Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.2

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.
Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.2

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.2

Question 1.
Fill in the blanks.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q1
(iii) Representation of data by using pictures is known as _______
Solution:
(i) 150 balls
(ii) Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q1.1
(iii) Pictograph

Question 2.
Draw a pictograph for the give data.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q2
(Choose your own suitable scales)
Solution:
Pictograph of Number of computers sold.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q2.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.2

Question 3.
The following table shows the number of tourists who visited the places in the month of May. Draw a pictograph.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q3
(Choose your own suitable scale)
Solution:
The pictograph for the number of tourists who visited various places:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q3.1

Question 4.
The following pictograph shows the number of students playing different games in a school
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.2 Q4
Answer the following questions.
(i) Which is the most popular game among the students?
(ii) Find the number of students playing kabaddi?
(iii) Which two games are played by an equal number of students?
(iv) What is the difference between the number of students playing Kho-Kho and Hockey?
(v) Which is the least popular game among the students?
Solution:
(i) Kabaddi is the most popular game among students.
(ii) There are 11 × 10 = 110 students playing kabaddi.
(iii) Kho-Kho and Hockey are played by an equal number of students.
(iv) Difference is 90 – 90 = 0.
(v) Basketball is the least popular game among students.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.2

Objective Type Questions

Question 5.
The representation of‘one picture to many objects’ in a pictograph is called
(a) Tally mark
(b) Pictoword
(c) Scaling
(d) Frequency
Solution:
(c) Scaling

Question 6.
The representation of ‘one picture too many objects’ in a Pictograph is called _____
(a) Tally mark
(b) Pictoword
(c) Scaling
(d) Frequency
Solution:
(c) Scaling

Question 7.
A Pictograph is also known as ______
(a) Pictoword
(b) Pictogram
(c) Pictophrase
(d) Pictograph
Solution:
(b) Pictogram

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

You can Download Samacheer Kalvi 6th Science 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 Science Solutions Term 1 Chapter 1 Measurements

Samacheer Kalvi 6th Science Measurements Textual Evaluation

I. Choose the correct answer.

Question 1.
The girth of a tree can be measured by
(a) metre scale
(b) metre rod
(e) plastic ruler
(d) measuring tape
Answer:
(d) measuring tape

Question 2.
The conversion of 7 m into cm gives
(a) 70 cm
(b) 7 cm
(c) 700 cm
(d) 7000 cm
Answer:
(c) 700 cm

Question 3.
Quantity that can be measured Is called
(a) Physical quantity
(b) Measurement
(c) unit
(d) motion
Answer:
(a) Physical quantity

Question 4.
Choose the correct one
(a) km > mm > cm > m
(b) km > mm > m > cm
c) km > m > cm > mm
(d) km > cm > m > mm
Answer:
(c) km > m > cm > mm

Question 5.
While measuring length of an object using a ruler, the position of your eye should be
(a) Left side of the point.
(b) Vertically above the point where the measurement is to be taken.
(c) Right side of the point
(d) Any where according to one’s convenience.
Answer:
(b) Vertically above the

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

II. True or False.

  1. We can say that mass of an object is 126 kg.
  2. Length of one’s chest can be measured by using metre scale.
  3. Ten millimetres makes one centimetre.
  4. A hand span is a reliable measure of length.
  5. The SI system of units is accepted everywhere in the world.

Answers:

  1. True
  2. False
  3. True
  4. False
  5. True

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

III. Fill in the blanks.

  1. SI Unit of length is symbolically represented as _____
  2. 500 gm = _____ kilogram
  3. Distance between Delhi and Chennai can be measured in _____
  4. 1 m = _____ cm.
  5. km = _____ m.

Answers:

  1. m
  2. 0.5
  3. Kilometre
  4. 100
  5. 5000

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

IV. Analogy

Question 1.
Sugar: Beam balance; Lime juice?
Answer:
Measuring Jar.

Question 2.
Height of a person : cm; length of your sharpened pencil lead?
Answer:
mm (mull metre)

Question 3.
Milk: volume; vegetables?
Answer:
mass

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

V. Match the following :

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 1
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 2

VI. Complete the given table
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 3
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 4

VII. Arrange in increasing order of unit.

Question 1.
1 Metre, 1 centimetre, 1 kilometre, and 1 millimetre.
Answer:
1 millimetre < 1 centimetre < 1 Metre < 1 kilometre.

VIII. Find the answer for the following questions within the grid.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 5

  1. 10-3 is one _____
  2. SI Unit of time _____
  3. Cross view of reading for a measurement leads to _____
  4. _____ is the one what a clock reads.
  5. _____ is the amount of substance present in an object
  6. _____ can be taken to get the final reading of the recordings of different of students for a single measurement.
  7. _____ is a fundamental quantity.
  8. _____ shows the distance covered by an automobile.
  9. A tailor use _____ to take measurements to stitch a cloth.
  10. Liquids are measured with this physical quantity.

Answers:

  1. Millimetre
  2. second
  3. error
  4. Time
  5. Mass
  6. Average
  7. Length
  8. Odometer
  9. Tape
  10. Litre

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

IX. Answer in a word or two.

Question 1.
What is the full form of SI system?
Answer:
An international system of unit

Question 2.
Name any one instrument used for measuring mass.
Answer:
Beam balance.

Question 3.
Find the odd one out: Kilogram, millimetre, centimetre, nanometre.
Answer:
Kilogram

Question 4.
What is the SI Unit of mass?
Answer:
Kilogram.

Question 5.
What are the two parts present in a measurement?
Answer:

  1. multiple
  2. sub

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

X. Answer in a sentence or two.

Question 1.
Define measurement.
Answer:
The comparison of an unknown quantity with some known quantity is known as measurement.

Question 2,
Define mass?
Answer:
Mass is the measure of the amount of matter in an object.

