance she walked in 6 days ?
Answer:
Distance between the school and her house = 1 km 875 m
Distance Gayatri walks everyday from , her house to the school and vice-versa = 1 km 875 m + 1 km 875 m = 3 km 750 m
Total distance Gayatri walked in 6 days
= 3 km 750 m × 6 = 22 km 500 m

Question 8.
The cloth required to make a shirt of school uniform for each boy is 1 m 80 cm. How many shirts can tailor stitch using 40 m. of cloth ? How much cloth will be left ?
Answer:
The cloth to be stitched = 40 m = 40 × 100 cm
(∵ 1 metre = 100 cm)
= 4000 cm
The cloth required for one shirt
= 1 m 80 cm
= 180 cm (∵ 1 metre =100 cms)
Number of shirts can be stitched = \(\frac{4000}{180}\)
= 22\(\frac{2}{9}\)
The tailor can stitch 22 shirts.
The cloth will be left = \(\frac{2}{9}\) × 180
= 40 cm

Question 9.
The rate of petrol is ₹ 60 per litre. A petrol bunk sells 750 litres of petrol on a day. How much money do they get at the end of the day ?
Answer:
The rate of 1 litre of petrol = Rs. 60
The rate of 750 litres of petrol = ₹ 60 × 750 = ₹ 45000
The money they get at the end of the day = ₹ 45,000

Students can practice TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Ex 4.1 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.1

Question 1.
Join the points given below. Name the line segments so formed in the figure.

Answer:

The line segments so formed in the figure are \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}\) and \(\overline{\mathrm{CA}}\).

Answer:

The line segments so formed in the figure are \(\overline{\mathrm{PQ}}, \overline{\mathrm{QR}}, \overline{\mathrm{RS}}, \overline{\mathrm{ST}}\) and \(\overline{\mathrm{TP}}\).

Question 2.
Name the following from the figure.

(i) Any five points.
(ii) Any five line segments.
(iii) Any three rays.
(iv) Any two lines.
Answer:
(i) A, B, C, D, 0 are the points.
(ii) \(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}}, \overline{\mathrm{DA}}, \overline{\mathrm{AC}}, \overline{\mathrm{BD}}\) are the line segments.
(iii) \(\overrightarrow{\mathrm{OB}}, \overrightarrow{\mathrm{OD}}, \overrightarrow{\mathrm{OC}}, \overrightarrow{\mathrm{OA}}\) are the rays.
(iv) \(\overrightarrow{\mathrm{AC}}\) and \(\overrightarrow{\mathrm{BD}}\) are the lines.

Question 3.
How many lines can be drawn through the points given below and make a rough figure for your answer.

(i) One point
(ii) Two distinct points
Answer:
(i) Many lines (infinite) can be drawn through one point.
(ii) Only one line can be drawn through two distinct points.

Question 4.
Which of the following has a definite length ?
i) Line
Answer:
A line has no definite length because it has no end points.

ii) Point
Answer:
A point has no definite length because it determines a location.

iii) Line segment
Answer:
A line segment has fixed length because it has two end points.

iv) Ray
Answer:
A ray is a portion of a line starting at a point and goes in one direction endlessly. So it has no definite length.

Question 5.
How many end points do the following have ?
(i) Line segment
Answer:
A line segment has two end points.

(ii) Ray
Answer:
A ray has only one end point.

(iii) Line
Answer:
A line has no end points.

Question 6.
Write ’True’ or ’False’.
(i) A line has no end points. ( )
Answer:
True

(ii) Ray is a part of a line. ( )
Answer:
True

(iii) A line segment has no definite length. ( )
Answer:
False

(iv) A line segment has only one end point. ( )
Answer:
False

(v) We can draw many lines through a point. ( )
Answer:
True

Question 7.
Draw and name :
(i) Line containing point P.
Answer:

(ii) Line passing through R.
Answer:

\(\overleftrightarrow{\mathrm{AB}}\) is a line passing through R.

Students can practice TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Ex 4.5 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.5

Question 1.
Draw a circle and name its centre, a radius, a diameter and an arc.
Answer:

‘O’ is the centre of the circle.
OA is the radius.
BC is the diameter.
AXB is an arc,
AZC is an arc.
BYC is an arc.

