Question

Given that one gross \(=144\) items, how many pencils are contained in 6 gross?

Short answer

There are 864 pencils in 6 gross.

Step-by-step solution

Write down the given information

We are given that 1 gross \(=144\) items (pencils in this case) and we need to find how many pencils are in 6 gross.

Set up the multiplication

To find the total number of pencils in 6 gross, multiply 6 by the number of pencils in 1 gross (144). \[6 \times 144\]

Perform the multiplication

Multiply 6 by 144 to find the total number of pencils in 6 gross. \[6 \times 144 = 864\]

Write the final answer

There are 864 pencils in 6 gross.

Key concepts

Arithmetic Calculations

Arithmetic calculations are the foundation of math and a crucial skill in daily life. Specifically, multiplication is one of the core arithmetic operations, alongside addition, subtraction, and division. In the text. Multiplication involves the combining of equal groups to find a total amount. Think of it as repeated addition. For instance, when we say '6 times 144', we are adding 144 together 6 times.

To improve understanding, visualization can be helpful. Imagine you have 6 boxes and each box contains 144 pencils. How many pencils do you have in total? This is exactly what the multiplication operation helps you to calculate.

Using a step-by-step approach for multiplication helps avoid mistakes, especially with larger numbers. Begin by writing down the numbers to be multiplied, one underneath the other, aligning the units, tens, hundreds, etc. Then, using the multiplication rules you've learned, multiply each digit accordingly and add up the partial results to get the final answer. It's a systematic process that, once understood, makes solving math problems much easier.

Math Problem Solving

Math problem solving is a critical skill that allows us to work through various types of mathematical challenges methodically. In our example, we approach the problem by first understanding what is given and what we need to find out. Breaking down the problem into steps helps us track our progress and ensure that each part of the problem is correctly solved.

In math problem solving, one must also be vigilant in the use of mathematical operations according to the context of the problem. The step-by-step process involves identifying the correct operation (multiplication in this case), executing it with precision, and checking to make sure the answer is reasonable.

Furthermore, enhancing student comprehension can be achieved by encouraging them to write down their reasoning and calculations, reinforcing the idea that math is not about memorization but understanding the 'why' and the 'how'. It's also useful to practice with different problems to gain familiarity and build confidence in their problem-solving abilities.

Units of Measurement

Understanding units of measurement is essential in interpreting real-world problems and expressing quantities clearly. In our exercise, 'gross' is a unit of measurement that is less commonly used but important in specific contexts, such as wholesale or manufacturing. A gross represents a group of 144 items.

In daily life, we use many standard units of measurement such as meters for distance, kilograms for weight, and seconds for time. When solving problems involving units of measurement, it's crucial to remain consistent with the units and convert if necessary to avoid errors in the result.

For students, grasping the concept of units and how they relate to each other can make math problems much more accessible. It can be helpful to explore real-world scenarios where different units of measurement are used, as well as practicing conversions between units. For example, knowing how to convert from gross to dozens or to individual items, as they may encounter such a need in different situations.