Question 3.
The distance between two places is 43.65 km. Convert it into metre and cm. 0
Answer:
(a) Convert km into metre
1 km = 1000m
∴ 43.65 km = 43.65 × 1000 = 43650.00 = 43650
= 43650 m.

(b) Convert km into cm.
1 km = 1000 m
1 m = 100 cm
1 km = 1000 × 100 cm
1 km = 100000 cm
∴ 43.65 km = 43.65 × 100000 = 4365000.00
= 4365000 cm.

Question 4.
What are the rules to be followed to make an accurate measurement with scale?
Answer:

  1. To avoid the parallax error.
  2. Your eye must be exactly in front of vertically above the point where the measurement has to be taken.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

XI. Solve the following.

Question 1.
The distance between your school and your house is 2250 m. Express this distance in kilometre.
Answer:
Distance between school and house is 2250 m.
1000 m = 1 km
∴ 2250 m = 2250 ÷ 1000 = 2.25 km.

Question 2.
While measuring the length of a sharpened pencil, reading of the scale at one end is 2.0 cm and at the other end is 12.1 cm. What is the length of the pencil?
Answer:
The difference between the two readings is the length of the pencil.
= 12.1 cm – 2.0 cm
= 10.1 cm or 10 cm and 1 mm.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

XII. Write in detail.

Question 1.
Explain two methods those you can use to measure the length of a curved line.
Answer:
Measuring the length of a curved line, by two methods.
First method – using a string.

  1. Draw a curved line AB on the paper.
  2. Place a string along the curved line.
  3. Make sure that the string covers e very bit of the curved line.
  4. Mark the points where the curved line begins and ends on the string.
  5. Now stretch the string along the length of a meter scale.
  6. Measure the distance between two markings of the string.
  7. This will give the length of a curved line.

Second method – using a divider.

  1. Draw a curved line AB on a paper.
  2. Separate the legs of the divider by 0.5 cm or 1 cm using a ruler.
  3. Place it on the curved line starting from one end. Mark the position of the other end.
  4. Move it along the line again and again cutting the line into number of segments of equal lengths.
  5. The remaining parts of the line can be measured using a scale.
  6. Count the number of segments.
  7. Length of the line = (No. of segments × length of each segment) + length of the left over part.

Question 2.
Fill in the following chart.
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 6
Answer:
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 7

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

Samacheer Kalvi 6th Science Measurements Additional Questions

I. Choose the correct answer:

Question 1.
In which SI unit, you can measure you height?
(a) Kilogram
(b) Litre
(c) Metre
(d) Second
Answer:
(c) Metre

Question 2.
What is the unit of electric current in SI system?
(a) Kelvin
(b) Ampere
(c) seconds
(d) Volt.
Answer:
(b) Ampere

Question 3.
_____ is used to measure the accurate time of the activity.
(a) Clock
(b) Watch
(c) Stop clock
(d) Sundial
Answer:
(c) Stop dock

Question 4.
These are the measurements used in measuring the volume of liquid.
(a) cylinder
(b) pipettes
(c) burettes
(d) All.
Answer:
(d) All

Question 5.
S.I unit for Volume is _____
(a) m2
(b) m
(c) m3
(d) none
Answer:
(c) m3

Question 6.
Twenty decimetre is equal to _____
(a) 2 km
(b) 20 cm
(c) 2 metre
(d) 200 mm
Answer:
(c) 2 metre

Question 7.
_____ is used to measure mass.
(a) Stop clock
(b) Beam balance
(c) Sundial
(d) Graduated cylinder
Answer:
(b) Beam balance

Question 8.
The metric system of units was created by the _____ in 1790.
(a) Greek
(b) Australians
(c) Russians
(d) French
Answer:
(d) French

Question 9.
The moon’s gravitational pull is one _____ of the earth’s pull.
(a) seventh
(b) sixth
(c) fifth
(d) fourth
Answer:
(b) Sixth

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

II. Find whether the following sentences are true or false. If false Correct the statement.

Question 1.
Kerosene is measured with the help of the graduated cylinder.
Answer:
True.

Question 2.
Length is a fundamental quantity.
Answer:
True.

Question 3.
On moon, the gravitational force is greater than earth.
Answer:
False. On moon the gravitational force is lesser than earth.

Question 4.
An electronic balance is a device used to find accurate mass.
Answer:
True.

Question 5.
Speedometer is a device used for indicating distance travelled by an automobile.
Answer:
False. Odometer js a device used for indicating distance travelled by an automobile.

Question 6.
A ruler or scale used now a days to measure length was invented by William Bedwell.
Answer:
True.

Question 7.
Length, mass and time are some of the derived quantities.
Answer:
False. Length, mass, and time are some of the fundamental quantities.

Question 8.
Leaves and piece of paper are heavier things.
Answer:
False. Leaves and piece of paper are lighter things.

Question 9.
National physical laboratory is located in Delhi.
Answer:
True.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

III. Analogy.

Question 1.
Potatoes : Kilogram; Water?
Answer:
Litre.

Question 2.
Stop clock : accurate time; _______ : accurate weight
Answer:
Electronic balance.

Question 3.
Mass : Balance; Length?
Answer:
measuring tape.

Question 4
Amount of matter: mass; Gravitational Pull?
Answer:
Weight.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

IV. Answer the following questions in one or two words.

Question 1
What are the materials needed to find the length of a banana?
Answer:
A meter scale, a string or thread, sketch pen..

Question 2.
What formula is used to measure area of your class room?
Answer:
My class room area = Length × Breadth

Question 3.
Give an example of a device used to find the accurate measurement of weight.
Answer:
Electronic balance.

Question 4.
In earlier days, which instruments are used to measure time?
Answer:
Sand clock and Sun dial.

Question 5.
What are the clocks used to measure a smaller duration of time?
Answer:
Electronic clock, Stop watch.