Question 2.
Shade the regions in the circle

(i) Sector with red.
(ii) Minor segment with yellow.
Answer:

Question 3.
Say ’True’ or ‘False’.
(i) We can locate only one centre in a circle. ( )
(ii) Diameter is twice the radius. ( )
(iii) An arc is a part of a circle. ( )
(iv) All chords are equal in length. ( )
(v) All radii are not equal in length in a circle. ( )
Answer:
i) True
ii) True
iii) True
iv) False

Question 4.
Take a circular sheet of paper. Fold it into two halves. Press the fold and open it. Do you find the crease of a diameter ? Repeat the same activity by changing the fold. How many diameters do you observe ? How many more diameters can be formed ?
Answer:
Fold a circular sheet of paper into two halves. Press the fold and open it. We find the crease (a line made on paper when it is pressed) of a diameter. We observe infinite number of diameters.

Students can practice TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Ex 4.4 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.4

Question 1.
Mark any four points A, B, C and D. Join them to make a quadrilateral. Name it.
Answer:

ABCD is a quadrilateral.
\(\overline{\mathrm{AB}}, \overline{\mathrm{BC}}, \overline{\mathrm{CD}}, \overline{\mathrm{DA}}\) are its sides,
A, B, C and D are the vertices.

Question 2.
PQRS is a quadrilateral. Answer the following.

(i) The opposite side of QR is …….
(ii) The angle opposite to ∠P is ………..
(iii) The adjacent sides ot \(\overline{\mathrm{P Q}}\) are …….
(iv) The adjacent angles of ∠S are …….
Answer:
i) PS
ii) ∠R
iii) \(\overline{\mathrm{P S}}\) and \(\overline{\mathrm{Q R}}\)
iv) ∠P and ∠R

Question 3.
Name the points marked in the figure.

i) The points in the interior of Quadrilateral.
ii) The points on the boundary of Quadrilateral.
iii) The points in the exterior of the Quadrilateral.
Answer:
i) The points in the interior of Quadrilateral are S and R.
ii) The point on the boundary of Quadrilateral is A, B, C, D and E.
iii) The points in the exterior of Quadrilateral are P, Q and T.

Students can practice TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers InText Questions to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Exercise InText Questions

Do This

Round off these numbers as directed:

Question 1.
48, 62, 81, 94, 27 to their nearest tens.
Answer:

• 48 is nearer to 50 than 40. So it is rounded off to 50.
• 62 is nearer to 60 than 70. So it is rounded off to 60.
• 81 is nearer to 80 than 90. So it is rouhded off to 80.
• 94 is nearer to 90 than 100. So it is rounded off to 90.
• 27 is nearer to 30 than 20. So it is rounded off to 30.

Question 2.
128, 275, 312, 695, 199 to their nearest hundreds.
Answer:
(i) 128 is nearer to 100 than 200.
So it is rounded off to 100.

(ii) 275 is nearer to 300 than 200.
So it is rounded off to 300.

(iii) 312 is nearer to 300 than 400.
So it is rounded off to 300.

(iv) 695 is nearer to 700 than 600.
So it is rounded off to 700.

(iv) 199 is nearer to 200 than 100.
So it is rounded off to 200.

Question 3.
7452, 8115, 3066, 7119, 9600 to their nearest thousands.
Answer:

• 7452 is nearer to 7000 than 8000. So it is rounded off to 7000.
• 8115 is nearer to 8000 than 9000. So it is rounded off to 8000.
• 3066 is nearer to 3000 than 4000. So it is rounded off to 3000.
• 7119 is nearer to 7000 than 8000. So it is rounded off to 7000.
• 9600 is nearer to 10000 than 9000. So it is rounded off to 10000.

Think, Discuss and Write

Discuss with your friends about rounding off numbers for ten thousands place.
Answer:
Rani and Uma both of them visited the Panchayat Office on their way back home and they observed the particulars on the wall.
Population of the village = 9,989.
The value 9,989 rounding off ten thousand.
Similarly, 10,007, 10,009, 10,015, ………… etc., are round off ten thousand.

