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

Exercise 5.2

1. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

(i) 3 to 9

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write the fractions for the clockwise revolution when the hour hand of the clock goes from 3 to 9. Hence, our quantity in consideration is the movement of the hour hand from 3 to 9. 

We will show the movement of the hour hand of the clock as follows,

From the above figure, we can see that the clock can be divided into two equal parts. 

This is because there are six equally spaced sections between 3 and 9. A clock has twelve equally spaced sections. So 3 to 9 is one part.  

The number of parts the hour hand of the clock moves when going from 3 to 9 is 1. This is the numerator of our fraction.

The total number of parts in the given figure is 2. This is the denominator of our fraction.

Therefore, the required fraction representing the movement of the hour hand from 3 to 9 is $\dfrac{1}{2}$.

The above movement of the clock is also said to be two right angles. This is because both the arms of the clock form a straight line. And a straight line comprises two right angles. 

(ii) 4 to 7

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write the fractions for the clockwise revolution when the hour hand of the clock goes from 4 to 7. Hence, our quantity in consideration is the movement of the hour hand from 4 to 7. 

We will show the movement of the hour hand of the clock as follows,

From the above figure, we can see that the clock can be divided into four equal parts as.

This is because there are three equally spaced sections between 4 and 7. A clock has twelve equally spaced sections. So 4 to 7 is one part.

The number of parts the hour hand of the clock moves when going from 4 to 7 is 1. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

Therefore, the required fraction representing the movement of the hour hand from 4 to 7 is $\dfrac{1}{4}$.

The above movement of the clock is also said to be one right angle. This is because both the arms of the clock are perpendicular to each other. And perpendicular lines form a right angle. 

(iii) 7 to 10

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write the fractions for the clockwise revolution when the hour hand of the clock goes from 7 to 10. Hence, our quantity in consideration is the movement of the hour hand from 7 to 10. 

We will show the movement of the hour hand of the clock as follows,

From the above figure, we can see that the clock can be divided into four equal parts.

This is because there are three equally spaced sections between 7 and 10. A clock has twelve equally spaced sections. So 7 to 10 is one part.

The number of parts the hour hand of the clock moves when going from 7 to 10 is 1. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

Therefore, the required fraction representing the movement of the hour hand from 7 to 10 is $\dfrac{1}{4}$.

The above movement of the clock is also said to be one right angle. This is because both the arms of the clock are perpendicular to each other. And perpendicular lines form a right angle. 

(iv) 12 to 9

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write the fractions for the clockwise revolution when the hour hand of the clock goes from 12 to 9. Hence, our quantity in consideration is the movement of the hour hand from 12 to 9. 

We will show the movement of the hour hand of the clock as follows,

From the above figure we can see that the clock can be divided into four equal parts.

This is because there are nine equally spaced sections between 12 and 9 (when going from 12 towards 9). A clock has twelve equally spaced sections. So 12 to 9 is three parts.

The number of parts the hour hand of the clock moves when going from 12 to 9 is 3. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

Therefore, the required fraction representing the movement of the hour hand from 12 to 9 is $\dfrac{3}{4}$.

The above movement of the clock is also said to be three right angles. This is because both the arms of the clock are perpendicular to each other. And perpendicular lines form a right angle. Since the hour hand of the clock moves 3 out of 4 parts, therefore, there are three right angles.

(v) 1 to 10

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write the fractions for the clockwise revolution when the hour hand of the clock goes from 1 to 10. Hence, our quantity in consideration is the movement of the hour hand from 1 to 10. 

We will show the movement of the hour hand of the clock as follows,

From the above figure, we can see that the clock can be divided into four equal parts.

This is because there are nine equally spaced sections between 1 and 10 (when going from 1 towards 10). A clock has twelve equally spaced sections. So 1 to 10 is three parts.

The number of parts the hour hand of the clock moves when going from 1 to 10 is 3. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

Therefore, the required fraction representing the movement of the hour hand from 1 to 10 is $\dfrac{3}{4}$.

The above movement of the clock is also said to be three right angles. This is because both the arms of the clock are perpendicular to each other. And perpendicular lines form a right angle. Since the hour hand of the clock moves 3 out of 4 parts, therefore, there are three right angles. 

(vi) 6 to 3

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write the fractions for the clockwise revolution when the hour hand of the clock goes from 6 to 3. Hence, our quantity in consideration is the movement of the hour hand from 6 to 3. 

We will show the movement of the hour hand of the clock as follows,

From the above figure, we can see that the clock can be divided into four equal parts.

