Back to the on-screen lesson ·
Seconds, minutes and hours, and the sixty between them.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will convert between seconds, minutes and hours, and say why time is the one unit here that does not go up in tens.
You can already read a clock, and you already know that half past means thirty minutes rather than fifty. That is the sixty in action; this lesson only writes it down as arithmetic.
You also know the method from the last two lessons: predict whether the number gets bigger or smaller, then multiply or divide by the step. The method stays the same. Only the step changes, from tens and thousands to sixty.
| Term | What it means |
|---|---|
| Second (s) | A short unit of time: about one slow count, one-Mississippi. |
| Minute (min) | Sixty seconds: one whole turn of a clock's second hand. |
| Hour (h) | Sixty minutes: one whole turn of a clock's minute hand. |
| Duration | How long something lasts, not what time it is. |
| Half an hour | Thirty minutes, because half of sixty is thirty. |
| Quarter of an hour | Fifteen minutes, because a quarter of sixty is fifteen. |
Everything else in this course goes up in tens, and time does not. $60$ seconds make a minute and $60$ minutes make an hour, so converting time means multiplying or dividing by $60$.
The rule you already have still works — a bigger unit needs a smaller number — but the number you multiply by has changed. $90$ minutes is $1.5$ hours, not $0.9$. You can see why on a clock: $90$ minutes is one whole hour, which is $60$ minutes, and then $30$ minutes more, which is half of the next hour.
So the method has the same five steps as before. Name the units. Predict the direction. Use the step, which is now $60$. Multiply or divide. Then check, and the best check for time is to ask whether the answer is more or less than one whole hour or minute.
Another way: action
Watch a clock's second hand go all the way round once. That whole circle is one minute, and sixty of those circles is an hour.
Another way: steps
Meters, grams and liters were invented all at once, and their inventors chose tens on purpose to make them easy. Time is much older. People in ancient Babylon, more than four thousand years ago, counted in sixties, and the way we split an hour and a minute comes from them.
Sixty is a handy number to share. It splits evenly into halves (30), thirds (20), quarters (15), fifths (12), sixths (10) and more. That is why a clock can show a quarter past or twenty to without any fractions of a minute. A hundred can only be split evenly into halves, quarters and fifths.
So time is the one exception in this course. Every time you convert a time, say to yourself: sixty, not a hundred.
Like lengths and masses, time has a ladder, with the biggest unit at the top.
| Unit | How many of the unit below |
|---|---|
| hour (h) | 60 minutes |
| minute (min) | 60 seconds |
| second (s) | — |
Going down the ladder, multiply by 60. Going up, divide by 60. To go two rungs, from hours to seconds, do both: $1$ h is $60$ min, and $60$ min is $60 \times 60 = 3600$ s. So there are three thousand six hundred seconds in one hour.
Above the hour, the steps change again: $24$ hours make a day and $7$ days make a week. Those are not sixties either. The only way to be safe is to check which two units you are moving between, and read the step from the ladder.
Some times come up so often that it is worth knowing them by heart.
| Part of an hour | Minutes | As a decimal |
|---|---|---|
| a quarter | 15 | 0.25 h |
| a half | 30 | 0.5 h |
| three quarters | 45 | 0.75 h |
Watch the decimals. Half an hour is $0.5$ h, and that is $30$ minutes, not $50$. The decimal is a part of the hour, and the minutes are a part of sixty. So $1.5$ h is one hour and thirty minutes, which is $90$ minutes, and $2.25$ h is two hours and fifteen minutes, which is $135$ minutes. Reading $1.5$ h as one hour fifty is the most common time mistake there is.
After every time conversion, check it two ways.
The second check is the one that catches dividing by 100. Someone who writes $90$ minutes as $0.9$ hours has an answer less than one hour, but $90$ minutes is more than one hour. The check shows the mistake before it can do any harm.
Times are often written in two units at once, like 1 h 20 min. To add or compare them, put everything in one unit first, usually the smaller one.
