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Haryana State Board HBSE 6th Class Maths Solutions Chapter 6 Integers Ex 6.3 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 6 Integers Exercise 6.3

Question 1.
Subtract:
(a) 35 – (20)
(b) 72 – (90)
(c) (-15) – (-18)
(d) (-20)-(13)
(e) 23 – (-12)
(f) (-32) – (-40)
Solution:
(a) 35 – (20) = 15.
(b) 72-(90) = -18.
(c) (-15) – (-18) = (-15) + 18 = 3.
(d) (-20) – 13 = -33.
(e) 23-(-12) = 23 + 12 = 35.
(f) (-32) – (-40) = (-32) + 40 = 8.

Question 2.
Fill in the blanks with >, < or = sign :
(a) (-3) + (-6) ……………. (-3) – (-6)
(b) (-21) – (-10) ……………. (-31) + (-11)
(c) 45-(-11) ……………. 57 +(-4)
(d.) (-25) -(-42) ……………. (-42) – (-25).
Solution:
(a) (-3) + (-6) = -9
and (-3)-(-6) = (-3) + 6 = 3
∵ (-9) < 3
∴ (-3) + (-6) < (-3) – (-6)

(b) (-21) – (-10) = -21 + 10 = -11
and (-31) + (-11) = – 42
∵ (-11) > (-42)
∴ (-21) – (-10) > (-31) + (-11)

(c) 45 – (-11) = 45+ 11 = 56
and 57 + (-4) = 53
56 > 53
∴ 45 – (-11) > 57 + (-4)

(d) (-25) – (-42) = (-25) + 42 = 17
and (-42) – (-25) = -42 + 25 = -17,
∵ 17 > -17
∴ (-25) – (-42) > (-42) – (-25).

Question 3.
Fill in the blanks :
(a) (-8) + = 0
(b) 13 + = 0
(c) 12 +(-12) =
(d) (-4) + =-12
(e) – 15 = – 10.
Solution:
(a) (-8) + 8 = 0
(b) 13 + (-13) = 0
(c) 12 + (-12) = 0
(d) (-4) + (-8) = -12
(e) 5 + (-15) = -10.

Question 4.
Find the value of:
(a) (-7)-8-(-25)
(b) (-13) + 32-8-1
(c) (-7) + (-8) + (-90)
(d) 50 – (-40) – (-2).
Solution:
(a) (-7) – 8 – (-25) = -7-8 + 25 = -15 + 25 = 10
(b) (-13) + 32 – 8 – 1 = 32 – 13 – 8 – 1
= 32 – 22 = 10
(c) (-7) + (-8) + (-90) = -7 – 8 – 90 = -105
(d) 50 – (-40) – (-2) = 50 + 40 + 2 = 92.

Haryana State Board HBSE 6th Class Maths Solutions Chapter 6 Integers Ex 6.2 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 6 Integers Exercise 6.2

Question 1.
Using the number line, write the integer which is :
(a) 3 more than 5
(b) 5 more than -5
(c) 6 less than 2
(d) 3 less than -2.
Solution:
(a) We want to find the integer which is 3 more than 5. So we start from 5 and proce 3 steps to the right of 5 to reach 8 as shown below. (Fig.)
∴ 3 more than 5 is 8.

(b) We want to find an integer which is 5 more than -5. So we start from -5 and proi 5 steps to the right of-5 to reach 0 as shown below (Fig.).

∴ 5 more than -5 is 0.

(c) We want to find an integer which is 6 less than 2. So we start from 2 and move 6 steps to the left of 2 to reach -4 as shown in Fig. , ∴ 6 less than 2 is -4.

(d) We want to find an integer is 3 less than -2. So we start from -2 and move 3 steps to the left to reach-5 as shown in Fig. 6.13.
∴ 3 less than -2 is -5.

