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These NCERT Solutions for Class 7 Maths Chapter 14 Symmetry Ex 14.3 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 14 Symmetry

Exercise 14.3

Question 1.
Name any two figures that have both line symmetry and rotational symmetry.
Answer:

Question 2.
Draw, wherever possible, a rough sketch of
(i) a triangle with both line and rotational symmetries of order more than 1.
(ii) a triangle with only line symmetry and no rotational symmetry of order more than 1.
(iii) a quadrilateral with a rotational symmetry of order more than 1 but not a line symmetry.
(iv) a quadrilateral with line symmetry but not a rotational symmetry of order more than 1.
Answer:
(i) An equilateral triangle has three lines of symmetry and rotational symmetry of order 3.

(ii) An isosceles triangle has only one line ofD symmetry but no rotational symmetry of order more than 1.
(iii) A parallelogram has no line of symmetry but I has a rotational symmetry of order 2. A
(iv) An isosceles trapezium has one line of symmetry but no rotational symmetry ofordermore than 1.

Question 3.
If a figure has two or more lines of symmetry, should it have rotational symmetry of order more than 1.
Answer:
Yes

Question 4.
Fill in the blanks:
Answer:

Question 5.
Name the quadrilaterals which have both line and rotational symmetry of order more than 1.
Answer:
The square, rectangle and a rhombus are the quadrilaterals having both line and rotational symmetry.

Question 6.
After rotating by 60° about a centre, a figure looks exactly the same as its original position.
At what other angles will this happen for the figure.
Answer:
The figure will look exactly the same as its original position at 120°, 180°, 240°, 300° and 360°.

Question 7.
Can we have a rotational symmetry of order more than 1 whose angle of rotation is (i) 45° (ii) 17°
Answer:
(i) 45° – yes
(ii) 17° – No

These NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Ex 15.3 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Exercise 15.3

Question 1:
What cross-sections do you get when you give a
(i) vertical cut
(ii) horizontal cut to the following solids?
(a) A brick
(b) A round apple
(c) A die
(d) A circular pipe
(e) An ice cream cone
Answer:

Solid	Shape of cross­section for vertical cut	Shape of cross­section for horizontal cut
(a) Brick	Rectangle	Rectangle
(b) A round apple	Circle	Circle
(c) A die	Square	Square
(d) A circular pipe	Circle	Rectangle
(e) An ice cream cone	Triangle	Circle

These NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Ex 15.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 7 Maths Chapter 15 Visualising Solid Shapes Exercise 15.2

Question 1.
Use isometric dot paper and make an isometric sketch for each one of the given shapes:

Answer:

Question 2.
The dimensions of a cuboid are 5 cm, 3 cm and 2 cm. Draw three different isometric sketches of this cuboid.
Answer:

Question 3.
Three cubes each with 2 cm edge are placed side by side to form a cuboid. Sketch an oblique
Answer:

Question 4.
Make an oblique sketch for each one of the given isometric shapes :

Answer:

Question 5.
Give (i) an oblique sketch and (ii) an isometric sketch for each of the following :
(a) A cuboid of dimensions 5 cm, 3 cm and 2 cm. (Is your sketch unique?)
(b) A cube with an edge 4 cm long.
An isometric sheet is attached at the end of the book. You could try to make on it some cubes or cuboids of dimensions specified by your friend.
Answer:
Sketch is not unique. There can be more shapes in different positions.

These NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.3 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.3

Question 1.
Write the fractions. Are all these fractions equivalent?

Answer:
(a) We can find fraction in each figure by the formula
\(\frac{\text { Dark part }}{\text { Total part }}\)
\(=\frac{1}{2}, \frac{2}{4}=\frac{1}{2}, \frac{3}{6}=\frac{1}{2}, \frac{4}{8}=\frac{1}{2}\)
These all fractions are equivalent.