For example, a family drives $2$ h $15$ min to a campsite and then hikes for $50$ min. In minutes, the drive is $2 \times 60 + 15 = 135$ min, and the whole trip is $135 + 50 = 185$ min. To write that back in hours and minutes, find how many whole sixties fit: $3 \times 60 = 180$, with $5$ left, so it is 3 h 5 min.
Notice that adding $15$ min and $50$ min gives $65$ min, which is more than an hour. In time, $65$ minutes is carried as one hour and five minutes, not left as sixty-five.
Short times are measured in seconds, and very short ones in parts of a second. A fast runner can finish a $100$ m race in about $10$ seconds. A stopwatch shows times like 12.4 s, where the $.4$ is four tenths of a second. Tenths of a second do go in tens, because they are part of the metric system: only the steps from seconds to minutes and from minutes to hours are sixties.
So a race time of 1 min 15.5 s means one minute and fifteen and a half seconds. In seconds alone it is $60 + 15.5 = 75.5$ s. Swimmers, skiers and track athletes are timed this way, and the winner is often decided by a few hundredths of a second.
Scientists time experiments in seconds too. In the next course, you will time how long it takes something to travel a distance, and use the time to work out its speed. Every one of those timings starts with a stopwatch reading and, often, a conversion between seconds and minutes.
Sometimes you know when something must finish and how long it takes, and you want to know when to start. A pizza needs $25$ minutes in the oven and dinner is at 6:00. Counting back $25$ minutes from 6:00 lands at 5:35. Counting back across the hour is where people slip, because the minutes wrap around at sixty, not at a hundred: $6{:}00$ is the same as $5{:}60$, and $60 - 25 = 35$.
A bus trip that takes $1$ h $40$ min and must arrive by 3:15 has to leave by 1:35. Take away the hour first, reaching 2:15, then the $40$ minutes: $2{:}15$ is $1{:}75$, and $75 - 40 = 35$, so 1:35. Writing the time in the borrowed form, like $1{:}75$, looks strange, but it is exactly what borrowing a ten looks like in ordinary subtraction, done with a sixty instead.
A youth soccer game has two halves of $30$ minutes each, with a $10$-minute break in between. A parent wants to know how long to park the car for.
The playing time is $2 \times 30 = 60$ minutes, and the break adds $10$, so the game lasts $70$ minutes. Parking meters in many American towns sell time in hours, so the parent converts: $70$ minutes is more than $60$, so it is more than one hour. One hour is $60$ minutes and there are $10$ left over, so the game is 1 h 10 min. Adding $10$ minutes to walk to and from the field, the parent pays for 1 h 20 min, or $80$ minutes.
If the parent had divided by 100 and thought $70$ minutes was $0.7$ of an hour, they would pay for less than an hour and come back to a parking ticket. The more-than-one check prevents exactly that.
A microwave's keypad lets you type a cooking time in minutes and seconds. Suppose a bag of popcorn says to cook it for 2.5 minutes. You cannot type 2.5, so you convert: $2.5 \times 60 = 150$ seconds, which is $2$ minutes and $30$ seconds. You type 2:30.
Someone who reads $2.5$ minutes as two minutes and fifty seconds would type 2:50 and cook it for $20$ seconds too long, which is enough to burn popcorn. Many microwaves will even accept 150 seconds typed straight in, and show it as 2:30 on the screen.
Cooks, coaches, nurses giving medicine on a schedule, and scientists timing an experiment all convert times like this. They always remember the same rule: time counts in sixties, so check the answer against one whole minute or hour.
After two lessons of tens, the hand wants to divide by a hundred, and $90$ minutes comes out as $0.9$ hours. It is $1.5$.
The way to catch it: $90$ minutes is more than an hour, so the answer must be more than $1$, and $0.9$ is not. Time is the exception in this course, and it is the only one.
The second mistake is reading a decimal hour as minutes: seeing $1.5$ h and saying one hour and fifty minutes. The $.5$ means half, and half an hour is thirty minutes. When you see a decimal hour, multiply the decimal part by $60$ to find the minutes: $0.5 \times 60 = 30$, and $0.25 \times 60 = 15$.
Name the two units.
$\text{have: h} \qquad \text{want: min}$
Know where you are and where you are going.
Predict the direction first.