Page No. 10(4)

Expand a number using place value.
Recall how you expand a two digit, three digit, four digit and five digit number.

Question 1.
Expand 64
Answer:

= (6 × 10) + (4 × 1)
= 60 + 4

Question 2.
Expand 325
Answer:

= (3 × 100) + (2 × 10) + (5 × 1)
= 300 + 20 + 5

Question 3.
Expand 5078
Answer:

= (5 × 1000) + (0 × 100) + (7 × 10) + (8 × 1)
= 5000 + 0 + 70 + 8

Question 4.
Expand 29500
Answer:

= (2 × 10000) + (9 × 1000) + (5 × 100) + (0 × 10) + (0 × 1)
= 20000 + 9000 + 500 + 0 + 0
= 20000 + 9000 + 500

D0 This

Now expand the numbers as given in the example.

Page No: 14 (6)
Write the following numbers in expanded form and the way of reading.
(i) 4,57,000
Answer:
Expanded form :
= (4 × 1,00,000) + (5 × 10,000) + (7 × 1000) + (0 × 100) + (0 × 10) + (0 × 1)
= 4,00,000 + 50,000 + 7,000

Read as:
Four lakh fifty seven thousand.

(ii) 3,05,400
Answer:
Expanded form :
(3 × 1,00,000) + (0 × 10,000) + (5 × 1000) + (4 × 100) + (0 × 10) + (0×1)
= 3,00,000 + 5,000 + 400

Read as:
Three lakh five thousand four hundred.

(iii) 3,09,390
Answer:
Expanded form :
= (3 × 1,00,000) + (0 × 10,000) + (9 × 1000) + (3 × 100) + (9 × 10) + (0 × 1)
= 3,00,000 + 0 + 9000 + 300 + 90 + 0

Read as:
Three lakh nine thousand three hundred ninety

(iv) 2,00,035
Answer:
Expanded form :
= (2 × 1,00,000) + (0 × 10,000) + (0 × 1000) + (0 × 100) + (3 × 10) + (5×1)
= 2,00,000 + 30 + 5

Read as:
Two lakh thirty five.

(Try These)

Question 1.
Give any five examples using daily life situations where the number of things counted would be more than 6 digits.
Answer:

• To calculate the population
• To calculate the money which is more than 1 lakh
• Count of white blood cells in the body
• Count of cells in a leaf
• Count of voters in Hyderabad city

Question 2.
Write the smallest and greatest of all two digit, three digit, four digit, five digit, six digit, seven digit, eight digit numbers.
Answer:

Page No: 18

Question 1.
Read the numbers given below.
(i) 41430495
Answer:
4,14,30,495 = Four crore fourteen lakh thirty thousand four hundred ninety five.

(ii) 304512031
Answer:
30,45,12,031 = Thirty crore forty five lakh twelve thousand thirty one.

(iii) 241800240
Answer:
24,18,00,240 = Twenty four crore, eighteen lakh two hundred forty.

(iv) 69697100
Answer:
6,96,97,100 = Six crore ninety six lakh ninety seven thousand one hundred.

(v) 100091409
Answer:
10,00,91,409 = Ten crore, ninety one thousand four hundred nine.

Question 2.
Write the expansion of 12735045
Answer:
1,27,35,045 = (1×10000000) + (2 × 1000000) + (7 × 100000)+ (3 × 10000) + (5 × 1000) + (0 × 100) + (4 × 10) + (5 × 1)

Do This:

Question 1.
Expand the numbers using commas,
(i) 999999999
Answer:
99,99,99,999
= (9 × 10,00,00,000) + (9 × 1,00,00,000) + (9 × 10,00,000) + (9 × 1,00,000) + (9 × 10,000) + (9 × 1,000) + (9 × 100) + (9 × 10) + (9×l)
= 90,00,00,000 + 9,00,00,000 + 90,00,000 + 9,00,000 + 90,000 + 9,000 + 900 + 90 + 9

(ii) 34530678
Answer:
3,45,30,678
= (3 × 1,00,00,000) + (4 × 10,00,000) + (5 × 1,00,000) + (3 × 10,000) + (0 × 1,000) + (6 × 100) + (7 × 10) + (8 × 1)
= 3,00,00,000 + 40,00,000 + 5,00,000 + 30,000 + 600 + 70 + 8

