Welcome to our lesson on telling time. Understanding how to read clocks is a fundamental skill we use every day. Today we'll learn how to calculate time intervals by solving the question: What time is 15 minutes after 1:30? To do this, we first need to understand how clocks work and how we measure time in hours and minutes.
A standard clock has two main hands: the hour hand and the minute hand. The shorter hand is the hour hand, which points to the current hour. The longer hand is the minute hand, which shows us the minutes past the hour. The clock face is divided into 12 sections, each representing 5 minutes, making a total of 60 minutes in one hour.
Let's look at the time 1:30. The hour hand is halfway between 1 and 2 because we've passed 1 o'clock but haven't reached 2 o'clock yet. The minute hand points directly at 6, which represents 30 minutes. This is because each number on the clock represents 5 minutes, so 6 times 5 equals 30 minutes past the hour.
Minutes are subdivisions of an hour, with 60 minutes making up one complete hour. When we add minutes to a given time, we're essentially moving the minute hand forward on the clock face. Every 5 minutes corresponds to one number on the clock, making it easier to count and visualize time changes.
Now we need to add 15 minutes to 1:30. Adding minutes means we move the minute hand clockwise around the clock face. Since 15 minutes equals three intervals of 5 minutes each, we'll move the minute hand three numbers forward from its current position at 6.
Starting from 30 minutes, let's add 15 minutes step by step. First, we move from 30 to 35 minutes, which is one 5-minute interval. Then we move to 40 minutes, which is our second interval. Finally, we reach 45 minutes after our third interval. So 30 plus 15 equals 45 minutes.
When adding minutes, we must check if we cross an hour boundary. Since we started at 1:30 and added only 15 minutes, we haven't reached 2:00 yet. The total is still in the 1 o'clock hour because 30 plus 15 equals 45, which is less than 60 minutes needed to complete a full hour.
Now we can put it all together. We're still in the 1 o'clock hour, and our minute hand shows 45 minutes. Therefore, 15 minutes after 1:30 is 1:45. The hour hand will have moved slightly closer to 2 o'clock, but it remains in the 1 o'clock position.
Here's our final answer visualized on the clock face. The hour hand is positioned between 1 and 2, closer to the 2 but still indicating it's 1 o'clock. The minute hand points to 9, which represents 45 minutes. This confirms that 15 minutes after 1:30 is indeed 1:45.
We can also solve this using simple addition. We start with 1:30, which means 1 hour and 30 minutes. Adding 15 minutes gives us 1 hour and 45 minutes. Since 45 minutes is less than 60, we don't need to carry over to the next hour, confirming our answer is 1:45.
Let's try another example to solidify our understanding. What time is 20 minutes after 2:45? We start at 45 minutes and add 20 minutes, giving us 65 minutes. Since 65 minutes equals 1 hour and 5 minutes, our final time is 3:05. This shows how we carry over when minutes exceed 60.
Students often make mistakes when adding time. One common error is forgetting to carry over when minutes exceed 60. Another mistake is miscounting the intervals on the clock face. Remember that each number represents 5 minutes, not 1 minute, so moving three numbers equals 15 minutes, not 3 minutes.