Lesson 4: Solve problems involving mixed units of time.

Property

To add mixed units of time, you can use different strategies such as combining like units, making the next whole unit (decomposition), or using compensation. All valid strategies will lead to the same correct answer.

Examples

Problem: Find the sum of $2$ hours $40$ minutes and $1$ hour $35$ minutes.

• Combining Like Units: Add hours and minutes separately: $(2+1)$ hours $(40+35)$ minutes = $3$ hours $75$ minutes. Since $75$ min = $1$ hr $15$ min, the total is $4$ hours $15$ minutes.
• Making the Next Whole Unit: Take $20$ minutes from $1$ hr $35$ min to complete the hour with $2$ hr $40$ min. This makes $3$ hours. The remaining time is $1$ hr $15$ min. Adding them gives $3$ hours + $1$ hour $15$ minutes = $4$ hours $15$ minutes.
• Compensation: Round $2$ hr $40$ min up to $3$ hours (by adding $20$ min). Add $3$ hours + $1$ hour $35$ minutes = $4$ hours $35$ minutes. Then, subtract the $20$ minutes you added: $4$ hr $35$ min - $20$ min = $4$ hours $15$ minutes.

Explanation

There are several effective methods for adding mixed units of time. You can combine the hours and minutes separately and then regroup, which is similar to the standard addition algorithm. Alternatively, you can use mental math strategies like decomposition (making a whole unit) or compensation (rounding and adjusting). Choosing the best strategy often depends on the specific numbers in the problem and your personal preference.

Property

When subtracting time, you may need to regroup from a larger unit. The key conversions are:

Examples

• Regrouping: To solve $5 \text{ hr } 20 \text{ min} - 2 \text{ hr } 45 \text{ min}$, regroup $1$ hour:

• Compensation: To solve $5 \text{ hr } - 1 \text{ hr } 50 \text{ min}$, subtract $2$ hours, then add back $10$ minutes:

• Decomposition: To solve $4 \text{ hr } 10 \text{ min} - 1 \text{ hr } 30 \text{ min}$, start at $4 \text{ hr } 10 \text{ min}$, subtract $1$ hour to get $3 \text{ hr } 10 \text{ min}$, then subtract $10$ minutes to get $3 \text{ hr}$, and finally subtract the remaining $20$ minutes to get $2 \text{ hr } 40 \text{ min}$.

Explanation

Subtracting mixed units of time often requires regrouping, similar to borrowing in standard subtraction. You can convert one larger unit (like an hour) into its equivalent smaller units (60 minutes) to make subtraction possible. Alternative strategies like compensation involve subtracting a simpler, rounded number and then adjusting the result. You can also use a number line to decompose the subtracted time and subtract it in easier parts.