Exercise 5.2
1. What fraction of a clockwise revolution does the hour hand turn through when it goes from:
Remember: A full revolution = 12 hours → so each hour = \(\frac{1}{12}\) of a revolution.
(a) 3 to 9
Clock showing 3 to 9
Hours moved: \(9 - 3 = 6\) → Fraction = \(\frac{6}{12} = \frac{1}{2}\)
Clock showing 3 to 9
(b) 4 to 7
Clock showing 4 to 7
Hours moved: \(7 - 4 = 3\) → Fraction = \(\frac{3}{12} = \frac{1}{4}\)
Clock showing 4 to 7
(c) 7 to 10
Clock showing 7 to 10
Hours moved: \(10 - 7 = 3\) → Fraction = \(\frac{3}{12} = \frac{1}{4}\)
Clock showing 7 to 10
(d) 12 to 9
Clock showing 12 to 9
Clockwise: \(12 \to 1 \to 2 \to ... \to 9\) = 9 hours → Fraction = \(\frac{9}{12} = \frac{3}{4}\)
Clock showing 12 to 9
(e) 1 to 10
Clock showing 1 to 10
Hours moved: \(10 - 1 = 9\) → Fraction = \(\frac{9}{12} = \frac{3}{4}\)
Clock showing 1 to 10
(f) 6 to 3
Clock showing 6 to 3
Clockwise: \(6 \to 7 \to 8 \to 9 \to 10 \to 11 \to 12 \to 1 \to 2 \to 3\) = 9 hours → Fraction = \(\frac{9}{12} = \frac{3}{4}\)
Clock showing 6 to 3
(a) \(\frac{1}{2}\) (b) \(\frac{1}{4}\) (c) \(\frac{1}{4}\) (d) \(\frac{3}{4}\) (e) \(\frac{3}{4}\) (f) \(\frac{3}{4}\)
2. Where will the hand stop if it:
(a) Starts at 12 and makes \(\frac{1}{2}\) revolution clockwise?
Clock showing start at 12
\(\frac{1}{2}\) of 12 hours = 6 hours → From 12 to 6 = 6 → stops at 6
Clock showing start at 12
(b) Starts at 2 and makes \(\frac{1}{2}\) revolution clockwise?
Clock showing start at 2
\(\frac{1}{2}\) of 12 hours = 6 hours → \(2 + 6 = 8\) → stops at 8
Clock showing start at 2
(c) Starts at 5 and makes \(\frac{1}{4}\) revolution clockwise?
Clock showing start at 5
\(\frac{1}{4}\) of 12 = 3 hours → \(5 + 3 = 8\) → stops at 8
Clock showing start at 5
(d) Starts at 5 and makes \(\frac{3}{4}\) revolution clockwise?
Clock showing start at 5
\(\frac{3}{4}\) of 12 = 9 hours → \(5 + 9 = 14 → 14 - 12 = 2\) → stops at 2
Clock showing start at 5
(a) 6 (b) 8 (c) 8 (d) 2
3. Which direction will you face if you start facing:
Remember: Full revolution = 360°, half = 180°, quarter = 90°.
(a) East and make \(\frac{1}{2}\) revolution clockwise?
Clockwise from East
From East → clockwise 180° → faces West
Clockwise from East
(b) East and make \(1\frac{1}{2}\) revolution clockwise?
Clockwise from East
Starting East, 1 full revolution brings you back to East, then half revolution (180°) more → faces West
Clockwise from East
(c) West and make \(\frac{3}{4}\) revolution anti-clockwise?
Anti-clockwise from West
Anti-clockwise 270° Starting from West → South → East → North → faces North
Anti-clockwise from West
(d) South and make one full revolution?
You end up facing the same direction → South
No need to specify direction — full revolution brings you back!
No need to specify direction — full revolution brings you back!
(a) West (b) East (c) South (d) South
4. What part of a revolution have you turned through if you stand facing:
(a) East and turn clockwise to face north?
Clockwise from East to North
We Start from East to South to West than North.
So we make 3 right angles → which is \(\frac{3}{4}\) revolution
Clockwise from East to NorthSo we make 3 right angles → which is \(\frac{3}{4}\) revolution
(b) South and turn clockwise to face east?
Clockwise from South to East
We Start from South to West to North than East.
So we make 3 right angles → which is \(\frac{3}{4}\) revolution
Clockwise from South to EastSo we make 3 right angles → which is \(\frac{3}{4}\) revolution
(c) West and turn clockwise to face east?
Clockwise from West to East
We Start from West to North than East.
