Logical reasoning · lesson 17 of 30 · free

Clocks: angles and time — Logical reasoning for kids

The minute hand goes all the way round (360°) in 60 minutes, so it moves 6° a minute. The hour hand moves 30° in an hour — half a degree a minute. Find where each hand points and subtract.

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How to think it through

30h − 5.5m — “the angle is the difference between where the two hands point”

  1. Minute hand angle (from 12) = minutes × 6.
  2. Hour hand angle = hours × 30 + minutes × 0.5.
  3. Angle between them = the difference; if it is more than 180°, take it away from 360°.

Use it for: Clock questions in Olympiads and aptitude tests, and reading analogue clocks.

Worked example: What is the smaller angle between the hour hand and the minute hand at 3:40? (in degrees) = 130

  1. Minute hand: 40 × 6 = 240°. Hour hand: 3 × 30 + 40 × 0.5 = 110°.
  2. Difference: 240 − 110 = 130°.

Check: 30 × 3 − 5.5 × 40 = 90 − 220 = −130, so 130° ✓

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