Question 6.
Who invented a ruler or scale?
Answer:
William Bedwell.

Question 7.
Which alloy is used to make the standard metre rod?
Answer:
An alloy of Platinum and iridium.

Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements

V. Match the following
Samacheer Kalvi 6th Science Solutions Term 1 Chapter 1 Measurements 8
Answers:
a. ii
b. iii
c. iv
d. i

VI. Answer the following In one or two sentences:

Question 1.
What is the international system of units or SI units?
Answer:
For the sake of uniformity all over the world, we have adopted a common set of units to express measurements that are called as an International system of units or SI units.

Question 2.
Give some examples of larger length measures.

  1. Height of the building,
  2. Length of a banner,
  3. Height of lamp post.

Question 3.
What are the unit of measurements of very small length?
Answer:

  1. Millimetre
  2. centimetre.

Question 4.
What is meant by parallax?
Answer:
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight.

Question 5.
What are the clock used by ancient people to measure day time?
Answer:

  1. sand clock
  2. sun clock.

Question 6.
Where are the electronic balances used?
Answer:
Electronic balances are used in grocery shops and jeweleries.

Question 7.
What is odometer?
Answer:
It is a device used for indicating distance travelled by automobile.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.1

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.
Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.1

Question 1.
Fill in the blanks.
(i) The collected information is called _____
(ii) An example of Primary data is ______
(iii) An example of a Secondary data is ______
(iv) The tally marks for number 8 in standard form is _____
Solution:
(i) Data
(ii) List of Absentees in a class
(iii) Cricket scores gathered from a website
(iv) Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q1

Question 2.
Viji threw a die 30 times and noted down the result each time as follows. Prepare a table on the numbers shown using Tally Marks.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q2
Solution:
We prepare a table using tally marks from the given information
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q2.1

Question 3.
The following list tells colours liked by 25 students. Prepare a table using Tally Marks.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q3
Solution:
We prepare the table using Tally marks as
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q3.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.1

Question 4.
The following are the marks obtained by 30 students in a class test out of 20 in Mathematics subject.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q4
Prepare a table using Tally Marks.
Solution:
We prepare a table using Tally Marks as
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q4.1
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q4.2

Question 5.
The table shows the number of calls recorded by a Fire Service Station in one year.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q5
Complete the table and answer the following questions.
(i) Which type of call was recorded the most?
(ii) Which type of call was recorded the least?
(iii) How many calls were recorded in all?
(iv) How many calls were recorded as False Alarm?
Solution:
The completed table is given below.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q5.1
(i) The call for “Other Fires” was recorded the most
(ii) The call for “Rescues” was recorded the least
(iii) The total of 35 calls was recorded
(iv) There are 7 calls were recorded as False alarm.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.1

Objective Type Questions

Question 6.
The tally marks for the number 7 in standard form is ________
(a) 7
(b) Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q6
(c) ✓✓✓✓✓✓✓
(d) Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q6.1
Solution:
(b) Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q6

Question 7.
The tally marks Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.1 Q7represent the number count
(a) 5
(b) 8
(c) 9
(d) 10
Solution:
(c) 9

Question 8.
The plural form of ‘datum’ is
(a) datum
(b) datums
(c) data
(d) datas
Solution:
(c) data

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.6

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 1 Chapter 1 Numbers Ex 1.6

Miscellaneous Practice Problems
Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.6
Question 1.
Try to open my locked suitcase which has the biggest 5 digits odd number as the password comprising the digits 7, 5, 4, 3 and 8. Find the password.
Solution:
Using a place value chart
The number should be the biggest odd
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.6 Q1
The password is 87543

Question 2.
As per the census of 2001, the population of four states are given below. Arrange the states in ascending and descending order of their population.
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.6 Q2
Solution:
All the four values have 8 digits
Comparing the leftmost digits we have 91276115, 72626809, 72147030, 68548437
Descending order: 91276115 > 72626809 > 72147030 > 68548437
Ascending order: 68548437 < 72147030 < 72626809 < 91276115
Ascending order: Rajasthan < Tamil Nadu < Madhy Pradesh < West Bengal
Descending order: West Bengal > Madhya Pradesh > TamilNadu > Rajasthan

Question 3.
Study the following table and answer the questions.
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.6 Q3
(i) How many tigers were there in 2011?
(ii) How many tigers were less in 2008 than in 1990?
(iii) Did the number of tigers increase or decrease between 2011 and 2014? If yes, by how much?
Solution:
(i) There are 1706 tigers in 2011

(ii) No. of tigers in 2008 = 1400
No. of tigers in 1990 = 3500
There were 2100 lesser tigers

(iii) No. of tigers in 2014 = 2226
No. of tigers in 2011 = 1706
Difference = 520
2226 > 1706
The number of tigers increased from 2011 to 2014.
Yes, the number of tigers increased, 520 more tigers are there in 2014.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.6

Question 4.
Mullaikodi has 25 bags of apples. In each bag there are 9 apples. She shares them equally amongst her 6 friends. How many apples do each get? Are there any apples left over?
Solution:
No of apple bags = 25
Apples in each bag = 9
Total no of apples = 25 × 9 = 225
Apples shared among her 6 friends = 225 ÷ 6
So, among her 6 friends, each of them get 37 apples and 3 apples are left over.