This is because there are nine equally spaced sections between 6 and 3 (when going from 6 towards 3). A clock has twelve equally spaced sections. So 6 to 3 is three parts.

The number of parts the hour hand of the clock moves when going from 6 to 3 is 3. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

Therefore, the required fraction representing the movement of the hour hand from 6 to 3 is $\dfrac{3}{4}$.

The above movement of the clock is also said to be three right angles. This is because both the arms of the clock are perpendicular to each other. And perpendicular lines form a right angle. Since the hour hand of the clock moves 3 out of 4 parts, therefore, there are three right angles.

2. Where will the hand of a clock stop if it:

(a) Starts at 12 and make $\dfrac{1}{2}$of a revolution, clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write where the hour hand of the clock stops when it starts at 12 and makes clockwise $\dfrac{1}{2}$ of a revolution. Hence, our quantity in consideration is the movement of the hour hand. 

From the given fraction we can see that the clock is divided into two equal parts.

The number of parts the hour hand of the clock moves is 1. This is the numerator of our fraction.

The total number of parts in the given figure is 2. This is the denominator of our fraction.

We will show the movement of the hour hand of the clock as follows,

Since the hour hand moves $\dfrac{1}{2}$ of a revolution, it will face the number that is in front of 12. This number is 6. 

Therefore, the hour hand of the clock will stop at 6 when it begins from 12 and makes $\dfrac{1}{2}$ of a clockwise revolution.

(b) Start at 2 and make $\dfrac{1}{2}$ of a revolution, clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write where the hour hand of the clock stops when it starts at 2 and makes clockwise $\dfrac{1}{2}$ of a revolution. Hence, our quantity in consideration is the movement of the hour hand. 

From the given fraction we can see that the clock is divided into two equal parts.

The number of parts the hour hand of the clock moves is 1. This is the numerator of our fraction.

The total number of parts in the given figure is 2. This is the denominator of our fraction.

We will show the movement of the hour hand of the clock as follows,

Since the hour hand moves $\dfrac{1}{2}$ of a revolution, it will face the number that is in front of 2. This number is 8. 

Therefore, the hour hand of the clock will stop at 8 when it begins from 2 and makes $\dfrac{1}{2}$ of a clockwise revolution.

(c) Start at 5 and make $\dfrac{1}{4}$ of a revolution, clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write where the hour hand of the clock stops when it starts at 5 and makes clockwise $\dfrac{1}{4}$ of a revolution. Hence, our quantity in consideration is the movement of the hour hand. 

From the given fraction we can see that the clock is divided into four equal parts.

The number of parts the hour hand of the clock moves is 1. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

We will show the movement of the hour hand of the clock as follows,

Since the hour hand moves $\dfrac{1}{4}$ of a revolution, it will face the number that is at a right angle to 5. This number is 8. 

Therefore, the hour hand of the clock will stop at 8 when it begins from 5 and makes $\dfrac{1}{4}$ of a clockwise revolution. 

(d) Starts at 5 and makes $\dfrac{3}{4}$ of a revolution, clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write where the hour hand of the clock stops when it starts at 5 and makes clockwise $\dfrac{3}{4}$ of a revolution. Hence, our quantity in consideration is the movement of the hour hand. 

From the given fraction we can see that the clock is divided into four equal parts.

The number of parts the hour hand of the clock moves is 3. This is the numerator of our fraction.

The total number of parts in the given figure is 4. This is the denominator of our fraction.

We will show the movement of the hour hand of the clock as follows,

Since the hour hand moves $\dfrac{3}{4}$ of a revolution, it will face the number of three right angles to 5. This number is 2.

Therefore, the hour hand of the clock will stop at 2 when it begins from 5 and makes $\dfrac{3}{4}$ of a clockwise revolution. 

3. Which direction will you face if you start facing:

(a) East and make $\dfrac{1}{2}$ of a revolution clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write which direction we will face if we start from the East and make clockwise $\dfrac{1}{2}$ of a revolution. Hence, our quantity in consideration is the direction-wise movement. 

We will show our movement when we begin from East as follows, 

Since we make$\dfrac{1}{2}$ of a revolution starting from the East, so we will face the direction that is in front of the East. This direction is West. 

Therefore, we will face West when we begin from East and make $\dfrac{1}{2}$ of a clockwise revolution.

(b) East and make $1\dfrac{1}{2}$ of a revolution clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

A mixed fraction is a fraction that is formed when a whole number and a fraction are combined together.