(iii) 510010051
Answer:
51,00,10,051
= (5 × 10,00,00,000) + (1 × 1 ,00,00,000) + (0 × 10,00,000) + (0 × 1,00,000) + (1 × 10,000) + (0 × 1000) + (0 × 100) + (5 × 10) + (1 × 1)
= 50,00,00,000 + 1,00,00,000 + 10,000 + 50 + 1

Question 2.
Read these numbers and write in words.
(i) 5,06,45,075
Answer:
Five crore six lakhs forty five thousand seventy five.

(ii) 12,36,99,140
Answer:
Twelve crore thirty six lakhs ninety nine thousand one hundred forty.

(iii) 2,50,00,350
Answer:
Two crore fifty lakhs three hundred fifty.

Try These

Question 1.
Name four important towns in your district. Note the distance between them in km. Express these in centimeters and millimeters.
Answer:

• Armar
• Bheemgal
• Balkonda
• Bodhan.

The distance between Armur and Bheemgal is 62 km.
1 km = 100000 cm
∴ 62 km = 62 × 100000 = 6200000 cm
= 6200000 × 10 = 62000000 mm (∵ 1cm = 10 mm)
The distance between Bheemgal and Balkonda is 29 km.
29 km = 29 × 100000 = 2900000 cm
= 2900000 × 10 mm = 29000000 mm
The distance between Balknoda and Bodhan is 66 km. .
66km = 66 × 100000= 6600000 cm
= 6600000 × 10 mm = 66000000 mm
The distance between Bodhan and Armur is 53 km.
53km = 53 × 100000 = 5300000 cm
= 5300000 × 10 mm = 53000000 mm

Question 2.
Can you tell where we use milligrams?
Answer:
We use milligrams to measure

• silver
• gold
• mercury
• platinum, etc.

Question 3.
A box contains 1,00,000 tablets (medicine) each weighing 20 mg. What is the weight of all the tablets in the box in both grams and kilograms ?
Answer:
The weight of 1 tablet = 20 mg
The total weight of 1,00,000 tablets = 1,00,000 × 20 mg = 20,00,000 mg
= \(\frac{2000000}{1000}\) grams (∵1 gram = 1000 milli grams)
= 2000 grams
= \(\frac{2000}{1000}\) kgs (∵ 1 kg = 1000 grams)
= 2 kgs

Question 4.
A petrol tanker contains 20,000 litres of petrol. Express the quantity of petrol in kilolitres and millilitres.
Answer:
The quantity of petrol in a petrol tanker is 20,000 litres.
= \(\frac{20000}{1000}\) kiloliters (∵ 1000 litres = 1 kilolitre)
= 20 kilolitres
We know that 1 litre = 1000 millilitres
∴ 20000 litres = 20000 × 1000 millilitres
= 20000000 millilitres

Think, Discuss and Write

Question 1.
You live in Ahmedabad and you trav-elled 400 m by bus to reach the nearest station. Then you take a train to reach Gandhi Nagar which is 15 km. away. Then you take a cab to reach your aunt’s house which is 18 km. away.
(i) How much distance did you travel to reach your aunt’s house ?
(ii) If you travel for 7 days like this how much distance would you travel ?
Answer:
(i) Travelled by bus = 400 m
Travelled by train =15 km
Travelled by cab = 18 km
∴ I travelled to reach my aunt’s house = 400 m + 15 km + 18 km
= 33 km 400 m = 33.4 kms.

(ii) The distance travelled by me in 7 days = 7 × 33.4 kms
= 233.8 kms (or) 233 km 800 m

Question 2.
Every child in your school bring a water bottle containing 2 litres of water. If all the water is poured into a container which has 2 kilo litre capacity of water it was found that it needed 600 litre more to be filled. How many children poured water bottles in the container ?
Answer:
Capacity of water container = 2 kilolitres
= 2 × 1000 lts = 2000 litres
Each student bring the capacity of water bottle = 2 lts.
Required water to fill the tank is = 600 l
Already filled water in the container
= (2000 – 600) litres = 1400 litres
∴ Number of children poured water in the container = \(\frac{1400}{2}\) = 700
∴ 700 children poured water bottles in the container.

