Problem 68 - Prealgebra

Question

Write a numerical expression for each verbal phrase. the product of ten and thirty

Step-by-Step Solution

Answer

The expression is \(10 \times 30\).

Step 1: Identify the Operation

The phrase 'the product of' indicates a multiplication operation. This means we will be multiplying two numbers together.

Step 2: Identify the Numbers

The numbers given in the phrase are 'ten' and 'thirty'. So, these are the numbers we will use in the multiplication operation.

Step 3: Write the Numerical Expression

Translate the verbal phrase to a numerical expression. The expression for 'the product of ten and thirty' is written as: \( 10 \times 30 \).

Key Concepts

Understanding Verbal Phrases in Math

In mathematics, verbal phrases are sentences that use words to describe mathematical operations and numbers. These phrases need to be translated into numerical expressions. Understanding verbal phrases is essential since many math problems, especially word problems, are presented in this form. For instance, the phrase "the product of ten and thirty" is a verbal phrase that signals a mathematical operation. In this case, "product" indicates multiplication.
To break down such phrases, focus on keywords like the following:

• Product which means multiplication.
• Sum which indicates addition.
• Difference suggesting subtraction.
• Quotient referring to division.

By identifying these keywords, you can convert the verbal cues into mathematical expressions effectively.

Basics of Multiplication

Multiplication is a basic arithmetic operation that is essentially repeated addition. It is symbolized by the sign \( \times \). When you multiply, you are adding a number to itself a certain number of times. For instance, the expression \( 10 \times 30 \) means you are adding 10 to itself 30 times (or vice versa).
This arithmetic operation has several properties, making it highly versatile in computations:

• Commutative Property: The order in which you multiply two numbers does not matter; \( a \times b = b \times a \).
• Associative Property: When three or more numbers are multiplied, the product is the same no matter how the numbers are grouped; \( (a \times b) \times c = a \times (b \times c) \).
• Distributive Property: Multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the products; \( a \times (b + c) = (a \times b) + (a \times c) \).

Understanding multiplication lays the foundation for advanced math topics.

Exploring Prealgebra Concepts

Prealgebra serves as an introduction to algebra, providing the basic concepts and skills needed for algebraic thinking. It focuses on familiarizing students with arithmetic involving whole numbers, fractions, and decimals. Another crucial element in prealgebra is understanding how to write and interpret numerical expressions like \( 10 \times 30 \).
In prealgebra, students learn to:

• Recognize patterns and understand mathematical relationships.
• Translate verbal phrases into mathematical expressions.
• Understand and apply properties of operations, such as the commutative and associative properties.

These skills not only improve numeracy but also lay the groundwork for solving algebraic equations, making prealgebra an essential educational stage.