Time and Temperature

Time and temperature are two measurements you encounter constantly, from planning your daily schedule to checking the weather forecast. Unlike length or weight, time uses a base-60 system (60 seconds in a minute, 60 minutes in an hour) rather than base-10, which makes arithmetic with time a bit different. Temperature conversions between Fahrenheit and Celsius require specific formulas. This page covers both.

Time Units and Conversions

Here are the standard time relationships:

To convert from a larger time unit to a smaller one, multiply. To convert from a smaller unit to a larger one, divide.

Adding and Subtracting Time

When adding or subtracting times, work with hours and minutes separately. If the minutes exceed 60, carry over to hours. If subtracting and you do not have enough minutes, borrow 1 hour (which gives you 60 extra minutes).

Adding time:

$\text{Add hours to hours, minutes to minutes. If minutes} \geq 60, \text{ carry 1 hour.}$

Subtracting time:

$\text{Subtract minutes from minutes. If not enough, borrow 1 hour} = 60 \text{ minutes.}$

Elapsed Time

Elapsed time is the amount of time that passes between a start time and an end time:

$\text{Elapsed time} = \text{End time} - \text{Start time}$

When working across AM and PM, it often helps to count forward in stages: first to the next full hour, then by complete hours, then any remaining minutes.

Temperature Conversion Formulas

The two common temperature scales are Fahrenheit (used in the US) and Celsius (used in most of the world and in science).

Fahrenheit to Celsius:

$C = \frac{5}{9}(F - 32)$

Celsius to Fahrenheit:

$F = \frac{9}{5}C + 32$

Key reference points:

Worked Examples

Example 1: Converting Hours to Minutes

Convert 3 hours and 45 minutes to total minutes.

First convert the hours: $3 \times 60 = 180$ minutes.

Then add the remaining minutes: $180 + 45 = 225$ minutes.

3 hours 45 minutes = 225 minutes.

Example 2: Adding Time

A flight departs at 10:48 AM and lasts 2 hours and 35 minutes. What time does it arrive?

Add the hours: $10 + 2 = 12$.

Add the minutes: $48 + 35 = 83$ minutes.

Since 83 minutes is more than 60, carry over: $83 - 60 = 23$ minutes, and add 1 hour.

$12 + 1 = 1 \text{ (PM)}, \quad 23 \text{ minutes}$

The flight arrives at 1:23 PM.

Example 3: Finding Elapsed Time

A shift starts at 7:15 AM and ends at 3:40 PM. How long is the shift?

Count from 7:15 AM to 3:15 PM: that is exactly 8 hours.

Then add the remaining 25 minutes (from 3:15 to 3:40).

Elapsed time: 8 hours and 25 minutes.

Example 4: Fahrenheit to Celsius

Convert 86 F to Celsius.

Apply the formula:

$C = \frac{5}{9}(86 - 32) = \frac{5}{9}(54) = \frac{270}{9} = 30$

86 F = 30 C.

Example 5: Celsius to Fahrenheit

A weather report says it is 15 C outside. What is that in Fahrenheit?

Apply the formula:

$F = \frac{9}{5}(15) + 32 = \frac{135}{5} + 32 = 27 + 32 = 59$

15 C = 59 F.

Practice Problems

Solve each problem before checking the answer.

Key Takeaways

• Time uses a base-60 system: 60 seconds per minute and 60 minutes per hour.
• When adding time, carry over if minutes reach 60 or more. When subtracting, borrow 1 hour as 60 minutes if needed.
• Elapsed time is found by subtracting the start time from the end time, counting carefully across AM/PM boundaries.
• Fahrenheit to Celsius: $C = \frac{5}{9}(F - 32)$.
• Celsius to Fahrenheit: $F = \frac{9}{5}C + 32$.
• Memorize key reference points (water freezes at 32 F / 0 C, boils at 212 F / 100 C) to sanity-check your conversions.

Return to Arithmetic for more foundational math topics.