Students can practice TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Ex 4.3 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.3

Question 1.
Name the angles, vertex and arms of the angles from the figure.

Answer:

Question 2.
Name the angles formed in the figure.

Answer:
∠DAB, ∠ABC, ∠BCD and ∠CDA are the angles formed in the figure.

Question 3.
Mark the points in the figure which satisfy all the three conditions.

(i) A, B iii the interior of ∠DOF
(ii) A, C in the exterior of ∠EOF
(iii) B on ∠DOE
Answer:

Question 4.
In which of the following figures, angles are formed?

Answer:
Angles are formed in the figures (i) and (iii).

Students can practice TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Ex 1.1 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 1 Knowing Our Numbers Exercise 1.1

Question 1.
Which is the greatest and the smallest among the following numbers ?
(i) 15432, 15892, 15370, 15524
Answer:
All the four numbers are of 5 digits.
The digits in ten thousands place in all the given numbers are same.
The digits in thousands place are also same.
So we move to hundreds place to compare them.
The digits in hundreds place are 4, 8, 3 and 5 respectively.
∴ 3 < 4 < 5 < 8
∴ The greatest number is 15892
The smallest number is 15370

(ii) 25073, 25289, 25800, 25623
Answer:
All the four numbers are of 5 digits. The digits in ten thousands place in all the given numbers are same. The digits in thousands place are also same. So we move to hundreds place to compare them.
The digits in hundreds place are 0, 2, 8, 6 respectively.
∴ 0 < 2 < 6 < 8
The greatest number is 25800
The smallest number is 25073

(iii) 44687, 44645, 44670, 44602
Answer:
All the four numbers are of 5 digits.
The digits in ten thousands place, thousands place and hundreds place are same in all the numbers.
So we move to tens place to compare them.
The digits in tens place are 8, 4, 7, 0 respectively.
∴ 0 < 4 < 7 < 8
∴ The greatest number is 44687.
The smallest number is 44602.

(iv) 75671, 75635, 75641, 75610
Answer:
All the four numbers are of 5 digits. The digits in ten thousands place, thousands place and hundreds place are same in all the numbers. So we move to tens place to compare them. The digits in tens place are 7, 3, 4, 1 respectively.
∴ 1 < 3 < 4 < 7
∴ The greatest number is 75671 The smallest number is 75610

v) 34895, 34891, 34899, 34893
Sol. All the four numbers are of 5 digits. The digits in ten thousands place, thousands place, hundreds place and tens place are same in all the numbers. So we move to units place to compare them.
The digits in units place are 5, 1, 9, 3 respectively.
∴ 1 < 3 < 5 < 9
∴ The greatest number is 34899
The smallest number is 34891

Question 2.
Write the numbers in ascending (in-creasing) order.
(i) 375, 1475, 15951, 4713
Answer:
We can say that 15951 is the greatest number and 375 is the smallest number by counting the digits in the numbers. Regarding 1475 and 4713 it is clear that 1475 < 4713
∴ 375 < 1475 < 4713 < 15951
The ascending order is 375, 1475, 4713, 15951

(ii) 9347, 19035, 22570, 12300
Answer:
The number with four digits (i.e.,) 9347 is the smallest number because the other numbers are of five digits.
In 19035, 22570, 12300 numbers, the greatest number is 22570.
Again 12300 < 19035
∴ 9347 < 12300 < 19035 < 22570
The ascending order is 9347, 12300, 19035, 22570

Question 3.
Write the numbers in descending (decreasing) order.
(i) 1876, 89715, 45321, 89254
Answer:
1876 is the smallest number because it has four digits while the other numbers are of five digits.
The other numbers are 89715, 45321, 89254.
45321 < 89254 < 89715 (∵ 2 < 7) ∴ The descending order is 89715, 89254, 45321, 1876. (∵ 89715 > 89254 > 45321 > 1876)

(ii) 3000, 8700, 3900, 18500
Answer:
18500 is the greatest number because it has five digits while the other numbers are of four digits.
The other numbers are 3000,8700,3900
3000 < 3900 < 8700 ∴ The descending order is 18500, 8700, 3900, 3000. (∵ 18500 > 8700 > 3900 > 3000)

