Time
🎯 In this topic you will
- Convert between time intervals expressed as decimals and mixed units.
⏰ Why Time is Tricky
Calculating times can be tricky because units of time do not usually come in 10s and 100s.
🔢 Time-Related Numbers
Look at each of these numbers. What does each number have to do with time?
60 12 365 30 100 7 366 24
🤔 The Challenge of Time Units
Why do the different units in time make it more tricky to calculate with time?
❓ EXERCISES
1. Copy and complete the table to show times in hours and in hours and minutes.
| Hours | Hours and minutes | Hours | Hours and minutes |
|---|---|---|---|
| $0.1$ hours | $0$ hours and $6$ minutes | $0.8$ hours | |
| $0.2$ hours | $0$ hours and $__$ minutes | $0.9$ hours | |
| $0.3$ hours | $1$ hour | ||
| $0.4$ hours | $1.1$ hours | ||
| $0.5$ hours | $2.2$ hours | ||
| $0.6$ hours | $3.8$ hours | ||
| $0.7$ hours | $4.9$ hours |
👀 Show answer
$0.3$ hours $=$ $0$ hours $18$ minutes
$0.4$ hours $=$ $0$ hours $24$ minutes
$0.5$ hours $=$ $0$ hours $30$ minutes
$0.6$ hours $=$ $0$ hours $36$ minutes
$0.7$ hours $=$ $0$ hours $42$ minutes
$0.8$ hours $=$ $0$ hours $48$ minutes
$0.9$ hours $=$ $0$ hours $54$ minutes
$1$ hour $=$ $1$ hour $0$ minutes
$1.1$ hours $=$ $1$ hour $6$ minutes
$2.2$ hours $=$ $2$ hours $12$ minutes
$3.8$ hours $=$ $3$ hours $48$ minutes
$4.9$ hours $=$ $4$ hours $54$ minutes
2. $4$ children are allowed to share a games console for $5$ hours. They decide to divide the $5$ hours equally between them.
a. How much time does each child get on the games console in hours?
b. Tom says that each child can have $1$ hour and $25$ minutes on the console. Tom is wrong. Explain why Tom is wrong and work out how many hours and minutes each child can have on the console.
👀 Show answer
b. $0.25$ hour $=$ $15$ minutes, not $25$ minutes. So each child gets $1$ hour $15$ minutes.
3. Ten athletes competed in a marathon run. These are their times.
Copy the table.
List the runners in the table from fastest to slowest.
Convert each of their times into hours, minutes and seconds and complete the table with the converted times.
| Runner | Hours | Minutes | Seconds |
|---|---|---|---|
👀 Show answer
$159.1$ minutes $=$ $2$ hours $39$ minutes $6$ seconds
$141.7$ minutes $=$ $2$ hours $21$ minutes $42$ seconds
$182.8$ minutes $=$ $3$ hours $2$ minutes $48$ seconds
$128.65$ minutes $=$ $2$ hours $8$ minutes $39$ seconds
$183.05$ minutes $=$ $3$ hours $3$ minutes $3$ seconds
🧠 Think like a Mathematician
You know that $12.5$ hours is not equal to $12$ hours and $5$ minutes.
Are there any times in hours that use the same digits as the same amount of time in hours and minutes?
Specialise by choosing particular times to check.
Generalise by writing a statement explaining what you have found out.
Follow-up Questions:
Show Answers
- 1: To convert decimal hours to minutes, multiply the decimal part by $60$. For example, $1.2$ hours gives $0.2 \times 60 = 12$ minutes, so it becomes $1$ hour $12$ minutes.
- 2: Usually the digits will not match because $0.1$ hour equals $6$ minutes, not $1$ minute. This means decimal digits do not represent minutes directly.
- 3: A decimal hour represents a fraction of $60$ minutes, so the decimal part must be multiplied by $60$. Therefore the digits after the decimal point rarely match the same number of minutes.