Question 5.
A Poultry has produced 15472 eggs and fits 30 eggs in a tray. How many trays do they need?
Solution:
Total eggs = 15472
No. of eggs in 1 tray = 30
No. of trays needed = 15472 ÷ 30 = 516
No. of trays needed = 516 [515 + 1 for remaining 22 eggs]

Challenging Problems (Text book Page No.36 & 37)

Question 6.
Read the table and answer the following questions.
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.6 Q6
Solution:
(i) Write the Canopus star’s diameter in words in the Indian and the International System.
(ii) Write the sum of the place values of 5 in Sirius star’s diameter in Indian System.
(iii) Eight hundred sixty-four million seven hundred thirty. Write in Indian System
(iv) Write the diameter in words of Arcturus star in the International System.
(v) Write the difference of the diameters of Canopus and Arcturus star in the Indian and the International Systems.
Solution:
(i) Canopus star’s diameter is 25941900 miles
Indian System: Two crores Fifty-Nine Lakh Forty-one thousand Nine Hundred
International System: Twenty-Five Million Nine Hundred Forty-One Thousand Nine Hundred.

(ii) Sirus star’s diameter = 1556500 miles
Sum of place values of 5 is 5 × 100000 + 5 × 10000 + 5 × 100
= 500000 + 50000 + 500
= 5,50,500

(iii) Given value is 864,000,730
In Indian System 86,40,00,730
Eighty-six crore forty lakhs seven hundred and thirty.

(iv) The diameter of the Arcturus Star is 19,888,800 miles
Nineteen Million Eight Hundred and Eighty-Eight Thousand Eight Hundred.

(v) The diameter of Canopus = 25941900
Diameter of Arcturus = 19888800
Difference = 6053100
In Indian System 60,53,100
Sixty lakh fifty-three thousand one hundred.
In International System 6,053,100
Six Million fifty-three thousand one hundred.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.6

Question 7.
Anbu asks Arivu Selvi to guess a five digit odd number. He gives the following hints.
i. The digit in the 1000s place is less than 5
ii. The digit in the 100s place is greater than 6
iii. The digit in the 10s place is 8
What is Arivu Selvi answer? Does she give more than one answer?
Solution:
63785, 53781

Question 8.
A Music concert is taking place in a stadium, A total of 7,689 chairs are to be put in rows of 90.
(i) How many rows will there be?
(ii) Will there be any chairs left over?
Solution:
(i) There will be 85 rows
(ii) Yes, there are 39 chairs left over.
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.6 Q8

Question 9.
Round off the seven-digit number 29,75,842 to the nearest lakhs and ten lakhs. Are they the same?
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.6 Q9
To the nearest lakhs = 30,00,000
To the nearest ten lakhs = 30,00,000
Yes, they are the same.

Question 10.
Find the 5 or 6 or 7 digit numbers from a newspaper or a magazine to get a rounded number to the nearest ten thousand.
Solution:
(i) 14276 \(\simeq\) 10000
(ii) 1,86945 \(\simeq\) 1,90000

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.6

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.5

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 1 Chapter 1 Numbers Ex 1.5

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.5
Question 1.
Fill in the blanks.
(i) The difference between the smallest natural number and the smallest whole number is _____
(ii) 17 × ___ = 34 × 17
(iii) When _____ is added to a number, it remains the same.
(iv) Division by ____ is not defined.
(v) Multiplication by ____ leaves a number unchanged.
Solution:
(i) 1
Hint: 1 – 0 = 1
(ii) 34
(iii) 0
(iv) 0
(v) 1

Question 2.

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.5

Say True or False.

  1. 0 is the identity for multiplication of whole numbers.
  2. Sum of two whole numbers is always less than their product.
  3. Both addition and multiplication are associative for whole numbers.
  4. Both addition and multiplication are commutative for whole numbers.
  5. Multiplication is distributive over addition for whole numbers.

Solution:

  1. False
  2. False
  3. True
  4. True
  5. True

Question 3.
Name the property being illustrated in each of the cases given below:

  1. 75 + 34 = 34 + 75
  2. (12 × 4) × 8 = 12 × (4 × 8)
  3. 50 + 0 = 50
  4. 50 × 1 = 50
  5. 50 × 42 = 50 × 40 + 50 × 2

Solution:

  1. Addition is commutative
  2. Multiplication is associative
  3. 0 is the additive identity
  4. 1 is the multiplicative identity.
  5. Distributivity of multiplication over addition

Question 4.
Use the properties of whole numbers and simplify.
(i) 50 × 102
(ii) 500 × 689 – 500 × 89
(iii) 4 × 132 × 25
(iv) 196 + 34 + 104
Solution:
(i) 50 × 102
= 50 × (100 + 2)
= (50 × 100) + (50 × 2)
= 5000 + 100 = 5100

(ii) 500 × 689 – 500 × 89
= 500 × (689 – 89)
= 344500 – 44500
= 300000
= 500 × (689 – 89)
= 500 × 600
= 3,00000

(iii) (4 × 132) × 25
= 4 × (132 × 25)
= (4 × 132) × 25
= 528 × 25
= 13200
= 4 × (132 × 25)
= 4 × 3300
= 13200

(iv) (196 + 34) + 104 = 196 + (34 + 104)
(196 + 34) + 104 = 230 + 104 = 334
196 + (34 + 104) = 196 + 138 = 334

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.5

Objective Type Questions

Question 5.
(53 + 49) × 0 is
(a) 102
(b) 0
(c) 1
(d) 53 + 49 + 0
Solution:
(b) 0
53 × 0 + 49 × 0 = 0 + 0 = 0

Question 6.
\(\frac{59}{1}\) is
(a) 1
(b) 0
(c) \(\frac{1}{59}\)
(d) 59
Solution:
(d) 59

Question 7.
The product of a non-zero whole number and its successor is always
(a) an even number
(b) an odd number
(c) zero
(d) none of these
Solution:
(a) an even number

Question 8.
The whole number that does not have a predecessor is
(a) 10
(b) 0
(c) 1
(d) none of these
Solution:
(b) 0
0 is the smallest whole number

Question 9.
Which of the following expressions is not zero?
(a) 0 × 0
(b) 0 + 0
(c) 2/0
(d) 0/2
Solution:
(c) 2/0