Mixed fractions are expressed as follows,

$W\dfrac{a}{b}$

Where $W$ are any whole number and $\dfrac{a}{b}$ is any fraction. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write which direction we will face if we start from the East and make clockwise $1\dfrac{1}{2}$ of a revolution. Hence, our quantity in consideration is the direction-wise movement. 

We will show our movement when we begin from East as follows, 

Since we make $1\dfrac{1}{2}$ of a revolution starting from the East, so after one complete revolution we will face the direction East. We will then make the remaining half revolution and we will face the direction that is in front of the East. This direction is West.  

Therefore, we will face West when we begin from East and make $1\dfrac{1}{2}$ of a clockwise revolution.

(c) West and make $\dfrac{3}{4}$ of a revolution clockwise?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write which direction we will face if we start from the West and make clockwise $\dfrac{3}{4}$ of a revolution. Hence, our quantity in consideration is the direction-wise movement. 

We will show our movement when we begin from West as follows, 

Since we make $\dfrac{3}{4}$ of a revolution starting from the West, we will face the direction that is at three right angles from the West. This direction is South.  

Therefore, we will face the South when we begin from the West and make $\dfrac{3}{4}$ of a clockwise revolution.

(d) South and make one full revolution? 

(Should we specify clockwise or anti-clockwise for this last question? Whynot?

Ans: We are required to write which direction we will face if we start from the South and make one full revolution.

Since it is not specified whether we have to move clockwise or anticlockwise, we will first assume that we have to make a clockwise revolution. 

We will show our movement when we begin clockwise revolution from South as follows, 

As we make 1 complete revolution starting from the South, so we reach back South.

Let us now assume that we move anticlockwise.

We will show our movement when we begin anticlockwise revolution from South as follows, 

As we make 1 complete revolution starting from the South, so we reach back South.

Therefore, we see that it is not necessary to specify clockwise or anti-clockwise. This is because in both cases we reach the same point after one complete revolution. 

4. What part of a revolution have you turned through if you stand facing:

(a) East and turn clockwise to face North?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write what part of a revolution we have turned if we start from the East and turn clockwise to face North. Hence, our quantity in consideration is the direction-wise movement. 

We will show our movement when we begin clockwise revolution from East to reach North as follows, 

From the above figure we can see that we move three right angles to reach the desired direction. The whole system is divided into four right angles.

Therefore, we turn $\dfrac{3}{4}$ of a revolution if we stand facing East and turn to North clockwise. 

(b) South and turn clockwise to face East?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write what part of a revolution we have turned if we start from the South and turn clockwise to face East. Hence, our quantity in consideration is the direction-wise movement. 

We will show our movement when we begin clockwise revolution from South to reach East as follows, 

From the above figure we can see that we move three right angles to reach the desired direction. The whole system is divided into four right angles.

Therefore, we turn $\dfrac{3}{4}$ of a revolution if we stand facing South and turn to East clockwise.

(c) West and turn clockwise to face East?

Ans: A fraction represents the part of a whole entity. All the parts of a fraction are equal. 

The numerator of the fraction represents the quantity in consideration whereas the denominator represents the whole quantity.

We are required to write what part of a revolution we have turned if we start from the East and turn clockwise to face North. Hence, our quantity in consideration is the direction-wise movement. 

We will show our movement when we begin clockwise revolution from South as follows, 

From the above figure we can see that we move 1straight angle to reach the desired direction. The whole system is divided into two straight angles.

Therefore, we turn $\dfrac{1}{2}$ of a revolution if we stand facing West and turn to East clockwise.  

5. Find the number of right angles turned through by the hour hand of a clock when it goes from:

(a) 3 to 6

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that are turned by the hour hand of the clock when it goes from 3 to 6.

To do so, we will draw the diagram for the movement of the hour hand of the clock from 3 to 6.

From the above diagram we can see that there is one right angle formed between 3 and 6.

Therefore, the number of right angles formed when the hour hand of the clock moves from 3 to 6is one right angle.

(b) 2 to 8

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that are turned by the hour hand of the clock when it goes from 2 to 8.

To do so, we will draw the diagram for the movement of the hour hand of the clock from 2 to 8.

From the above diagram we can see that there are two right angles formed between 2 and 8.

Therefore, the number of right angles formed when the hour hand of the clock moves from 2 to 8are two right angles.

(c) 5 to 11

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that are turned by the hour hand of the clock when it goes from 5 to 11.

