Quarter past & quarter to
Year 3 students working towards NSW Stage 2 outcome MA2-NSM-02 learn why a quarter of an hour is 15 minutes. They read quarter past with the minute hand on the 3, half past on the 6 and quarter to on the 9, along with o'clock on the 12.
Students write these times as digital times, remembering that quarter to uses the hour that is still running (quarter to 4 is 3:45), describe the minute hand's turn as a quarter or a half, and find short durations such as quarter past to half past.
Theory
Quarter past and quarter to are special times on the clock. Quarter past is 15 minutes past the hour, when the minute hand points to the 3. Quarter to is 15 minutes before the next hour, when the minute hand points to the 9. This Year 3 page shows both on an analog clock and matches them to digital times like 2:15 and 3:45.
One hour is 60 minutes. A quarter of an hour is one of four equal parts, so a quarter is \(\dfrac{1}{4}\) of an hour, or 15 minutes. A half of an hour is \(\dfrac{1}{2}\) of an hour, or 30 minutes. At o'clock the minute hand points to the 12, and at half past it points to the 6.
Quarter past means 15 minutes after the hour. The minute hand points to the 3 because it has gone a quarter of the way around the clock. Quarter past 9 is the digital time \(9\!:\!15\).
Quarter to means 15 minutes before the next hour. The minute hand points to the 9, which is 45 minutes past. There is still a quarter of an hour to go, so we count it as "to" the next hour. Quarter to 12 is the digital time \(11\!:\!45\).
These facts help you name quarter past and quarter to.
How to read quarter past and quarter to
- Look at the minute hand. On the 3 it is quarter past (15 minutes). On the 9 it is quarter to (45 minutes past). On the 12 it is o'clock, and on the 6 it is half past (30 minutes).
- Look at the hour hand. For quarter past, say the hour it has just passed. For quarter to, say the next hour it is heading toward.
- Say or write the time. Quarter past 9 is \(9\!:\!15\). Quarter to 12 is \(11\!:\!45\), because the hour is still 11 and the minutes are 45.
How long between quarter and half hours
- Change each time to minutes past. Quarter past is 15, half past is 30 and quarter to is 45.
- Take the smaller from the bigger when both times are in the same hour. Each step from one quarter to the next is 15 minutes.
| \(\text{minute hand}\) | \(\to\) | \(3 = 15\text{ min}\) |
| \(\text{hour hand}\) | \(\to\) | \(\text{just past }2\) |
The time is quarter past 2, or \(2\!:\!15\).
| \(\text{minute hand}\) | \(\to\) | \(9 = 45\text{ min}\) |
| \(\text{hour hand}\) | \(\to\) | \(\text{before }4\) |
The time is quarter to 4, or \(3\!:\!45\).
| \(\text{quarter to }8\) | \(=\) | \(15\text{ min before }8\) |
| \(\text{hour}\) | \(=\) | \(7,\ \text{minutes} = 45\) |
The digital time is \(7\!:\!45\). The hour is still 7 because 8 has not come yet.
| \(45 - 15\) | \(=\) | \(30\text{ minutes}\) |
| \(30\text{ min}\) | \(=\) | \(\text{half an hour} = \text{half a turn}\) |
The minute hand makes half a turn, so 30 minutes pass. From quarter past to quarter to is half an hour.
| \(\text{half past }1\) | \(=\) | \(1\!:\!30\) |
| \(\text{quarter to }2\) | \(=\) | \(1\!:\!45\) |
| \(45 - 30\) | \(=\) | \(15\text{ minutes}\) |
The lesson lasts 15 minutes, which is a quarter of an hour.
Common pitfalls
Frequently asked questions
What is quarter past?
Quarter past is 15 minutes after the hour. The minute hand points to the 3, because it has gone a quarter of the way around the clock. Quarter past 9 is the same as the digital time \(9\!:\!15\).
What is quarter to?
Quarter to is 15 minutes before the next hour. The minute hand points to the 9, which is 45 minutes past. Quarter to 12 is the same as the digital time \(11\!:\!45\).
How many minutes are in a quarter of an hour?
There are 15 minutes in a quarter of an hour. One hour is 60 minutes, and \(60 \div 4 = 15\).
Why is quarter to 12 the same as 11:45?
Quarter to 12 means 15 minutes before 12 o'clock. The hour has not reached 12 yet, so it is still 11, and the minutes are 45. That is why it is written \(11\!:\!45\).
Where does the minute hand point for quarter past and quarter to?
For quarter past the minute hand points to the 3, which is 15 minutes. For quarter to the minute hand points to the 9, which is 45 minutes past, or 15 minutes to the next hour.
Is quarter past the same as half past?
No. Quarter past is 15 minutes past and the minute hand is on the 3. Half past is 30 minutes past and the minute hand is on the 6. Half past is later than quarter past.