Question 2.
Use a number line and add the following integers :
(a) 9 + (-6)
(b) 5 + (-11)
(c) (-1) + (-7)
(d) (-5) + 10
(e) (-1) + (-2) + (-3)
(f) (-2) + 8 + (-4).
Solution:
(a) 9 + (—6) = 3

(b) 5 + (-11) = -6

(c) (-1) + (-7) = -8

(d) (-5) + 10 = 5

(e) (-1) + (-2) + (-3) = -6

(f) (-2) + 8 + (-4). or 8 + (-2) + (-4) = 8 + (-6) = 2

Question 3.
Add without using a number line:
(a) 11 + (-7)
(b) (-13) + 18
(c) (-10) + (+19)
(d) (-250) + (+150)
(e) (-380) + (-270)
(f) (-217) + (-100).
Solution:
(a) 11 + (-7) = 4
(b) (-13) + 18 = 5
(c) (-10) + (+19) = 9
(d) (-250) + (+150) = -100
(e) (-380) + (-270) = -650
(f) (-217) + (-100) = -317.

Question 4.
Find the sum of:
(a) 137 and -354
(b) -52 and 52
(c) -312 , 39 and 192
(d) -50, -200 and 300.
Solution:
(a) 137 + (-354) = -217
(b) (-52) + (52) = 0,
(c) (-312) + 39 + 192 = (-312) + 231 = -81,
(d) (-50) + (-200) + 300 = (-250) + 300 = 50.

Question 5.
Find the value of:
(а) (-7) + (-9) + 4 + 16
(b) (37) + (-2) + (-65) + (-8).
Solution:
(a) (-7) + (-9) + 4 + 16 = (-16) + 20 = 4.
(b) (37) + (-2) + (-65) + (-8) =
37 + (-2 – 65 – 8) = 37 + (-75) = -38.
Note : Additive Inverse : Numbers such as 3 and -3, 2 and -2, added to each other give the sum zero. They are called additive inverse of each other.

Haryana State Board HBSE 6th Class Maths Solutions Chapter 6 Integers Ex 6.1 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 6 Integers Exercise 6.1

Question 1.
Write opposites of the following :
(a) Increase in weight
(b) 30 km north
(c) 326 BC
(d) Loss of Rs. 700
(e) 100 m above sea level.
Solution:
(a) Decrease in weight,
(b) 30 km south,
(c) 326 AD,
(d) Gain of Rs. 700,
(e) 100 m below sea level.

Question 2.
Represent the following numbers as integers with appropriate signs :
(a) An aeroplane is flying at a height of two thousand metres above the ground.
(b) A sub-marine is moving at a depth of eight hundred, metres below the sea level.
(c) A deposit of Rs. two hundred.
(d) Withdrawal of Rs. seven hundred.
Solution:
(a) +2000,
(b) -800,
(c) +200,
(d) -700.

Question 3.
Represent the following numbers on a number line :
(a) +5 (b) -10 (c) +8 (d) -1 (e) -6.
Solution:

Question 4.
Adjacent is a vertical line, representing integers. Observe it and locate the following points :
(a) If point D is +8, then which point, is -8 ?
(b) Is point. G a negative integer or a positive integer ?
(c) Which is the point, opposite to H ?
(d) Write integers for points B and E.
(e) Which point, marked on this number line has the least, value, if) Arrange all the points in decreasing order of value.
Solution:
(a) F,
(b) negative integer,
(c) A,
(d) +4, -10,
(e) E,
(f) D, C, B, A, O, H, G, F, E.

Question 5.
Following is the list of temperatures of five places in India, on a particular day of the year.

(a) Write the temperatures of these places in the form of integers in the blank column.
(b) Following is the number line representing the temperature in degree Celsius.

Plot the name of the city against its temperature.
(c) Which is the coolest place ?
(d) Write the names of the places whose temperatures are above 10°C.
Solution:
(a) -10°C, -2°C, +30°C, + 20°C, -5°C
(b)

(c) Siachin is the coolest place.
(d) Delhi and Ahmedabad.

