Important Formulas: Racing Seconds | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download

Introduction

• Time helps us know when things start, end, and how long they last.

• Everyday activities (waking up, going to school, playing, sleeping) happen at specific times.

• Units of time: seconds, minutes, hours.

Using a Clock

Hands of a clock:

• Hour hand = short → shows hours

• Minute hand = long → shows minutes

• Second hand = thin → shows seconds

Reading Time:

1. Check hour hand.

2. Check minute hand (each number = 5 min.).

3. Check second hand (each number = 5 sec.).

Example 1: If the minute hand is on 3 and the hour hand is past 11, the time is 11:15 (3 × 5 = 15 minutes), or quarter past 11.

Example 2: If the minute hand is on 10 and the hour hand is past 5, the time is 5:50 or 10 minutes to 6 (12 – 10 = 2 × 5 = 10 minutes).

Measuring Time

Seconds

• Smallest commonly used unit of time.

• 60 seconds = 1 minute.

• Examples: blinking, snapping fingers, saying “go!”

Minutes

• 1 minute = 60 seconds.

• Used for short tasks (tying shoelaces, sipping water, reading a paragraph).

Hours

• 1 hour = 60 minutes = 3,600 seconds.

• Used for longer activities (watching cartoons, playing, homework).

Converting Time Units

We can convert between hours, minutes, and seconds.

We know:

• 1 hour = 60 minutes

• 1 minute = 60 seconds

So,

• To go downwards (hours → minutes → seconds), we multiply by 60.

• To go upwards (seconds → minutes → hours), we divide by 60.

Example 1: Convert 2 hours into minutes

2 hours = 2 × 60 = 120 minutes

Example 2: Convert 5 minutes into seconds

5 minutes = 5 × 60 = 300 seconds

Example 3: Convert 3600 seconds into hours

Step 1: Convert seconds to minutes
3600 ÷ 60 = 60 minutes

Step 2: Convert minutes to hours
60 ÷ 60 = 1 hour

So, 3600 seconds = 1 hour.

2 hours = 2 × 60 = 120 minutes

Time Duration (Elapsed Time)

Definition: How long something lasts.

Formula: Time duration = End time − Start time

Examples:

• Football match: 1:15 p.m. – 1:42 p.m. → Duration = 27 min

• Yoga: Start 5:35 a.m., End 6:55 a.m. → Duration = 1 h 20 min

Tips: Subtract minutes first, then hours. Borrow 1 hour as 60 minutes if needed.

Time Formats

24-Hour Clock → 12-Hour Clock

Rules:

1. 00:00–00:59 hours → Add a.m. (midnight)

2. 01:00–11:59 hours → Add a.m. directly

3. 12:00–12:59 hours → Add p.m. directly (no change)

4. 13:00–23:59 hours → Subtract 12:00 and add p.m.

Examples:

• 0045 hours → 12:45 a.m.

• 1430 hours → 2:30 p.m.

12-Hour Clock → 24-Hour Clock

Rules:

1. 12:00–12:59 a.m. → Subtract 12:00

2. 1:00 a.m.–12:59 p.m. → Write as is

3. 1:00 p.m.–11:59 p.m. → Add 12:00

Examples:

• 12:20 a.m. → 00:20

• 5:45 p.m. → 17:45

Why 24-Hour Clock is Useful

No confusion between morning and evening

• 19:00 is clearly evening, unlike 7:00

Easier to calculate time duration

• Example: 09:30 → 14:30 → 5 hours

Time in a.m. and p.m.

1. What is a.m. and p.m.?

• a.m. (ante meridiem) → Before midday (from 12 midnight to 12 noon)

• p.m. (post meridiem) → After midday (from 12 noon to 12 midnight)

2. Why use a.m. and p.m.?

To avoid confusion between morning and evening times.

• Example: 6:00 a.m. = morning

• 6:00 p.m. = evening

Example:

• Hour hand between 4 and 5, minute hand on 3 → 4:15

• Morning → 4:15 a.m.

• Evening → 4:15 p.m.

• Also called quarter past 4

3. Special Rules for 12 o’clock

• 12:00 noon → midday (not written with a.m./p.m.)

• 12:00 midnight → night (not written with a.m./p.m.)

Special Time Terms

• Quarter past → 15 minutes after the hour

• Half past → 30 minutes after the hour

• Quarter to → 15 minutes before the next hour

Practice & Examples

1. Elapsed time:

   • 03:18 p.m. – 08:18 p.m. → 5 h

   • 09:15 a.m. – 11:30 a.m. → 2 h 15 min

2. Comparing durations:

   • Who took longest/least time?

   • Use subtraction of start and end times.

3. Conversion exercises:

   • Seconds ↔ minutes ↔ hours

   • 120 sec → 2 min

   • 2 h 15 min → 135 min