/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 79 Simplify. $$100(75)$$... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 79

Simplify. $$100(75)$$

Short Answer

Expert verified
The simplified result is 7500.

Step by step solution

01

Understand the Problem

The problem requires us to simplify the expression \(100(75)\), which means multiplying \(100\) by \(75\). This is a straightforward multiplication problem.
02

Multiply the Numbers

To find the product of \(100\) and \(75\), we can multiply them directly: \[ 100 \times 75 = 7500 \]Alternatively, break it into smaller parts. Multiply \(100\) by \(75\) in two steps: First, calculate \(100 \times 70 = 7000\), then calculate \(100 \times 5 = 500\), and finally add the results: \[ 7000 + 500 = 7500 \]
03

Verify the Solution

Re-checking the calculations, we find that the multiplication \(100 \times 75 = 7500\) is correctly computed, confirming our solution is accurate.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Simplification
Simplification in mathematics often involves reducing a complex expression to its simplest form. In our exercise, simplifying the expression \(100(75)\) means we need to express it in its most straightforward form, which is carried out by performing the multiplication. Simplification helps to make problems easier to solve and understand. It often means reducing the size or complexity of a mathematical expression while retaining its original value. By breaking down larger calculations into smaller parts, you can confirm the result is the simplest form of your expression.
Breaking Down the Product
When we talk about the product in mathematics, we're referring to the result you get when you multiply numbers together. In this exercise, the term "product" applies to multiplying 100 and 75.

The core task here is finding the product by multiplying directly or by breaking down the multiplication into simpler steps. Here are some steps to better grasp:
  • Use direct multiplication to quickly get the product: \( 100 \times 75 \).
  • Alternatively, simplify the task by breaking it into parts: \(100\times(70 + 5)\) which becomes \(100\times 70\) and \(100\times 5\).
  • After breaking down, add the two products: 7000 and 500, resulting in 7500.
This approach not only simplifies the multiplication but also aids in verifying the result by confirming each step independently.
Understanding Arithmetic Computation
Arithmetic computation refers to basic mathematical operations like addition, subtraction, multiplication, and division. In this exercise, our focus is on multiplication, a fundamental arithmetic computation. Multiplication helps us find the total number of items when we have groups of the same size.

Performing the arithmetic computation of \(100\times 75\) involves a simple yet crucial process:
  • Determine the factors to multiply, in our case 100 and 75.
  • Choose a method to multiply, whether directly or by breaking into parts, based on what seems easiest.
  • As seen, dividing it into more manageable parts or carrying it out as a single step can both be effective solutions.
These computations are essential for efficient problem-solving in various mathematical tasks, enhancing both speed and accuracy.

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Most popular questions from this chapter

At 11: 00 in the morning in Superior, Wisconsin, Jim notices the temperature is 15 degrees below zero Fahrenheit. Write this temperature as a negative number. At noon it has warmed up by 8 degrees. What is the temperature at noon?

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$33-(-22)-66$$

Find the wind chill temperature if the thermometer reads \(10^{\circ} \mathrm{F}\) and the wind is blowing at 25 miles per hour.

Tracking Inventory By definition, inventory is the total amount of goods contained in a store or warehouse at any given time. It is helpful for store owners to know the number of items they have available for sale in order to accommodate customer demand. This table shows the beginning inventory on May 1 st and tracks the number of items bought and sold for one month. Determine the number of items in inventory at the end of the month. $$\begin{array}{|llll|} \hline \text { Dife } & \text { Uranstation } & \begin{array}{c} \text { What whires of } \\ \text { Thite sysiblity } \end{array} & \begin{array}{l} \text { Which of } \\ \text { thits sold } \end{array} \\ \hline \text { May 1 } & \text { Beginning Inventory } & 400 & \\\ \text { May 3 } & \text { Purchase } & 100 & \\ \text { May 8 } & \text { Sale } & & 700 \\ \text { May 15 } & \text { Purchase } & 600 & \\ \text { May 19 } & \text { Purchase } & 200 & \\ \text { May 25 } & \text { Sale } & &400 \\ \text { May 27 } & \text { Sale } && 300 \\ \text { May 31 } & \text { Ending Inventory } & & \\ \hline \end{array}$$

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$-10-1+16$$
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