Question

If a pencil manufacturer produces 288,125 pencils, how many gross of pencils can be sold? (A gross is 144 pencils.)

Short answer

2000 gross of pencils can be sold.

Step-by-step solution

Understanding the Question

We need to determine how many 'gross' of pencils are in 288,125 pencils. A 'gross' refers to a unit of measure equal to 144 items. So, we start by understanding that we need to divide the total number of pencils by 144.

Setting up the Division

To find the number of gross, we perform the division of the total pencils by the number in a gross. The operation we'll set up is: \( \frac{288,125}{144} \).

Performing the Division

Now, we calculate \( 288,125 \div 144 \). Divide 288,125 by 144 to find the number of complete gross units that can be formed.

Calculating the Result

Perform the division: \( 288,125 \div 144 = 2000.86805 \). We only consider the whole number part of the division since you cannot sell a part of a gross in completed inventory terms. This results in 2000 complete gross of pencils.

Key concepts

Unit Conversion

Unit conversion is a critical skill when it comes to solving mathematical problems related to different measurement systems. In this exercise, we dealt with the concept of a "gross," which is a less common unit of measure but essential in certain contexts, such as bulk sales or production inventories.

A gross is equivalent to 144 items. So, understanding unit conversion here involves knowing that you can convert total items into groups or units of 144. This can simplify large number manipulations, which are common in commerce and larger operations.

Why is this important? Well, in real-world applications, you might need to order materials, or sell products in bulk, such as pencils in this case. By converting to the appropriate unit, understanding becomes easier and practical decisions can be more effectively made. Knowing that a gross equals 144 items allows you to swiftly translate between individual item quantities and bulk measurements.

Problem-Solving Steps

Approaching problems methodically is crucial in obtaining accurate results. Let's see how breaking down the problem into steps helped solve this exercise.

- **Understanding the Question:** The first step involves recognizing what we need to find. Here, it's about determining the total number of "gross" in a given number of pencils. Understanding that a gross equals 144 pencils is essential.

- **Setting Up the Division:** With a solid grasp of the question, we proceeded to set up the problem for division. In this case, we need to divide the total pencils by the size of each gross. This translates into writing the operation as \( \frac{288,125}{144} \).

- **Performing the Division:** With everything set in place, calculating the division gives us the number of complete "gross" that can be made from the pencils available. This involves actually performing the division operation.

Breaking complex questions down into these understandable and manageable steps is beneficial because it turns an overwhelming task into a series of smaller, more manageable tasks. This strategy can be applied beyond just mathematical problems, into various real-world challenges.

Whole Number Division

Whole number division is crucial when the result must be in complete units without fractions. At times, especially in contexts such as inventory and sales, only whole units are significant. In our exercise, only whole "gross" of pencils can be sold, meaning we focus solely on the whole number result of our division.

When we calculated \( 288,125 \div 144 \), the result was 2000.86805.

However, since you can't sell a fraction of a gross, only the whole part—2000 in this scenario—was taken as our answer.

Why is whole number division important? It ensures that calculations remain practical in real-life applications, where partial results cannot be used. Furthermore, focusing on the whole number component simplifies decision-making in supply chains and sales. Remember that rounding should not be a factor here, as we need complete groups for transactions.