Question 6.
In each of the following pairs, which number is to the right of the other on the number line ?
(a) 2, 9,
(b) -3, -8,
(c) 0, -1,
(d) -11, 10,
(e) -6, 6,
(f) 1, -100.
Solution:
(a) 9, (b) -3, (c) 0, (d) 10, (e) 6, (f) 1.

Question 7.
Write all the integers between the given pairs (write them in the increasing order).
(a) 0 and -7
(b) -4 and 4-
(c) -S and -15
(d) -30 and -23.
Solution:
(a) -6,-5,-4,-3,-2,-1.
(b) -3, -2, -1, 0, 1, 2, 3.
(c) -14, -13, -12, -11, -10, -9.
(d) -29, -28, -27, -26, -25, -24.

Question 8.
(a) Write four negative integers greater than -20.
(b) Write four negative integers less than -10.
Solution:
(a) -19, -18, -17, -16, (b) —11, -12, -13, -14.

Question 9.
For the following statements, write true (T) or false (F). If the statement is false, correct the statement.
(a) -8 is to the right of-10 on a number line.
(b) -100 is to the right of -50 on a number line.
(c) Smallest negative number is -1.
(d) -26 is larger than -25.
Solution:
(a) T,
(b) F, -100 is to the left of -50 on the number line,
(c) F, there is no smallest negative number,
(d) F, -26 is smaller than -25.

Question 10.
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 w,e 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 dine, in which direction should we move to reach -1 ?

Solution:
(a) 2,
(b) -4,
(c) left,
(d) right.

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes InText Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes InText Questions

Try These (Page 110)

Question 1.
Take post card. Use divider to measure its two adjacent sides.
Solution:
Open the divider. Place the end point of one of its arms at A and the second end point at B.
Without disturbing the opening, lift the divider and place it pn the ruler. Ensure that one end point is at the zero mark of the ruler. Now read the mark against the other end point. Similarly, measure its breadth BC.

Question 2.
Select any three objects having a flat top. Measure all the sides of the top using a divider and a ruler.
Solution:
(i) Open the divider. Place the end point of one of its arms at A and the second end point at B. Without disturbing the opening, lift the divider and place it on the ruler. Ensure that one end point is at the zero mark of the ruler. Now read the mark against the other end point. Similarly measure its breadth BC.
(ii) We can measure length and breadth of a playing card in the same way as above.
(iii) Similarly, we can measure the three sides of a triangular sheet ABC.

Try These (Page 114)

Question 1.
What is the angle name for half a revolution ? ‘
Solution:
The name of the angle for half a revolution is straight angle.

Question 2.
What is the angle name for one fourth revolution ?
Solution:
The name of the angle for one fourth revolution is right angle.

Question 3.
Draw 5 other situations of one fourth, half and three fourth revolution on a clock.
Solution:

Note : There is no special name for three fourth of a revolution.

Try These (Page 116-117)

Question 1.
The clock moves from 12 to 5. Is the revolution of the hour- hand more than 1 right angle ? [Fig.]
Solution:
Yes, the revolution of the hour-hand is more than 1 right angle.

Question 2.
What does the angle look like ? The clock moves 5 to 9. Is the angle moved by hour-hand more than 1 right angle ? [Fig.]
Solution:
The angle looks like obtuse angle.
Yes, the angle moved by hour hand is more than 1 right angle.

Question 3.
Draw the following and check the angle with your RA tester.
(a) going from 12 to 2, (b) from 6 to 7, (c) from 4 to 8, (d) from 2 to 5.
Solution:

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Ex 5.4 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.4

Question 1.
What is the measure of (i) a right angle, (ii) a straight angle ?
Solution:
(i) The measure of a right angle is 90°.
(ii) The measure of a straight angle is 180°.

Question 2.
Say True or False :
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle < 90°.
(c) The measure of a reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m ∠A = 530 and m ∠B 35°, then m∠A > m ∠B.
Solution:
(a) True,
(b) False,
(c) True,
(d) True,
(e) True.