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.5

Question 10.
Which of the following is not true?
(a) (4237 + 5498) + 3439 = 4237 + (5498 + 3439)
(b) (4237 × 5498) × 3439 = 4237 × (5498 × 3439)
(c) 4237 + 5498 × 3439 = (4237 + 5498) × 3439
(d) 4237 × (5498 + 3439) = (4237 × 5498) + (4237 × 3439)
Solution:
(c) 4237 + 5498 × 3439 = (4237 + 5498) × 3439

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 2 Introduction to Algebra Ex 2.2

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 1 Chapter 2 Introduction to Algebra Ex 2.2

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 2 Introduction to Algebra Ex 2.2
Question 1.
Find in the blanks.
(i) The algebraic statement of ‘f’ decreased by 5 is _______
(ii) The algebraic statement of ‘s’ divided by 5 is _______
(iii) The verbal statement of ‘2m – 10’ is _______
(iv) If A’s age is ‘n’ years now, 7 years ago A’s age was ______
(v) If ‘p – 5’ gives 12 then ‘p’ is ______
Solution:
(i) f – 5
(ii) \(\frac { s }{ 5 }\)
(iii) 10 less than 2 times m (or) Take away 10 from the product of 2 and m
(iv) n – 7
(v) 17
Hint: n – 5 = 12⇒ n = 12 + 5 = 17

Question 2.
Say True or False.
(i) 10 more to three times ‘c’ is ‘3c + 13’.
(ii) If the cost of 10 rice bags is Rs ‘t’, then the cost of 1 rice bag is Rs \(\frac{t}{10}\)
(iii) The statements ‘x’ divided by 3 and 3 divided by ‘x’ are the same.
(iv) The product of ‘q’ and 20 is ‘20q’.
(v) 7 less to 7 times ‘y’ is ‘7 – 7y’.
Solution:
(i) False
(ii) True
(iii) False
(iv) True
(v) False

Question 3.
Express the following verbal statement to algebraic statement.
(i) ‘t’ is added to 100
(ii) 4 times ‘q’
(iii) 8 is reduced by ‘y’
(iv) 56 added to 2 times ‘x’
(v) 4 less to 9 times of ‘y’
Solution:
(i) t + 100
(ii) 4q
(iii) 8 – y
(iv) 2x + 56
(v) 9y – 4

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 2 Introduction to Algebra Ex 2.2

Question 4.
Express the following algebraic statement to verbal statement.
(i) x ÷ 3
(ii) 5n – 12
(iii) 11 + 10x
(iv) 70s
Solution:
(i) x divided by 3
(ii) 12 less to 5 times n
(iii) 11 added to 10 times x
(iv) 70 times s

Question 5.
The teacher asked two students to write the algebraic statement for the verbal statement “8 more than a number” on the board. Vetri wrote ‘8 + x’ but Maran wrote ‘8x’. Who gave the correct answer?
Solution:
Let the number be x; 8 more than the number = 8 + x.
Vetri gave the correct answer as 8 + x.

Question 6.
Answer the following questions:
(i) If ‘n’ takes the value 3 then find the value of ‘n + 10’
(ii) If ‘g’ is equal to 300. What is the value of ‘g – 1’ and ‘g + 1’?
(iii) What is the value of s; if ‘2s – 6’ gives 30?
Solution:
(i) Given n = 3
then n + 10 = 3 + 10 = 13
n + 10 = 13

(ii) Given g = 300
g – 1 = 300 – 1 = 299
g + 1 = 300 + 1 = 301
g – 1 = 299; g + 1 = 301

(iii) Given 2s – 6 = 30
From the table:
2 × 18 – 6 = 30
s = 18
Samacheer Kalvi 6th Maths Term 1 Chapter 2 Introduction to Algebra Ex 2.2 Q6

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 2 Introduction to Algebra Ex 2.2

Question 7.
Complete the table and find the value of ‘k’ for which \(\frac { k }{ 3 }\) gives 5.Samacheer Kalvi 6th Maths Term 1 Chapter 2 Introduction to Algebra Ex 2.2 Q7
Solution:
Given: k ÷ 3 = 5 From the above table we find that
15 ÷ 3 = 5
k = 5
Samacheer Kalvi 6th Maths Term 1 Chapter 2 Introduction to Algebra Ex 2.2 Q7.1

Objective Type Questions

Question 8.
The value of ‘y’ in y + 7 = 13 is
(a) y = 5
(b) y = 6
(c) y = 7
(d) y = 8
Solution:
(b) y = 6

Question 9.
6 less to ‘n’ gives 8 is represented as
(a) n – 6 = 8
(b) 6 – n = 8
(c) 8 – n = 6
(d) n – 8 = 6
Solution:
(a) n – 6 = 8

Question 10.
The value of ‘c’ for which \(\frac{3c}{4}\) gives 18 is
(a) c = 15
(b) c = 21
(c) c = 24
(d) c = 27
Solution:
(c) c = 24

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 2 Introduction to Algebra Ex 2.2

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.4

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 1 Chapter 1 Numbers Ex 1.4

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.4
Question 1.
Fill in the blanks.
(i) The nearest 100 of 843 is _____
(ii) The nearest 1000 of 756 is ______
(iii) The nearest 10,000 of 85654 is ______
Solution:
(i) 800.
The digit in tens place is 4 < 5
(ii) 1000.
The digit in hundred places is 7 ≥ 5
(iii) 90,000.
The digit in a thousand places is 5 ≥ 5

Question 2.
Say True or False.
(i) 8567 is rounded off as 8600 to the nearest 10.
(ii) 139 is rounded off as 100 to the nearest 100.
(iii) 1,70,51,972 is rounded off as 1,70,00,000 to the nearest lakh.
Solution:
(i) False
(ii) True
(iii) False