$\text{min is smaller, so the number gets bigger}$
A smaller unit needs a bigger number.
Find the step between them.
$1\ \text{h} = 60\ \text{min}$
Sixty, not a hundred.
Multiply by the step.
$1.5 \times 60 = 90$
One hour is 60 and half an hour is 30 more.
Write the answer and check it.
$1.5\ \text{h} = 90\ \text{min} > 60\ \text{min}$
More than one hour, as it should be. Not 150.
Name the two units.
$\text{have: s} \qquad \text{want: min}$
Going up the ladder this time.
Predict the direction first.
$\text{min is bigger, so the number gets smaller}$
A bigger unit needs a smaller number.
Find the step between them.
$60\ \text{s} = 1\ \text{min}$
One turn of the second hand.
Divide by the step.
$150 \div 60 = 2.5$
Two whole minutes is 120 seconds, and 30 seconds is half a minute more.
Write the answer with its unit.
$150\ \text{s} = 2.5\ \text{min}$
Two and a half minutes. Not 1.5.
Check it against one minute.
$150 > 60, \text{ so more than } 1\ \text{min}$
And less than three, since three minutes is 180 seconds.
Count the whole hours first.
$8{:}15 \to 2{:}15 \text{ is } 6\ \text{h}$
Nine, ten, eleven, twelve, one, two: six hours.
Count the extra minutes.
$2{:}15 \to 2{:}45 \text{ is } 30\ \text{min}$
From a quarter past to a quarter to.
Write the length in two units.
$6\ \text{h}\ 30\ \text{min}$
A duration, not a time on the clock.
Convert the hours to minutes.
$6 \times 60 = 360\ \text{min}$
Sixty minutes in each hour.
Add the extra minutes.
$360 + 30 = 390\ \text{min}$
The whole day in minutes.
Write it in hours too.
$390 \div 60 = 6.5\ \text{h}$
Half an hour is 0.5 of an hour.
Check the two answers agree.
$6.5\ \text{h} = 6\ \text{h}\ 30\ \text{min}$
The decimal half is thirty minutes, not fifty.
Predict the direction first.
$\text{h is bigger, so the number gets smaller}$
Decide before calculating.
Check more or less than one.
Divide by the step.
A walk takes $5$ hours and a half. How many minutes is that?
Answer: unit: min
Complete the worked solution: a movie lasts $2$ h $30$ min. How many minutes is that?
Predict the direction first.
$\text{h} \to \text{min: bigger number}$
Minutes are the smaller unit.
Convert the whole hours.
$2 \times 60 =$ p min
Sixty minutes in each hour.
Add the extra minutes.
$\text{that} + 30 =$ q min
Both parts are now in minutes.
Match each duration to the same duration in a different time unit.
| 1.5 minutes | 120 minutes | 2.5 hours | |
|---|---|---|---|
| 90 seconds | |||
| 2 hours | |||
| 150 minutes |
An egg boils for $10$ minutes. How many seconds is that?
Answer: unit: s
Fill in each time in the unit the table asks for.
| time | |
|---|---|
| $6$ h in minutes | |
| $360$ s in minutes | |
| $330$ min in hours |
A song lasts $240$ seconds. How long is that in minutes?
Answer: unit: min
In a reading challenge, a student reads for $25$ minutes every day for $6$ days. How many hours is that altogether?
Answer: unit: h
A family's trip to visit relatives is $1$ hours on a train and then $37$ minutes walking. How many minutes is the whole trip?
Answer: unit: min
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Fill in each time in the unit the table asks for.
| time | |
|---|---|
| $6$ h in minutes | |
| $360$ s in minutes | |
| $330$ min in hours |
You can convert times. Tell someone why 90 minutes is 1.5 hours rather than 0.9 hours.
18. Your turn: is 90 minutes 0.9 hours or 1.5 hours?, step 2
$90 > 60, \text{ so more than } 1\ \text{h}$
That rules out 0.9 at once.
18. Your turn: is 90 minutes 0.9 hours or 1.5 hours?, step 3
$90 \div 60 = 1.5\ \text{h}$
One hour and a half.