To do so, we will draw the diagram for the movement of the hour hand of the clock from 5 to 11.

From the above diagram we can see that there are two right angles formed between 5 and 11.

Therefore, the number of right angles formed when the hour hand of the clock moves from 5 to 11 are two right angles.

(d) 10 to 1

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that are turned by the hour hand of the clock when it goes from 10 to 1.

To do so, we will draw the diagram for the movement of the hour hand of the clock from 10 to 1.

From the above diagram we can see that there is one right angle formed between 10 and 1.

Therefore, the number of right angles formed when the hour hand of the clock moves from 10 to 1 is one right angle.

(e) 12 to 9

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that are turned by the hour hand of the clock when it goes from 12 to 9.

To do so, we will draw the diagram for the movement of the hour hand of the clock from 12 to 9.

From the above diagram we can see that there are three right angles formed between 12 and 9.

Therefore, the number of right angles formed when the hour hand of the clock moves from 12 to 9 are three right angles.

(f) 12 to 6

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that are turned by the hour hand of the clock when it goes from 12 to 6.

To do so, we will draw the diagram for the movement of the hour hand of the clock from 12 to 6.

From the above diagram we can see that there are two right angles formed between 12 and 6.

Therefore, the number of right angles formed when the hour hand of the clock moves from 12 to 6 are two right angles. 

6. How many right angles do you make if you start facing:

(a) South and turn clockwise to West?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that we make if we turn clockwise from South to West. 

To do so, we will draw the diagram for the movement of the revolution.

From the above diagram we can see that there is one right angle formed when we turn from South to West clockwise. 

Therefore, the number of right angles formed when we move from South to West in a clockwise direction is one.

(b) North and turn anti-clockwise to East?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that we make if we turn anti-clockwise from North to East. 

To do so, we will draw the diagram for the movement of the revolution.

From the above diagram we can see that there are three right angles formed when we turn from North to East anticlockwise. 

Therefore, the number of right angles formed when we move from North to East in an anticlockwise direction are three.

(c) West and turn to West?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that we make if we turn from West to West. 

To do so, we will draw the diagram for the movement of the revolution. We will consider the direction of revolution to be clockwise. 

From the above diagram we can see that there are four right angles formed when we turn from West to West clockwise. 

Therefore, the number of right angles formed when we move from West to West arefour.

(d) South and turn to North?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell the number of right angles that we make if we turn clockwise from South to North. 

To do so, we will draw the diagram for the movement of the revolution.

From the above diagram we can see that there are two right angles formed when we turn from South to North clockwise. 

Therefore, the number of right angles formed when we move from South to North in a clockwise direction are two.

7. Where will the hour hand of a clock stop if it starts:

(a) From 6 and turn through 1 right angle?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell where the hour hand of a clock will reach when it begins from 6 and turns through 1 right angle. 

To do so, we will draw the diagram for the movement of the hour hand of the clock.

From the above diagram we can see that one right angle from 6 is at 9. 

Therefore, the hour hand of the clock will stop at 9 when it begins from 6 and turns through 1 right angle.

(b) From 8 and turns through 2 right angles?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell where the hour hand of a clock will reach when it begins from 8 and turns through 2 right angles.  

To do so, we will draw the diagram for the movement of the hour hand of the clock.

From the above diagram we can see that two right angles from 8are at 2. 

Therefore, the hour hand of the clock will stop at 2 when it begins from 8 and turns through 2 right angles.

(c) From 10 and turns through 3 right angles?

Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.

Therefore, the measure of a right angle is $90^\circ $.

We are required to tell where the hour hand of a clock will reach when it begins from 10 and turns through 3 right angles.  

To do so, we will draw the diagram for the movement of the hour hand of the clock.

From the above diagram we can see that three right angles from 10are at 7. 

Therefore, the hour hand of the clock will stop at 7 when it begins from 10 and turns through 3 right angles.

(d) From 7 and turns through 2 straight angles?

Ans: A straight angle is that angle that is formed over a straight line. We know that the measure of an angle over a straight line is $180^\circ $.

Therefore, the measure of a straight angle is $180^\circ $.

We are required to tell where the hour hand of a clock will reach when it begins from 7 and turns through 2straight angles.

To do so, we will draw the diagram for the movement of the hour hand of the clock.

From the above diagram we can see that two straight angles from 7are at 7. 

Therefore, the hour hand of the clock will stop at 7 when it begins from 7 and turns through 2 straight angles.

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

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