Question 3.
Write down the measures of:
(a) some acute angles.
(b) some obtuse angles.
(Give two examples of each).
Solution:
(a) 30° and 60° are acute angles.
(b) 110° and 120° are obtuse angles.

Question 4.
Measure the angles given below, using the Protractor and write down the measure.

Solution:
(a) 45°,
(b) 125°,
(c) 90°,
(d) ∠1 = 40°, ∠2 = 125°, ∠3 = 95°.

Question 5.
Which angle has a large measure ?

First estimate and then measure. Measure of Angle A =
Measure of Angle B =
Solution:
Measure of ∠A = 40° and measure of ∠B = 65°
∴ ∠B > ∠A.

Question 6.
From these two angles, which has a larger measure ? Estimate and then confirm by measuring them.

Solution:
∠A = 45° and ∠B = 60°
∴ ∠B > ∠A.

Question 7.
Fill in the blanks with acute, obtuse, right or straight :
(a) An angle whose measure is less than that of a right angle is ………………
(b) An angle whose measure is greater than that of a right angle is ………………
(c) An angle whose measure is the sum of the measures of two right angles is ………………
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is ………………
(e) When the sum of the measures of two angles is that of a straight angle, one of them should be ……………… or ………………
Solution:
(a) acute,
(b) obtuse,
(c) straight,
(d) acute,
(e) acute, obtuse.

Question 8.
Find the measure of the angle shown in each figure. (First estimate with your eye and then find the actual measure with a protractor).

Solution:
(a) 40°, (b) 65°, (c) 130°, (d) 135°.

Question 9.
Find the angle measure between the hands of the clock in each figure :

Solution:
(a) 90°, (b) 30°, (d) 180°.

Question 10.
Investigate : In the given figures, protractor shows 30° Look at the same figure through a magnifying glass. Does the angle becomes larger ? Does the size of the angle change ?

Solution:
No, No.

Question 11.
Measure and classify each angle.

Solution:

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Ex 5.5 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.5

Question 1.
Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter U.
(d) The letter C.
Solution:
(a) The adjacent edges of a table and
(c) The line segments forming the letter ‘L’.

Question 2.
Let \(\overline{\mathrm{PQ}}\) be the perpendicular to the line segment \(\overline{\mathrm{XY}}\). Let \(\overline{\mathrm{PQ}}\) and \(\overline{\mathrm{XY}}\) intersect in the point A.
(a) How is the point A placed in \(\overline{\mathrm{XY}}\) ?
(b) What is the mea¬sure of ∠PAY ?

Solution:
(a) Point A lies between X and Y.
(b) Measure of ∠PAY = 90°.

Question 3.
There are two “set squares” in your box.
What are the measures of the angles that are formed at their corners ? Do they have any angle measure that is common?
Solution:

(i) 90°, 60° and 30°,
(ii) 90°, 45° and 45°, common angle = 90°.

Question 4.
Study the diagram. The line T is perpendicular to line im\
(a) Is CE = EG ?
(b) Does PE bisect CG ?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true ?
(i) AC > FG, (ii) CD = GH, (Hi) BC < EH.

Solution:
(a) Yes, CE = EG. .
(b) Yes, PE bisects CG.
(c) PE is the perpendicular bisector of DF and BH.
(d) (i) T, (ii) T, (Hi) T.

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Ex 5.6 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.6

Question 1.
Name the types of following triangles :
(a) Triangle with lengths of sides 7 cm, 8 cm and. 9 cm.
(b) ΔABC with AB = 8.7 cm, AC = 7 cm arid BC = 6 cm.
(c) ΔPQR such that PQ = QR = PR = 5 cm.
(d) ΔDEF with m ∠D = 90°.
(e) ΔXYZ with m∠Y = 90° and XY = YZ.
(f) ΔLMN with m ∠L = 30°, m ∠M = 70° and m ∠N = 80°.
Solution:
(a) Scalene triangle.
(b) Scalene triangle.
(c) Equilateral triangle.
(d) Right-angled triangle.
(e) Isosceles right-angled triangle.
(f) Acute-angled triangle.

Question 2.
Match :

Solution:
(i) → (e),
(ii) →(g),
(iii) → (a),
(iv) → (f),
(v) → (d),
(vi) → (c),
(vii) → (b).

Question 3.
Name each of the following triangles in two different ways : (You may judge the nature of the angle by observation).


Solution:
(a) Isosceles, Acute-angled.
(b) Scalene, Right-angled.
(c) Isosceles, Obtuse-angled.
(d) Isosceles, Right-angled.
(e) Equilateral, Acute-angled.
(f) Scalene, Obtuse-angled.

Question 4.
Try to construct triangles using matchsticks. Some are shown here. Can you make a triangle with

(a) 3 matchsticks ?
(b) 4 matchsticks ?
(c) 5 matchsticks ?
(d) 6 matchsticks ?
(Remember, you have to use all the available matchsticks in each case)
Name the type of triangle in each case.
Solution:
(a) Yes, we can make an equilateral triangle with 3 matchsticks. [Fig. (i)]
(b) No, we cannot make a triangle with 4 matchsticks.
(c) Yes, we can make an isosceles triangle with 5 matchsticks. [Fig. (ii)]
(d) Yes, we can make an equilateral triangle with 6 matchsticks. [Fig. (iii)]

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Ex 5.7 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.7

Question 1.
Say True or False :
(a) Eachangleofarectangleisarightangle.
(b) The opposite sides of a rectangle are equal in length.
(c) The diagonals of a square are perpendicular to one another.
(d) All the sides of a rhombus are of equal length.
(e) All the sides of a parallelogram are of equal length.
(f) The opposite sides of a trapezium are parallel.
Solution:
(a) True,
(b) True,
(c) True,
(d) True,
(e) False,
(f) False.

Question 2.
Give reasons for the following :
(а) A square can be thought of as a special rectangle.
(b) A rectangle can be thought of as a special parallelogram.
(c) A square can be thought of as a special rhombus.
(d) Squares, rectangles, parallelograms are all quadrilaterals.
(e) Square is also a parallelogram.
Solution:
(a) All the properties of a rectangle are there in a square.
(b) All the properties of a || gm are there in a rectangle.
(c) All the properties of a rhombus are there in a square.
(d) All are four-sided closed plane figures.
(e) All the properties of a || gm are there in a square.

Question 3.
A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral ?
Solution:
A square is a regular quadrilateral.

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Ex 5.8 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.8

Question 1.
Examine whether the following are polygons. If any one among them is not, say why.

Solution:
(a) Not a polygon, since it is not closed.
(a) Yes, it is a polygon.
(b) Not a polygon, since it is not closed by line segments.
(c) Not a polygon, since it is not closed by line segments.

Question 2.
Name each polygon:

Solution:
(a) Quadrilateral,
(b) Triangle,
(c) Pentagon,
(d) Hexagon,
(e) Octagon,
(f) Decagon.

Question 3.
Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle.
Identify the type of the triangle you have drawn.

Solution:
Equilateral triangle BDF.

Question 4.
Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.
Solution:
Quadrilateral CDGH is the required rectangle.

Question 5.
A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.
Solution:
\(\overline{\mathrm{AC}}, \overline{\mathrm{AD}}, \overline{\mathrm{BD}}, \overline{\mathrm{BE}}\) and \(\overline{\mathrm{CE}}\) are the required five diagonals of pentagon ABCDE.

Haryana State Board HBSE 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Ex 5.9 Textbook Exercise Questions and Answers.

Haryana Board 6th Class Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 5.9

Question 1.
Match the following :


Solution:
(a) (ii),
(b) (iv),
(c) (v),
(d) (iii),
(e) (i).

Question 2.
What shape is :
(a) Your instruments box ?
(b) A brick ?
(c) A matchbox ?
(d) A road-roller ?
(e) A sweet laddu ?
Solution:
(a) Cuboid,
(b) Cuboid,
(c) Cuboid,
(d) Cylinder,
(e) Sphere.