Problem 29 - Prealgebra

Question

Write a numerical expression for each verbal phrase. nine multiplied by five

Step-by-Step Solution

Answer

The numerical expression is \(9 \times 5 = 45\).

Step 1: Identify the Numbers

The verbal phrase 'nine multiplied by five' includes the numbers 9 and 5. These numbers will be part of our numerical expression.

Step 2: Identify the Operation

The word 'multiplied by' in the phrase indicates the mathematical operation of multiplication.

Step 3: Construct the Expression

Combine the numbers and the operation to form the expression. Since we are multiplying 9 by 5, the expression is written as \(9 \times 5\).

Step 4: Simplify the Expression

Calculate the result of the expression by performing the multiplication: \(9 \times 5 = 45\).

Key Concepts

Understanding Mathematical Operations

Mathematical operations are at the core of arithmetic calculations. They include basic operations such as addition, subtraction, multiplication, and division. In the exercise, we focused on multiplication, one of the key operations. Each operation has symbols designated to represent them in numerical expressions. For example, the plus sign (+) symbolizes addition, and the multiplication sign (×) symbolizes multiplication.
When dealing with mathematical operations, recognizing these symbols is essential for forming correct expressions from verbal descriptions. Understanding these basics can simplify many problems and open doors to more complex mathematical concepts.

The Role of Multiplication

Multiplication is a mathematical operation that signifies repeated addition. Instead of adding the same number multiple times, you can multiply it by a specific number. For example, in the problem 'nine multiplied by five', you are essentially adding the number 9 five times: 9 + 9 + 9 + 9 + 9.
With multiplication, we express this more efficiently as \(9 \times 5\). Multiplication is a fundamental operation and is often used to simplify larger addition problems. It is important to become comfortable with this operation because it plays a critical role in problem-solving across various areas of mathematics and science.

Deciphering Verbal Phrases

Verbal phrases in mathematics are descriptions that outline numerical operations using words instead of symbols or numbers. Being able to translate verbal phrases into numerical expressions is a valuable skill in problem solving. In our example, 'nine multiplied by five' uses words to describe a simple multiplication operation.
To successfully turn verbal phrases into usable mathematical expressions, follow these steps:

• Identify key numbers and terms.
• Determine the operation based on the verbal cue ('multiplied by' indicates multiplication).
• Translate these elements into a formal numerical expression like \(9 \times 5\).

Learning to decode verbal phrases can greatly enhance your ability to tackle word problems effectively.

Approach to Problem Solving

Problem-solving in mathematics involves a systematic approach to finding solutions. It's important to follow a structured path when faced with a problem in order to reach a correct solution. The solution to the verbal phrase "nine multiplied by five" highlights this process well.
Here’s a step-by-step manner of approaching similar problems:

• Break down the problem into identifiable numbers and operations (such as identifying the numbers 9 and 5 and the operation 'multiplied by').
• Formulate the numerical expression using mathematical operations identified (e.g., \(9 \times 5\)).
• Solve the expression by performing the required operation (multiply 9 by 5 to get 45).

By understanding these steps and practicing them, you develop a solid framework for addressing mathematical challenges, thus making problem-solving easier and more efficient.