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

(i) 4 to 10

(ii) 2 to 5

(iii) 7 to 10

(iv) 8 to 5

(v) 11 to 5

(vi) 6 to 3

Also find the number of right angles turned in each case.

In one complete revolution, the hour hand of a clock covers 12 hours (numbers).

So, 1 hour movement = $\dfrac{1}{12}$ of a revolution.

Also, one complete revolution = 4 right angles, so 1 hour = $\dfrac{1}{3}$ of a right angle and 3 hours = 1 right angle.

(i) From 4 to 10 (clockwise), hour hand moves through 6 hours.

Fraction of revolution = $\dfrac{6}{12}$ = $\dfrac{1}{2}$

Number of right angles = $\dfrac{6}{3}$ = 2

∴ Fraction of revolution = $\dfrac{1}{2}$ and number of right angles = 2.

(ii) From 2 to 5 (clockwise), hour hand moves through 3 hours.

Fraction of revolution = $\dfrac{3}{12}$ = $\dfrac{1}{4}$

Number of right angles = $\dfrac{3}{3}$ = 1

∴ Fraction of revolution = $\dfrac{1}{4}$ and number of right angles = 1.

(iii) From 7 to 10 (clockwise), hour hand moves through 3 hours.

Fraction of revolution = $\dfrac{3}{12}$ = $\dfrac{1}{4}$

Number of right angles = $\dfrac{3}{3}$ = 1

∴ Fraction of revolution = $\dfrac{1}{4}$ and number of right angles = 1.

(iv) From 8 to 5 (clockwise), hour hand moves through 9 hours.

Fraction of revolution = $\dfrac{9}{12}$ = $\dfrac{3}{4}$

Number of right angles = $\dfrac{9}{3}$ = 3

∴ Fraction of revolution = $\dfrac{3}{4}$ and number of right angles = 3.

(v) From 11 to 5 (clockwise), hour hand moves through 6 hours.

Fraction of revolution = $\dfrac{6}{12}$ = $\dfrac{1}{2}$

Number of right angles = $\dfrac{6}{3}$ = 2

∴ Fraction of revolution = $\dfrac{1}{2}$ and number of right angles = 2.

(vi) From 6 to 3 (clockwise), hour hand moves through 9 hours.

Fraction of revolution = $\dfrac{9}{12}$ = $\dfrac{3}{4}$

Number of right angles = $\dfrac{9}{3}$ = 3

∴ Fraction of revolution = $\dfrac{3}{4}$ and number of right angles = 3.