(b) We can find fraction in each figure by the formula Dark part Total part
\(\frac{\text { Dark part }}{\text { Total part }}\)
\(=\frac{4}{12}=\frac{1}{3}, \frac{3}{9}=\frac{1}{3}, \frac{2}{6}=\frac{1}{3}, \frac{6}{15}=\frac{2}{5}\)
These all are not equivalent fractions.

Question 2.
Write the fractions and pair up the equivalent fractions from each row.

Answer:
Equivalent fraction would be then

(a) and (ii) = \(\frac { 1 }{ 2 }\)
(b) and (iv) = \(\frac { 2 }{ 3 }\)
(c) and (i) = \(\frac { 1 }{ 3 }\)
(d) and(v)= \(\frac { 1 }{ 4 }\)
(e) and (iii) = \(\frac { 3 }{ 4 }\)

Question 3.
Replace □ in each of the following by the correct number:

Answer:

Question 4.
Find the equivalent fraction of \(\frac { 3 }{ 5 }\) having
(a) denominator 20 1
(b) numerator 9
(c) denominator 30
(d) numerator 27
Answer:
To find an equivalent fraction, we may multiply/divide both the numerator and the denominator by the same number.

(a)	To make denominator 20, we need to multiple both by 4	\(\frac { 12 }{ 20 }\)
(b)	To make numerator 9, we need to multiple both by 3	\(\frac { 9 }{ 15 }\)
(c)	To make denominator 30, we need to multiple both by 6	\(\frac { 18 }{ 30 }\)
(d)	To make numerator 27, we need to multiple both by 9	\(\frac { 27 }{ 45 }\)

Question 5.
Find the equivalent fraction of \(\frac { 36 }{ 48 }\) with
(a) numerator 9
(b) denominator 4
Answer:

(a)	To make numerator 9, we need to divide both by 4	\(\frac { 9 }{ 12 }\)
(b)	To make denominator 4, we need to divide both by 12	\(\frac { 3 }{ 4 }\)

(a) Hence, the equivalent fraction is \(\frac { 9 }{ 12 }\)
(b) Hence, the equivalent fraction is \(\frac { 3 }{ 4 }\)

Question 6.
Check whether the given fractions are equivalent:
(a) \(\frac{5}{9}, \frac{30}{54}\)
(b) \(\frac{3}{10}, \frac{12}{50}\)
(c) \(\frac{7}{13}, \frac{5}{11}\)
Answer:
(a) \(\frac{5}{9}, \frac{30}{54}\)
We have 5 x 54 = 270
and 9 x 30 = 270
Here 5 x 54 = 9 x 30
\(\frac{5}{9}\) and \(\frac{30}{54}\) are equivalent fractions.

(b) \(\frac{3}{10}, \frac{12}{50}\)
We have 3 x 50 = 150
and 10 x 12 = 120
Here 3 x 50 ≠ 10 x 12
\(\frac{3}{10}\) and \(\frac{12}{50}\) are not equivalent fractions.

(c) \(\frac{7}{13}, \frac{5}{11}\)
We have 7 x 11 = 77 and 5 x 13 = 65
Here 7 x 11 ≠ 5 x 13
\(\frac{7}{13}\) anCl \(\frac{5}{11}\) ecluivalent fractions.

Question 7.
Reduce the following fractions to simplest form:
(a) \(\frac { 48 }{ 60 }\)
(b) \(\frac { 150 }{ 60 }\)
(c) \(\frac { 84 }{ 98 }\)
(d) \(\frac { 12 }{ 52 }\)
(e) \(\frac { 7 }{ 28 }\)
Answer:
To reduce the fraction to simplest form, we need to find the HCF of numerator and denominator

