Telling Time and Working Out Time Intervals

Two hands, two scales

A clock face has twelve numerals. Both hands point at them. They mean different things.

Hand	Points at	A numeral means
short	hours	that hour
long	minutes	five minutes

The short hand at $3$ means 3 o’clock. The long hand at $3$ means 15 minutes.

That is the part that confuses people. The same numeral serves both hands. For the minute hand, you multiply by five.

$$\text{minute hand at } 3 \;\Rightarrow\; 3 \times 5 = 15 \text{ minutes}$$

Reading to the nearest minute

Between each pair of numerals there are five small marks. Each is one minute.

So a long hand two marks past the $4$ reads:

$$4 \times 5 = 20 \quad\Rightarrow\quad 20 + 2 = 22 \text{ minutes}$$

Long hand at	Minutes
$12$	$0$
$3$	$15$
$6$	$30$
$9$	$45$

Words for common times

Words	Means
quarter past	$15$ minutes past
half past	$30$ minutes past
quarter to	$45$ minutes past, or $15$ to the next hour

A quarter of an hour is $15$ minutes, because an hour has $60$ minutes and $60 \div 4 = 15$.

Why time does not work like ordinary numbers

Ordinary numbers carry at ten. Time carries at sixty.

$$60 \text{ minutes} = 1 \text{ hour}$$

So $2{:}45$ plus $30$ minutes is not $2{:}75$. There is no such time. The minutes pass $60$ and roll into the next hour:

$$45 + 30 = 75 \text{ minutes} = 1 \text{ hour and } 15 \text{ minutes}$$ $$2{:}45 + 30 \text{ min} = 3{:}15$$

This is the same idea as carrying in column addition, with sixty in place of ten.

Finding how long something lasted

Count on from the start to the end. Go to the next whole hour first, then carry on. That keeps every number small.

A film starts at $2{:}40$ and ends at $4{:}15$. How long is it?

Step	From	To	Time
1	$2{:}40$	$3{:}00$	$20$ min
2	$3{:}00$	$4{:}00$	$1$ hour
3	$4{:}00$	$4{:}15$	$15$ min

$$1 \text{ hour} + 20 + 15 = 1 \text{ hour } 35 \text{ minutes}$$

Counting on avoids borrowing across sixty, which is where most mistakes happen.

Word problems with time, distance and money

The same counting-on method handles a lot of everyday problems.

A bus takes $25$ minutes. It leaves at $9{:}50$. When does it arrive?

$$9{:}50 \rightarrow 10{:}00 \text{ is } 10 \text{ min}$$

$15$ minutes remain, so it arrives at $10{:}15$.

Money works the same way. Convert to one unit first, exactly as with measurement units.

A pen costs $1$ dollar $40$. You buy $3$. What is the total?

Work in cents:

$$3 \times 140 = 420 \text{ cents} = 4 \text{ dollars } 20$$

Worked examples

Common mistakes

Practice problems