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Chapter 1: Problem 60

Write the following expressions in words, using the word product. \((5)(6)=30\)

Short Answer

Expert verified
The product of 5 and 6 is 30.

Step by step solution

01

Identify the Factors

We begin by identifying the numbers that are multiplied together in the given expression. Here, the numbers are 5 and 6.
02

Express the Multiplication Using Words

Using the word "product," express the multiplication of the numbers identified in the previous step. The expression translates to "the product of 5 and 6."
03

State the Result

Finally, state the result of the multiplication in a complete sentence. We write "The product of 5 and 6 is 30."

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Key Concepts

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

Factors
Factors are the numbers or quantities being multiplied together to get a new number. When solving problems, understanding factors is critical as they are the building blocks of multiplication. For instance, in the equation \((5)(6) = 30\), 5 and 6 are the factors. These numbers combine to create a product, which is 30 in this example.
Understanding factors helps solve a multitude of mathematical problems, and aids in breaking down complex equations into smaller, manageable parts. Here's why factors are important:
  • They simplify algebraic equations by identifying common elements.
  • Enable the decomposition of complex numbers into simpler forms for easier calculations.
  • Help in understanding division, as every factor of a number divides that number without leaving a remainder.
Recognizing and working with factors is essential in improving mathematical agility and precision.
Multiplication
Multiplication is one of the basic operations of arithmetic, often thought of as repeated addition. It involves adding a number to itself a specific number of times. In our example, \(5\) repeated \(6\) times, or \(6\) repeated \(5\) times, results in the product \(30\).
The multiplication process can be illustrated in various ways:
  • Number line: Imagine hopping \(5\) spaces \(6\) times on a number line and landing on \(30\).
  • Arrays: Picture arranging objects in \(5\) rows of \(6\) objects each, creating a total of \(30\).
Multiplication is crucial in everyday mathematics and serves as a foundation for more complex operations like exponents and algebra. It simplifies operations that would otherwise involve adding numerous times.
Mathematical Expressions
Mathematical expressions are combinations of numbers and symbols representing a value or relationship. They are a core part of mathematics, enabling the representation of complex ideas in a simple, readable format.
In the expression \((5)(6) = 30\), it succinctly shows the operation needed to achieve the result of 30. Here鈥檚 why understanding expressions is important:
  • They convey operations like addition, subtraction, multiplication, and division in a concise language.
  • Simplify complex calculations by breaking them into sequential steps.
  • Enable mathematical reasoning and problem-solving across various fields, such as physics, computer science, and engineering.
Fluency in interpreting and formulating mathematical expressions empowers learners to tackle both simple and complex mathematical challenges with confidence.

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Most popular questions from this chapter

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{l} 12 \\ 34 \\ 56 \\ 78 \\ \hline \end{array}$$

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The application problems that follow may involve more than merely division. Some may require addition, subtraction, or multiplication, whereas others may use a combination of two or more operations. Fitness Walking The guidelines for fitness now indicate that a person who walks \(10,000\) steps daily is physically fit. According to The Walking Site on the Internet, it takes just over \(2,000\) steps to walk one mile. If that is the case, how many miles do you need to walk in order to take \(10,000\) steps? (image cannot copy)

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 36 \\ 46 \\ \hline \end{array}$$

Find the mode and the range for each set of numbers. [Example 20] $$11,27,18,11,72,11$$
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