Question

Change 74 days into weeks and write the remainder in days. A. 10 wk 4 da B. 5 wk 1 da C. 8 wk 3 da D. 9 wk 6 da

Short answer

The correct answer is A. 10 wk 4 da.

Step-by-step solution

Understand the Relationship Between Weeks and Days

First, it is crucial to remember that one week equals seven days. This relationship will be used to convert total days into weeks and days by dividing.

Divide Total Days by Days Per Week

Take the total number of days, which is 74, and divide it by 7 (the number of days in a week). \[74 \,\div\, 7 = 10 \,\text{remainder} \,4\] This division tells us that there are 10 full weeks in 74 days, with a remainder of 4 days.

Write the Conversion Result

Combine the result from the division: 10 full weeks and the 4-day remainder. This gives us the final conversion as 10 weeks and 4 days.

Key concepts

Division

To understand converting 74 days into weeks, the concept of division plays a fundamental role. Division is a mathematical operation where we split a number into equal parts. Here, we divide 74 days by 7 days (the number of days in a week). This action helps us determine how many whole weeks can fit into 74 days. Performing the division, \[74 \,\div\, 7 = 10 \,\text{whole weeks}\] shows us that we can fit 10 weeks into 74 days. This result tells us the full weeks contained within our total days.

Remainder

Once we perform division to convert days into weeks, a remainder often comes into play. It is the leftover part of the division when a number doesn't divide evenly. In our example,\[74 \,\div\, 7 = 10 \,\text{remainder} \,4\] means that 74 divided by 7 results in 10 full weeks and 4 extra days. The remainder here is 4, telling us about the days that don't complete another full week. Understanding the remainder is key to time conversions and many other applications in mathematics.

Time Conversion

Time conversion involves changing the units of time to another form while keeping the overall duration the same. When converting days to weeks, knowing that a week consists of 7 days is essential. By converting units,

• We gain a clearer understanding of time durations in context.
• We make event planning and scheduling easier.

In our example, converting 74 days to weeks helps us visualize the period as 10 weeks and 4 days instead of counting daily, which is often more convenient.

Arithmetics

Arithmetics is the branch of mathematics dealing with numbers and basic operations: addition, subtraction, multiplication, and division. It forms the bedrock for calculations, including the conversion of days to weeks. In this process:

• We perform division to find out how many times one quantity (days in a week) fits into another (total days).
• We use subtraction to understand remainders (e.g., after subtracting 70 from 74, 4 remain).

Arithmetics ensures accuracy and clarity in time conversions and many other everyday scenarios.

Prealgebra

Prealgebra is a foundational level of mathematics that prepares students for algebra. It covers essential concepts such as basic operations and number manipulation, including division and remainders. In the context of our day-to-week conversion:

• Prealgebra skills help students understand time intervals effectively.
• They develop strategies for solving problems involving units of time.

Focusing on these principles in prealgebra ensures a solid base for more complex mathematical learning and practical applications like time conversion.