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

Core Concepts: Directions and Clock Revolutions

To solve the problems in Exercise 5.2, we must look at how a full circle is divided. A complete revolution is one full turn of $360^\circ$. If we divide this full turn into four equal parts, each part represents $\frac{1}{4}$ of a revolution, which is exactly one right angle ($90^\circ$).

For directions, we use the four cardinal points: North (N), East (E), South (S), and West (W). When moving clockwise, the order is N $\rightarrow$ E $\rightarrow$ S $\rightarrow$ W. Moving from North to East is $\frac{1}{4}$ of a revolution. Moving from North to South is $\frac{1}{2}$ of a revolution, and moving from North to West clockwise is $\frac{3}{4}$ of a revolution.

For a clock, the dial is divided into 12 hours. A full turn takes 12 hours. Therefore, each hour represents $\frac{1}{12}$ of a complete revolution. A 3-hour movement (like 12 to 3) is $\frac{3}{12} = \frac{1}{4}$ of a revolution (1 right angle). A 6-hour movement is $\frac{6}{12} = \frac{1}{2}$ of a revolution (2 right angles). Using these ratios, we can easily calculate any fractional movement on a clock dial!

Step-by-Step Method to Solve Ex 5.2 Problems

1. Identify the Total Units — For clock questions, the total units are always 12 hours. For direction questions, the total directions are 4 main points.
2. Count the Steps Moved — Calculate how many hours the hand has traveled or how many direction quadrants have been crossed clockwise or anticlockwise.
3. Form the Fraction — Write the fraction as (Steps Moved / Total Units). For example, if a clock hand moves 9 hours, the fraction is 9/12.
4. Simplify and Convert — Simplify the fraction to its lowest terms (e.g., 9/12 simplifies to 3/4). To find the number of right angles, remember that each 1/4 of a revolution equals 1 right angle.

Worked Examples from NCERT Exercise 5.2

• Example 1: What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 3 to 9? Step 1: Count the hours passed from 3 to 9: 4, 5, 6, 7, 8, 9 (total 6 hours). Step 2: Express as a fraction of the total 12 hours: 6/12. Step 3: Simplify the fraction: 6/12 = 1/2. Answer: 1/2 revolution.
• Example 2: Where will the hand of a clock stop if it starts at 5 and makes 1/4 of a revolution clockwise? Step 1: Calculate the hours in 1/4 of a revolution: (1/4) of 12 hours = 3 hours. Step 2: Add 3 hours to the starting point: 5 + 3 = 8. Answer: The hand will stop at 8.
• Example 3: Which direction will you face if you start facing East and make 1/2 of a revolution clockwise? Step 1: 1/2 of a revolution is a straight turn (2 right angles). Step 2: Moving clockwise from East, the first quarter lands on South, and the second quarter lands on West. Answer: You will face West.

Pro Exam Tips & Avoiding Silly Mistakes

1. Watch the Direction: Always check if the question specifies clockwise or anticlockwise. Turning $\frac{1}{4}$ of a revolution clockwise from North lands you on East, but anticlockwise lands you on West.
2. Draw a Quick Sketch: Draw a small '+' on your rough sheet and label N, S, E, W. For clock problems, sketch a quick circle with 12, 3, 6, and 9 marked. Visualizing prevents calculation errors!
3. Full Revolution Rule: Keep in mind that completing 1 full revolution (clockwise or anticlockwise) always brings you back to your starting position.

Practice Questions with Solutions

• Q: Where will the hand of a clock stop if it starts at 2 and makes 1/2 of a revolution clockwise? A: Step 1: Find the number of hours in 1/2 of a revolution. 1/2 of 12 hours = 6 hours. Step 2: Add these hours to the starting number. 2 + 6 = 8. Final answer: The hand of the clock will stop at 8.
• Q: What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 4 to 10? A: Step 1: Count the hours from 4 to 10. 10 - 4 = 6 hours. Step 2: Form the fraction with total hours. Fraction = 6/12. Step 3: Simplify the fraction. 6/12 = 1/2. Final answer: 1/2 of a revolution.
• Q: Which direction will you face if you start facing West and make 3/4 of a revolution anticlockwise? A: Step 1: Identify that 3/4 of a revolution consists of 3 right angles (each of 90 degrees). Step 2: Move anticlockwise (opposite of clock hands) starting from West. Step 3: 1st turn anticlockwise takes you to South. 2nd turn takes you to East. 3rd turn takes you to North. Final answer: You will face North.
• Q: Find the number of right angles turned by the hour hand of a clock when it goes from 12 to 9 clockwise. A: Step 1: Count the hours from 12 to 9 clockwise. That is 9 hours. Step 2: Express this as a fraction of a full turn: 9/12 = 3/4 of a revolution. Step 3: Since 1/4 of a revolution equals 1 right angle, 3/4 of a revolution equals 3 right angles. Final answer: 3 right angles.

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