So we make 2 right angles → which is \(\frac{2}{4} = \frac{1}{2}\) revolution
Clockwise from West to EastSo we make 2 right angles → which is \(\frac{2}{4} = \frac{1}{2}\) revolution
(a) \(\frac{3}{4}\) (b) \(\frac{3}{4}\) (c) \(\frac{1}{2}\)
5. Find the number of right angles turned through by the hour hand when it goes from:
Remember: One right angle = 90° = 3 hours on clock.
(a) 3 to 6
From 3 to 6 = 6 -3 = 3 hours
So 3 Hours = \(3 \div 3 = 1\) right angle
From 3 to 6 = 6 -3 = 3 hours
So 3 Hours = \(3 \div 3 = 1\) right angle
(b) 2 to 8
From 2 to 8 = 8 - 2 = 6 hours
So 6 Hours = \(6 \div 3 = 2\) right angles
From 2 to 8 = 8 - 2 = 6 hours
So 6 Hours = \(6 \div 3 = 2\) right angles
(c) 5 to 11
From 5 to 11 = 11 - 5 = 6 hours
So 6 Hours = \(6 \div 3 = 2\) right angles
From 5 to 11 = 11 - 5 = 6 hours
So 6 Hours = \(6 \div 3 = 2\) right angles
(d) 10 to 1
From 10 to 1 = 11 → 12 → 1 = 3 hours
So 3 Hours = \(3 \div 3 = 1\) right angle
From 10 to 1 = 11 → 12 → 1 = 3 hours
So 3 Hours = \(3 \div 3 = 1\) right angle
(e) 12 to 9
From 12 to 9 = 12 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 = 9 hours
So 9 Hours = \(9 \div 3 = 3\) right angles
From 12 to 9 = 12 → 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9 = 9 hours
So 9 Hours = \(9 \div 3 = 3\) right angles
(f) 12 to 6
From 12 to 6 = 12 → 1 → 2 → 3 → 4 → 5 → 6 = 6 hours
So 6 Hours = \(6 \div 3 = 2\) right angles
From 12 to 6 = 12 → 1 → 2 → 3 → 4 → 5 → 6 = 6 hours
So 6 Hours = \(6 \div 3 = 2\) right angles
(a) 1 (b) 2 (c) 2 (d) 1 (e) 3 (f) 2
6. How many right angles do you make if you start facing:
(a) South and turn clockwise to west?
Clockwise from South to West
South → West = 90° → 1 right angle
Clockwise from South to West
(b) North and turn anti-clockwise to east?
Anti-clockwise from North to East
North → East anti-clockwise = \( \frac {3}{4}\) revolution = 3 right angles
Anti-clockwise from North to East
(c) West and turn to west?
From West to West
West → West: Either Clockwise or Anti-clockwise, we make 4 right angles → Full circle → back to West.
So we make 4 right angles, we endup facing the same direction.
From West to WestSo we make 4 right angles, we endup facing the same direction.
(d) South and turn to north?
From South to North
South → North: Either Clockwise or Anti-clockwise, we make 2 right angles → Half circle → back to North.
So we make 2 right angles, we endup facing the same direction North.
From South to NorthSo we make 2 right angles, we endup facing the same direction North.
(a) 1 (b) 3 (c) 0 (d) 2
7. Where will the hour hand stop if it starts from:
Remember: 1 right angle = 3 hours, 1 straight angle = 2 right angles = 6 hours.
(a) 6 and turns through 1 right angle?
Clock hands from 6 to 9
1 right angle = 3 hours → \(6 + 3 = 9\) → stops at 9
Clock hands from 6 to 9
(b) 8 and turns through 2 right angles?
Clock hands from 8 to 2
From 8 → 11 = 3 hours = 1 right angle
Then from 11 → 2 = 3 hours = 1 right angle
So total 6 hours = 2 right angles
Clock hands from 8 to 2Then from 11 → 2 = 3 hours = 1 right angle
So total 6 hours = 2 right angles
(c) 10 and turns through 3 right angles?
Clock hands from 10 to 7
From 10 → 1 = 3 hours = 1 right angle
Then from 1 → 4 = 3 hours = 1 right angle
Then from 4 → 7 = 3 hours = 1 right angle
So total 9 hours = 3 right angles
Clock hands from 10 to 7Then from 1 → 4 = 3 hours = 1 right angle
Then from 4 → 7 = 3 hours = 1 right angle
So total 9 hours = 3 right angles
(d) 7 and turns through 2 straight angles?
Clock hands from 7 to 7
From 7 → 1 = 6 hours = 2 right angles = 1 straight angle
Then from 1 → 7 = 6 hours = 2 right angles = 1 straight angle
So total 12 hours = 2 straight angles → back to 7
Clock hands from 7 to 7Then from 1 → 7 = 6 hours = 2 right angles = 1 straight angle
So total 12 hours = 2 straight angles → back to 7