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.4

Question 3.
Round off the following to the given nearest place.
(i) 4065; hundred
(ii) 44,555; thousand
(iii) 86943; ten thousand
(iv) 50,81,739; lakh
(v) 33,75,98,482; Ten crore
Solution:
(i) We have to round off 4065 to hundreds
The place value is a hundred
The digit in hundreds place is 0
The digit to the right is 6 > 5
Adding 1 to 0 ⇒ 0 + 1 = 1
Changing the digits to the right of 41 to zeros
4065 \(\simeq\) 4100 ⇒ 4100
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q3
(ii) To round off 44555 to thousands
The digit in the thousands place is 4
digit to the right is 5 = 5.
Adding 1 to the thousand place value digit 4 ⇒ 4 + 1 = 5
Changing the digits to the right of 45 to zeros we get 45000
44555 \(\simeq\) 45000
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q3.1
(iii) To round off 86,943 to ten thousand
The digit in ten thousand places is 8
The digit to the right is 6 > 5
Adding 1 to 8 ⇒ 8 + 1 = 9.
Changing the digits to the right of 9 to zeroes we get 90,000
86943 \(\simeq\) 90,000
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q3.2
(iv) To round off 5081739 to lakhs
The digit in the lakhs place is 0
The digit to the right is 8 > 5
Adding 1 to 0 ⇒ 1 + 0 = 1
Changing the digits right off 51 to zeros
We get 51,00,000
5081739 \(\simeq\) 51,00,000
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q3.3
(v) To round off 337598482 to ten crore
The digit in the ten crores place is 3
The digit to the right is 3 < 0
The digit in ten crore place remains the same 3.
Changing the digit to the right of 3 zeros we get 30,00,00,000
33,75,98,482 \(\simeq\) 30,00,00,000
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q3.4

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.4

Question 4.
Estimate the sum of 157826 and 32469 rounded off to the nearest ten thousand.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q4

Question 5.
Estimate by rounding off each number to the nearest hundred.
(i) 8074 + 4178
(ii) 1768977 + 130589
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 1 Numbers Ex 1.4 Q5

Question 6.
The population of a city was 43,43,645 in the year 2001 and 46,81,087 in the year 2011. Estimate the increase in population by rounding off to the nearest thousand.
Solution:
Population in 2001 = 43,43,645
Population in 2011 = 46,81,087
Increase in population = 46,81,087 – 43,43,645 = 3,37,442
When rounded off to the nearest thousand = 3,37,000

Objective Type Questions

Question 7.
The number which on rounding off to nearest thousands given 11000 is
(a) 10345
(b) 10855
(c) 11799
(d) 10056
Solution:
(b) 10855
In 10855, the digit in a hundred places is 8 ≥ 5. So 11000

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 1 Numbers Ex 1.4

Question 8.
The estimation to the nearest hundred of 76812 is
(a) 77000
(b) 76000
(c) 76800
(d) 76900
Solution:
(c) 76800

Question 9.
The number 9785764 is rounded off to nearest lakh as
(a) 9800000
(b) 9786000
(c) 9795600
(d) 9795000
Solution:
(a) 9800000
In ten thousand places, the digit is 8 5. So 9800000

Question 10.
The estimated difference of 167826 and 2765 rounded off to the nearest thousand is
(a) 180000
(b) 165000
(c) 140000
(d) 155000
Solution:
(b) 165000

Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

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.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Question 1.
Study and complete the following pattern.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 1
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 2

Question 2.
Find next three numbers in the following number patterns,
i) 50, 51, 53, 56, 60,…
ii) 77, 69, 61, 53,…
iii) 10, 20, 40, 80, …..
iv) \(\frac{21}{33}, \frac{321}{444}, \frac{4321}{5555}\)
Solution:
i) The pattern generating these numbers is
50, 50 + 1, 51 + 2, 53 + 3, 56 + 4, 60 + 5, 65 + 6, 71 + 7,
∴ 50, 51, 53, 56, 60, 65, 71, 78, ……
∴ The next three numbers will be 65, 71, 78

ii) The pattern generating these numbers is
77, 77 – 8, 69 – 8, 61 – 8, 53 – 8, 45 – 8, 37 – 8, 29
77, 69, 61, 53, 45, 37, 29, 21,
∴ The next three numbers will be 45, 37, 29.

iii) The pattern generating these numbers is
10, 10 + 10, 20 + 20, 40 + 40, 80 + 80, 160 + 160, 320 + 320,….
10, 20, 40, 80, 160, 320, 640,….
∴ The next three numbers will be 160, 320, 640.

iv) The pattern generating these numbers is
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 50

Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Question 3.
Consider the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,… Observe and complete the following table by understanding the number pattern followed. After filling the table discuss the pattern followed in addition and subtraction of the numbers of the sequence.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 51
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 52

Question 4.
Complete the following patterns.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 53
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 54
Rotate the figure 90°C clockwise to get the next figure.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 55
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 56
* Move the circled arrow to each comer clockwise and place the square to the opposite comer of the arrow, in first row.
* Copy the first row in the second row.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 57
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 58
Rotate the arrow inside the square 90° anticlockwise direction so that the arrow pointing each comer anticlockwise.

Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Question 5.
Find HCF of the following pair of numbers by Euclid’s game.
(i) 25 and 35
(ii) 36 and 12
(iii) 15 and 29
Solution:
(i) HCF of (25, 35 – 25)
25 = 5 × 5
10 = 2 × 5
HCF of (25, 10) = 5

(ii) HCF of (36, 36 – 12)
36 = 2 × 2 × 3 × 3
24 = 2 × 2 × 2 × 3
HCF of (36, 24) = 2 × 2 × 3 = 12

(iii) HCF of (15, 29 -15)
15 = 3 × 5 × 1
14 = 2 × 7 × 1
HCF of (15, 14) = 1

Question 6.
Find HCF of 48 and 28. Also find the HCF of 48 and the number Obtained by finding their difference.
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 60

Question 7.
Give instructions to fill in a bank withdrawal form issued in a bank.
Solution:

  • The name should be written in capital letters from left to right.
  • Write the date of withdrawal on the right top comer of the form.
  • Write the amount (in words) to be withdrawn in the space provided.
  • Write the amount (in figures) to be withdrawn in the box provided.
  • Put your signature at the right bottom above the ‘signature of the depositor’.

Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Question 8.
Arrange the name of your classmates alphabetically.
Solution:
Name of my classmates is given below.

  1. Akila
  2. Akshaya
  3. Bharathi
  4. Divya
  5. Ezhil
  6. Fathima
  7. Gayathri
  8. Hlelen
  9. Irusammal
  10. Joy
  11. Kaviya
  12. Lakshmi
  13. Monika
  14. Nisha
  15. Olin
  16. Patsy
  17. Queenlin
  18. Ratha
  19. Sindhu
  20. Vidhya

Question 9.
Follow and execute the instructions given below?
i) Write the number 10 in the place common to the three figures
ii) Write the number 5 in the place common for square and circle only.
iii) Write the number 7 in the place common for triangle and circle only.
iv) Write the number 2 in the place common for triangle and square only.
v) Write the numbers 12,14 and 8 only in square, circle and triangle respectively.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 84
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 85

Question 10.
Fill in the following information.
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 86
Solution:
Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1 88

Samacheer Kalvi 6th Maths Solutions Term 3 Chapter 5 Information Processing Ex 5.1

Objective Type Questions

Question 11.
The next term in the sequence 15, 17, 20, 22, 25, is
(a) 28
(b) 29
(c) 27
(d) 26
Solution:
(c) 27

Question 12.
What will be the 25th letter in the pattern? ABCAABBCCAAABBBCCC
(a) B
(b) C
(c) D
(d) A
Hint:
Write A, B, C with increasing number of A, B, and C
Solution:
(a) B

Question 13.
The difference between 6th term and 5th term in the Fibonacci sequence is
(a) 6
(b) 8
(c) 5
(d) 3
Solution:
(d) 3

Question 14.
The 11th term in the Lucas sequence 1, 3, 4, 7,… is
(a) 199
(b) 76
(c) 123
(d) 47
Solution:
(a) 199

Question 15.
If the Highest Common Factor of 26 and 54 is 2, then HCF of 54 and 28 is
(a) 26
(b) 2
(c) 54
(d) 1
Solution:
(b) 2

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.3

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.
Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.3

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.3

Question 1.
Read the given Bar Graph which shows the percentage of marks obtained by Brinda in different subjects in an assessment test.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q1
Observe the bar graph and answer the following questions.
(i) 1 unit = ___ % of marks on vertical line.
(ii) Brinda has scored maximum marks in _____ subject.
(iii) Brinda has scored minimum marks in ______ subject.
(iv) The percentage of marks scored by Brinda in Science is _____
(v) Brinda scored 60% marks in the subject ______
(vi) Brinda scored 20% more in _______ subject than _____ subject.
Solution:
(i) 10
(ii) Mathematics
(iii) Language
(iv) 65%
(v) English
(vi) Mathematics, English

Question 2.
Chitra has to buy Laddus in order to distribute to her friends as follows:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q2
Draw a Bar Graph for this data.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q2.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.3

Question 3.
The fruits liked by the students of a class are as follows:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q3
Draw a Bar Graph for this data.
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q3.1

Question 4.
The pictograph below gives the number of absentees on different days of the week in class six. Draw the Bar graph for the same.
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q4
Solution:
Samacheer Kalvi 6th Maths Term 1 Chapter 5 Statistics Ex 5.3 Q4.1

Samacheer Kalvi 6th Maths Solutions Term 1 Chapter 5 Statistics Ex 5.3

Objective Type Questions

Question 5.
A bar graph can be drawn using
(a) Horizontal bars only
(b) Vertical bars only
(c) Both horizontal bars and Vertical bars
(d) Either horizontal bars or vertical bars
Solution:
(d) Either horizontal bars or vertical bars

Question 6.
The spaces between any two bars in a bar graph _____
(a) can be different
(b) are the same
(c) are not the same
(d) all of these
Solution:
(b) are the same

Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 1 Numbers Ex 1.3

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.
Samacheer Kalvi 6th Maths Solutions Term 2 Chapter Chapter 1 Numbers Ex 1.3

Tamilnadu Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 1 Numbers Ex 1.3

Miscellaneous Practice Problems

Question 1.
Every even number greater than 2 can be expressed as the sum of two prime numbers. Verify this statement for every even number up to 16.
Solution:
Even numbers greater then 2 upto 16 are 4, 6, 8, 10, 12, 14 and 16
4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7 (or) 5 + 5
12 = 5 + 7
14 = 7 + 7 (or) 3 + 11
16 = 5 + 11 (or) 3 + 13

Question 2.
Is 173 a prime? Why?
Solution:
yes, because it has two factors.

Question 3.
For which of the numbers, from n = 2 to 8, is 2n – 1 a prime?
Solution:
Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 1 Numbers Ex 1.3 Q3
For n = 2, 3, 4, 6 and 7 it is prime.

Question 4.
Explain your answer with the reason for the following statements.
(i) A number is divisible by 9, if it is divisible by 3.
(ii) A number is divisible by 6, if it is divisible by 12.
Solution:
(i) False 42 is divisible by 3 but it is not divisible by 9
(ii) True 36 is divisible by 12. Also divisible by 6.

