Problem 4 - Prealgebra

Question

A use the tables of conversion factors given in this section and other sections in this chapter to make the following conversions. (Round your answers to the nearest hundredth.) [Example 1] 4 hours 40 minutes to a. Minutes b. Hours

Step-by-Step Solution

Answer

4 hours 40 minutes is 280 minutes or 4.67 hours.

Step 1: Convert Hours to Minutes

First, we need to convert the 4 hours into minutes. We know that 1 hour is 60 minutes. Therefore, for 4 hours, we have: \[ 4 \times 60 = 240 \text{ minutes} \]

Step 2: Add Additional Minutes

Next, we add the remaining 40 minutes to the 240 minutes we calculated in Step 1. \[ 240 + 40 = 280 \text{ minutes} \] Thus, 4 hours and 40 minutes equals 280 minutes.

Step 3: Convert Minutes to Hours in Decimal Form

Now we convert the total minutes back to hours in decimal form. Since 1 hour is 60 minutes, we divide the total minutes by 60:\[ \frac{280}{60} \approx 4.67 \text{ hours} \]Rounding to the nearest hundredth gives 4.67 hours.

Key Concepts

Conversion Factors

Conversion factors are essential for transforming units from one measurement to another. They act like multipliers or dividers that adjust your quantity from one unit to another. For example, when converting from hours to minutes, we use the conversion factor of 60 because there are 60 minutes in one hour. Imagine conversion factors like bridges connecting two worlds, allowing you to move seamlessly from minutes to hours or vice versa.

• Use the conversion factor to multiply or divide your initial value.
• Be sure to set up your equation so units cancel out, leaving you with your desired unit.
• Examine your final units; if it matches your target unit, you've applied the conversion factor correctly.

Soon, this becomes second nature, and you'll effortlessly move between units with confidence.

Minutes to Hours

Converting minutes to hours is a common requirement in time management and planning. The idea is simple but extremely useful. Remember that there are 60 minutes in an hour.
To convert from minutes to hours, simply divide the total number of minutes by 60. If you have a specific time expressed in minutes and need it in hours, perform this division.
For example, converting 120 minutes:

• Divide 120 by 60 to get 2 hours: \[ \frac{120}{60} = 2 \text{ hours} \]

Keep in mind that if the number of minutes isn't a direct multiple of 60, you'll end up with a decimal representing the fraction of an hour. This is why understanding decimal form conversion is helpful.

Decimal Form Conversion

Decimal form conversion allows us to express fractional parts of hours in a more understandable and usable form. Instead of saying "4 hours and 40 minutes," decimal notation condenses this into a single number, such as "4.67 hours."
To achieve this, after converting minutes to hours, take any leftover minutes and express them as a fraction of an hour. For instance, if you convert 280 minutes:

• First divide by 60: \[ \frac{280}{60} \approx 4.67 \]
• This result shows 4 full hours and some extra minutes expressed as a decimal, rounded to two decimal places.
• This method maintains precision, especially useful in scheduling or when using calculators and spreadsheets.

Always round your decimal to the nearest hundredth for consistency unless specified otherwise. Understanding this will make time calculations more straightforward and visually clear.