(a)	HCF of 48 and 60 is 12, So dividing by 12 on both numerator and denominator	\(\frac { 4 }{ 5 }\)
(b)	HCF of 150 and 60 is 12, So dividing by 30 on both numerator and denominator	\(\frac { 5 }{ 2 }\)
(c)	HCF of 84 and 98 is 14, So dividing by 14 on both numerator and denominator	\(\frac { 6 }{ 7 }\)
(d)	HCF of 12 and 52 is 4, So dividing by 4 on both numerator and denominator	\(\frac { 3 }{ 13 }\)
(e)	HCF of 7 and 28 is 7, So dividing by 7 on both numerator and denominator	\(\frac { 1 }{ 4 }\)

Question 8.
Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?
Answer:
Fraction of pencils used by Ramesh
\(=\frac{\text { Used pencil }}{\text { Total pencil }}=\frac{10}{20}=\frac{1}{2}\)
Fraction of pencils used by Sheelu
\(=\frac{\text { Used pencil }}{\text { Total pencil }}=\frac{25}{50}=\frac{1}{2}\)
Fractions of pencils used by Jamaal
\(=\frac{\text { Used pencil }}{\text { Total pencil }}=\frac{40}{80}=\frac{1}{2}\)
Yes, they have all used up an equal fraction of his/her pencils i.e. \(\frac{1}{2}\)

Question 9.
Match the equivalent fractions and write two more for each.

(i)	\(\frac { 250 }{ 440 }\)	(a) \(\frac { 2 }{ 3 }\)
(ii)	\(\frac { 180 }{ 200 }\)	(b) \(\frac { 2 }{ 5 }\)

(iii)	\(\frac { 660 }{ 990 }\)	(c) \(\frac { 1 }{ 2 }\)
(iv)	\(\frac { 180 }{ 360 }\)	(d) \(\frac { 5 }{ 8 }\)
(v)	\(\frac { 220 }{ 550 }\)	(e) \(\frac { 9 }{ 10 }\)

Answer:

(i)	\(\frac { 250 }{ 440 }\)(Dividing both numerator and denominator by 50)	(d) \(\frac { 5 }{ 8 }\)
(ii)	\(\frac { 180 }{ 200 }\) (Dividing both numerator and denominator by 20)	(e) \(\frac { 9 }{ 10 }\)

(iii)	\(\frac { 660 }{ 990 }\) (Dividing both numerator and denominator by 330)	(a) \(\frac { 2 }{ 3 }\)
(iv)	\(\frac { 180 }{ 360 }\) (Dividing both numerator and denominator by 180)	(c) \(\frac { 1 }{ 2 }\)
(v)	\(\frac { 220 }{ 550 }\) (Dividing both numerator and denominator by 110)	(b) \(\frac { 2 }{ 5 }\)

 

These NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.2

Question 1.
Draw number lines and locate the points on them:
(a) \(\frac{1}{2}, \frac{1}{4}, \frac{3}{4}, \frac{4}{4}\)
(b) \(\frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \frac{7}{8}\)
(c) \(\frac{2}{5}, \frac{3}{5}, \frac{8}{5}, \frac{4}{5}\)
Answer:
(a) These fraction lies between 0 and 1 in the number line. We can divide the distance between 0 and 1 on the number into four equal parts, then each point will represent these fractions.

(b) These fraction lies between 0 and 1 in the number line. We can divide the distance between 0 and 1 on the number into 8 equal parts, then each point will represent these fractions.

(c) These fraction lies between 0 and 1 in the number line. We can divide the distance between 0 and 1 on the number into 5 equal parts, then each point will represent these fractions.

Question 2.
Express the following as mixed fractions:
(a) \(\frac{20}{3}\)
(b) \(\frac{11}{5}\)
(c) \(\frac{17}{7}\)
(d) \(\frac{28}{5}\)
(e) \(\frac{19}{6}\)
(f) \(\frac{35}{9}\)
Answer:
A mixed fraction is whole and part a combination of
To convert an improper fraction to a
mixed fraction, follow these steps:
1. Divide the numerator by the denominator.
2. Write down the whole number answer.
3. Then write down any remainder above the denominator.