Samacheer Kalvi 6th Maths Solutions Term 2 Chapter Chapter 1 Numbers Ex 1.3

Question 5.
Find A as required
(i) The greatest 2 digit number 9A is divisible by 2.
(ii) The least number 567A is divisible by 3.
(iii) The greatest 3 digit number 9A6 is divisible by 6.
(iv) The number A08 is divisible by 4 and 9.
(v) The number 225A85 is divisible by 11.
Solution:
(i) A number is divisible by 2 if it is an even number.
Greatest 2 digit even number is 98.
∴ A = 8

(ii) A number is divisible by 3 if the sum of its digits is divisible by 3
Sum of digits of 567A = 5 + 6 + 7+ A = 18 + A
∴ 18 is divisible by 3
∴ A maybe 0
The number will be 5670

(iii) A number is divisible by 6 if it is divisible by both 2 and 3
9A6 is even and so divisible by 2
If A = 9 then the sum of digits will be = 24 which is divisible by 3.
The number will be 996 and A = 9

(iv) 08 is divisible by 4, so A08 is divisible by 4.
If A = 1 then the sum of digits will be 9 which is divisible by 9.
The number will be 108 and A = 1

(v) 5 + A + 2 – (8 + 5 + 2) = 7 + A – 15 = -8 + A
∴ A = 8

Question 6.
Numbers divisible by 4 and 6 are divisible by 24. Verify this statement and support your answer with an example.
Solution:
False 12 is divisible by both 4 and 6. But not divisible by 24

Question 7.
The sum of any two successive odd numbers ir always divisible by 4. Justify this statement with an example.
Solution:
True.
The sum of any two consecutive odd numbers is divisible by 4
For example 11 + 13 = 24, divisible by 4
Also, all the consecutive odd numbers are of the form 4n + 1 or 4n + 3
Their sum = 4x + 4 which is divisible by 4.

Question 8.
Find the length of the longest rope that can be used to measure exactly the ropes of length lm 20 cm, 3m 60 cm and 4 m.
Solution:
Length of ropes are 4 m, 3 m 60 cm and lm 20 cm = 400 cm, 360 cm, 120 cm
Finding HCF (400, 360, 120)
10, 9 and 3 has no common divisor
HCF (400, 360, 120) = 2 × 2 × 2 × 5 = 40
The length of the rope will be 40 cm
Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 1 Numbers Ex 1.3 Q8

Samacheer Kalvi 6th Maths Solutions Term 2 Chapter Chapter 1 Numbers Ex 1.3

Challenge Problems

Question 9.
The sum of three prime numbers is 80. The difference of two of them is 4. Find the numbers.
Solution:
Three prime numbers 2, 37, 41
Sum 2 + 37+ 41 = 80
The difference between two of them 41 – 37 = 4

Question 10.
Find the sum of all the prime numbers between 10 and 20 and check whether that sum is divisible by all the single-digit numbers.
Solution:
Prime numbers between 10 and 20 are 11, 13, 17 and 19
Sum = 11 + 13 + 17 + 19 = 60
60 is divisible by 1, 2, 3, 4, 5 and 6.

Question 11.
Find the smallest number which is exactly divisible by all the numbers from 1 to 9.
Solution:
To find the smallest number we have to Find the LCM (1, 2, 3, 4, 5, 6, 7, 8, 9)
LCM is 2 × 3 × 2 × 5 × 7 × 2 × 3 = 2520
The required number is 2520
Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 1 Numbers Ex 1.3 Q11

Question 12.
The product of any three consecutive number is always divisible by 6. Justify this statement with an example.
Solution:
2 × 3 × 4 = 24 is divisible by 6.

Question 13.
Malarvizhi, Karthiga and Anjali are friends and natives of the same village. They work in different places. Malarvizhi comes to her home once in 5 days. Similarly, Karthiga and Anjali come to their homes once in 6 days and 10 days respectively. Assuming that they met each other on the 1st of October, when will all the three again?
Solution:
Find the LCM (5, 6, 10)
LCM (15, 25, 30) = 5 × 6 = 30
They meet again after 30 days
∴ They met on 1st October
They will meet again on 31st October
Samacheer Kalvi 6th Maths Solutions Term 2 Chapter 1 Numbers Ex 1.3 Q13

Question 14.
In an apartment consisting of 108 floors, two lifts A & B starting from the ground floor, stop at every 3rd and 5 th floors respectively. On which floors, will both of them stop together?
Solution:
LCM of 3 and 5 = 3 × 5 = 15
The lifts stop together at floors 15, 30, 45, 60, 75, 90 and 105.

Samacheer Kalvi 6th Maths Solutions Term 2 Chapter Chapter 1 Numbers Ex 1.3

Question 15.
The product of 2 two-digit numbers is 300 and their HCF is 5. What are the numbers?
Solution:
Given that HCF of 2 numbers is 5
The numbers may like 5x and 5y
Also given their product = 300
5x × 5y = 300
⇒ 25xy = 300
⇒ \(x y=\frac{300}{25}\)
⇒ xy = 12
The possible values of x andy be (1, 12) (2, 6) (3, 4)
The numbers will be (5x, 5y)
⇒ (5 × 1, 5 × 12) = (5, 60)
⇒ (5 × 2, 5 × 6) = (10, 30)
⇒ (5 × 3, 5 × 4) = (15, 20)
(5, 60) is impossible because the given the numbers are two digit numbers.
The remaining numbers are (10, 30) and (15, 20)
But given that HCF is 5
(10, 30) is impossible, because its HCF = 10
The numbers are 15, 20

Question 16.
Find whether the number 564872 is divisible by 88?
Solution:
564872 Divisibility by 8
564872 It is divisible by 8
Divisibility by 11
5 + 4 + 7 = 16
6 + 8 + 2 = 16
16 – 16 = 0
It is divisible by both 8 and 11 and hence divisible by 88.

Question 17.
Wilson, Mathan and Guna can complete one round of a circular track in 10, 15 and 20 minutes respectively. If they start together at 7 a.m from the starting point, at what time will they meet together again at the starting point?
Solution:
LCM (10, 15, 20) = 60
∴ They will meet at 8 a.m