Question 4.
Compare the numbers by placing appropriate symbol (< or >) in the space given.
(i) 3854 ………………… 15200
Answer:
3854 < 15200 (ii) 4895 …………………. 4864 Answer: 4895 > 4864

(iii) 99454 ………………….. 99445
Answer:
99454 > 99445

(iv) 14500 ………………….. 14499
Answer:
14500 > 14499

Question 5.
Write the numbers in words :
(i) 72642
Answer:
72,642 = Seventy two thousand six hundred forty two

(ii) 55345
Answer:
55,345 = Fifty five thousand three hundred forty five

(iii) 66600
Answer:
66,600 = Sixty six thousand six hundred

(iv) 30301
Answer:
30,301 = Thirty thousand three hundred one

Question 6.
Write the numbers in figures:
(i) Forty thousand two hundred seventy.
Answer:
40,270

(ii) Fourteen thousand sixty four.
Answer:
14,064

(iii) Nine thousand seven hundred.
Answer:
9,700

(iv) Sixty thousand.
Answer:
60,000

Question 7.
Form four digit numbers with the digits 4, 0, 3, 7 and find which is the greatest and the smallest among them ?
Answer:
The digits given are 4, 0, 3, 7.
The four digit numbers formed with the digits are
4037, 4073, 4370, 4307, 4730, 4703
3047, 3074, 3470, 3407, 3704, 3740
7034, 7043, 7304, 7340, 7403, 7430
The greatest number is 7430
The smallest number is 3047

Question 8.
Write the following numbers.
(i) the smallest four digit number
Answer:
1000

(ii) the greatest four digit number
Answer:
9999

(iii) the smallest five digit number
Answer:
10000

(iv) the greatest five digit number
Answer:
99999

Students can practice TS 6th Class Maths Solutions Chapter 2 Whole Numbers Ex 2.1 to get the best methods of solving problems.

TS 6th Class Maths Solutions Chapter 2 Whole Numbers Exercise 2.1

Question 1.
Which of the statements are true (T) and which are false (F). Correct the false statements.
(i) There is a natural number that has no predecessor.
Answer:
True (T)

(ii) Zero is the smallest whole number.
Answer:
True (T)

(iii) All whole numbers are natural numbers.
Answer:
False(F)

(iv) A whole number that lies on the number line lies to the right side of another number is the greater number.
Answer:
True (T)

(v) A whole number on the left, of another number on the number line, is greater.
Answer:
False (F)
Correct form : A whole number on the left of another number on the number line is smaller.

(vi) We can’t show the smallest whole number on the number line.
Answer:
False (F)
Correct form : We can show the smallest whole number on the number line.

(vii) We can show the greatest whole number on the number line.
Answer:
False (F)
Correct form : We can’t show the greatest whole number on the number line.

Question 2.
How many whole numbers are there between 27 and 46?
Answer:

There are 18 whole numbers between 27 and 46.

Question 3.
Find the following using number line.
(i) 6 + 7 + 7
Answer:

(ii) 18 – 9
Answer:

(iii) 5 × 3
Answer:

Start from 0, move 5 units to the right each time, making 3 such moves. We will reach 15. So, 5 × 3 = 15

Question 4.
In each pair, state which whole number on the number line is on the right of the other number.
(i) 895 ; 239
(ii) 1001 ; 10001
(iii) 10015678 ; 284013
Answer:
(i) 895 is on the right of 239. .
(ii) 10001 is on the right of 1001.
(iii) 10015678 is on the right of 284013.

Question 5.
Mark the smallest whole number on the number line.
Answer:

Question 6.
Choose the appropriate symbol from < or >
(i) 8 ……… 7
(ii) 5 ……… 2
(iii) 0 ………. 1
(iv) 10 ………. 5
Answer:
(i) 8 > 7
(ii) 5 > 2
(iii) 0 < 1
(iv) 10 > 5

Question 7.
Place the successor of 11 and predecessor of 5 on the number line.
Answer:

Successor (that comes next) of 11 is 12.
Predecessor (that comes before) of 5 is 4.