Question 3.
Express the following as improper fractions:
(a) 7\(\frac{3}{4}\)
(b) 5\(\frac{6}{7}\)
(c) 2\(\frac{5}{6}\)
(d) 10\(\frac{3}{5}\)
(e) 9\(\frac{3}{7}\)
(f) 8\(\frac{4}{9}\)
Answer:
We can express a mixed fraction as improper fraction in this way

These NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths 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 and 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°.
Answer:
(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 the following:
Measure of Triangle Types of Triangle
(i) 3 sides of equal length (a) Scalene
(ii) 2 sides of equal length right angled (b) Isosceles
(iii) All sides are of different length angled (c) Obtuse
(iv) 3 acute angles angled (d) Right
(v) 1 right angle (e) Equilateral
(vi) 1 obtuse angle angled (f) Acute
(vii) 1 right angle with two sides of equal length (g) Isosceles
Answer:
(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 angle by observation)

Answer:
(a) Acute angled triangle and Isosceles triangle
(b) Right-angled triangle and scalene triangle
(c) Obtuse-angled triangle and Isosceles triangle
(d) Right-angled triangle and Isosceles triangle
(e) Equilateral triangle and acute angled triangle
(f) Obtuse-angled triangle and scalene triangle

Question 4.
Try to construct triangles using match sticks. 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)
If you cannot make a triangle, think of reasons for it.
Answer:
(a) 3 matchsticks: This is an acute angle triangle and it is possible with 3 matchsticks to make a triangle because sum of two sides is greater than third side.
(b) 4 matchsticks: This is a square, hence with four matchsticks we cannot make triangle.

(c) 5 matchsticks: This is an acute angle triangle and it is possible to make triangle with five matchsticks, in this case sum of two sides is greater than third side.

(d) 6 matchsticks: This is an acute angle triangle and it is possible to make a triangle with the help of 6 matchsticks because sum of two sides is greater than third side.

These NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.7

Question 1.
Say true or false:
Each angle of a rectangle is a right angle.
The opposite sides of a rectangle are equal in length.
The diagonals of a square are perpendicular to one another.
All the sides of a rhombus are of equal length.
All the sides of a parallelogram are of equal length.
The opposite sides of a trapezium are parallel.
Answer:
(a) True
(b) True
(c) True
(d) True
(d) False
(f) False

Question 2.
Give reasons for the following:
(a) 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 quadrilateral.
(e) Square is also a parallelogram.
Answer:
(a) Because its all angles are right angle and opposite sides are equal.
(b) Because its opposite sides are equal and parallel.
(c) Because its four sides are equal and diagonals are perpendicular to each other.
(d) Because all of them have four sides.
(e) Because its opposite sides are equal and parallel.

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?
Answer:
A square is a regular quadrilateral because all the interior angles are of 90° and all sides are of same length.

These NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.8

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


Answer:
(a) As it is not a closed figure, therefore, it is not a polygon.
(b) It is a polygon because it is closed by line segments.
(c) It is not a polygon because it is not made by line segments.
(d) It is not a polygon because it not made only by line segments, it has curved surface also.

Question 2.
Name each polygon:

Answer:
(a) Quadrilateral
(b) Triangle
(c) A pentagon
(d) An octagon

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.
Answer:
ABCDEF is a regular hexagon and triangle thus formed by joining AEF is an isosceles triangle.

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.
Answre:
ABCDEFGEI is a regular octagon and CDGE1 is a 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.
Answer:
ABCDE is the required pentagon and its diagonals are AD, AC, BE and BD.

These NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.9 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.9

Question 1.
Match the following:

Answer:

Question 2.
What shape
(a) Your instrument box?
(b) A brick?
(c) A match box?
(d) A road-roller?
(e) A sweet laddu?
Answer:
(a) Cuboid
(b) Cuboid
(c) Cuboid
(d) Cylinder
(e) Sphere

These NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.3

Question 1.
Match the following:

(i) Straight angle	(a) Less than one-fourth of a revolution
(ii) Right angle	(b) More than half a revolution
(iii) Acute angle	(c) Half of a revolution
(iv) Obtuse angle	(d) One-fourth a revolution
(v) Reflex angle	(e) Between 1/4 and 1/2 of a revolution one complete revolution

Answer:
(I) — (c)
(ii) — (d)
(iii) — (a)
(iv) — (e)
(v) — (b)

Question 2.
Classify each one of the following angles as right, straight, acute, obtuse or reflex:


Answer:
(a) Acute angle
(b) Obtuse angle
(c) Right angle
(d) Reflex angle
(e) Straight angle
(f) Acute angle

These NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.2

Question 1.
What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3
Answer:
(a) When the hour hand goes from 3 to 9 clockwise. It will rotate by 2 right angles or 180°.
Fraction = \(\begin{equation}
\frac{180^{\circ}}{360^{\circ}}=\frac{1}{2}
\end{equation}\)

(b) When the hour hand goes from 4 to 7 clockwise. It will rotate by 1 right angle or 90°.
Fraction = \(\begin{equation}
\frac{90^{\circ}}{360^{\circ}}=\frac{1}{4}
\end{equation}\)

(c) When the hour hand goes from 7 to 10 clockwise, it will rotate by 1 right angle or 90°.
Fraction = \(\begin{equation}
\frac{90^{\circ}}{360^{\circ}}=\frac{1}{4}
\end{equation}\)

(d) When the hour hand goes from 1 to 10 clockwise. It will rotate by 3 right angles or 270°.
Fraction = \(\begin{equation}
\frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}
\end{equation}\)

(e) When the hour hand goes from 1 to 10 clockwise. It will rotate by 3 right angles or 270.
Fraction = \(\begin{equation}
\frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}
\end{equation}\)

(f) When the hour hand goes from 6 to 3 clockwise. It will rotate by 3 right angles or 270.
Fraction = \(\begin{equation}
\frac{270^{\circ}}{360^{\circ}}=\frac{3}{4}
\end{equation}\)

Question 2.
Where will the hand of a clock stop if it:
starts at 12 and make \(\frac{1}{2}\) of a revolution, clockwise?
starts at 2 and makes \(\frac{3}{4}\) of a revolution, clockwise?
starts at 5 and makes \(\frac{1}{4}\) of a revolution, clockw ise?
starts at 5 and makes \(\frac{3}{4}\) of a revolution, clockwise?
Answer:
(a) At 6
(b) At 8
(c) At 8
(d) At 2

Question 3.
Which direction will you face if you start facing:
(a) east and make \(\frac { 1 }{ 2 }\) of a revolution clockwise?
(b) east and make 1\(\frac { 1 }{ 2 }\) of a revolution clockwise?
(c) west and make \(\frac { 3 }{ 4 }\) of a revolution, anti-clockwise? 4
(d) south and make one full revolution? (Should we specify clockwise or anti-clockwise for this last question? Why not?)
Answer:

(For answer (d), it is immaterial whether we turn clockwise or anticlockwise, because one full revolution will bring us back to the original position)

Question 4.
What part of a revolution have you turned through if you stand facing
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
Answer:
(a) \(\frac { 3 }{ 4 }\)
(b) \(\frac { 3 }{ 4 }\)
(c) \(\frac { 1 }{ 2 }\)

Question 5.
Find the number of right angles turned through by the hour hand of a clock when it goes from
(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 6
Answer:
(a) One right angle

(b) Two right angles

(c) Two right angles

(d) One right angle

(e) Three right angles

(f) Two right angles

Question 6.
How many right angles do you make if you start facing
(a) south and turn clockwise to west?
(b) north and turn anti-clockwise to east?
(c) west and turn to west?
(d) south and turn to north?
Answer:
(a) One right angle

(b) Three right angles

(c) Four angles

(d) Two right angles

Question 7.
Where will the hour hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7 and turns through 2 straight angles?
Answer: