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Chapter 1: Problem 97

In the following exercises, determine if each is an expression or an equation. $$9 路 6 = 54$$

Short Answer

Expert verified
It is an equation.

Step by step solution

01

Understand the Definitions

An expression is a mathematical phrase that can contain numbers, variables, and operation symbols. It does not have an equality sign (=). An equation is a mathematical statement that asserts the equality of two expressions, and it must contain an equality sign (=).
02

Identify the Components

Examine the given mathematical statement: 9 路 6 = 54. It has numbers (9, 6, and 54), an operation symbol (multiplication: 路), and an equality sign (=).
03

Determine if It Is an Expression or an Equation

Since the statement contains an equality sign (=) and shows that two expressions are equal (9 路 6 and 54), it is an equation.

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Key Concepts

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

Expressions
In mathematics, an expression is a combination of numbers, variables, and operation symbols arranged in a meaningful way. Expressions do not have an equality sign, which means they do not assert that one side equals another. For example, the mathematical expression 3 + 4 simply shows the sum of 3 and 4. Expressions can be more complex and include variables too, such as 2x - 5 . Here are some key points about expressions:
  • They can be simplified or evaluated.
  • They do not show any relationship or comparison between two quantities.
  • They often form parts of larger equations.
Understanding expressions is essential because they are the building blocks of more complex mathematical concepts and statements.
Equality Sign
The equality sign = is a fundamental symbol in mathematics. It is used to show that two expressions are equal in value. The presence or absence of an equality sign is what distinguishes an equation from an expression. For instance, in the equation 9 路 6 = 54 , the equality sign asserts that the product of 9 and 6 is equal to 54. Here are some important facts about the equality sign:
  • It indicates that the values on either side of it are the same.
  • It is a crucial component for forming equations.
  • Understanding its role helps in solving mathematical problems and understanding relationships between quantities.
Mastering the concept of the equality sign is vital for progressing in algebra and higher-level mathematics.
Mathematical Statement
A mathematical statement is a declarative sentence that is either true or false. It often involves expressions and can be an equation when it includes an equality sign. In the given example, 9 路 6 = 54 , the mathematical statement asserts a fact that can be verified. Statements like these are fundamental in reasoning and problem-solving. Key properties of mathematical statements include:.
  • They can be simple or complex.
  • They provide the basis for proofs and logical reasoning.
  • In equations, they show a balanced relationship between two sides.
Being able to analyze and understand mathematical statements is crucial for any student trying to master the subject.

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Most popular questions from this chapter

Helen bought a 24-pound turkey for her family's Thanksgiving dinner and wants to know what time to put the turkey in to the oven. She wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey: (a) First, by multiplying \(24 \cdot 20\) to find the total number of minutes and then multiplying the answer by \(\frac{1}{60}\) to convert minutes into hours. (b) Next, by multiplying \(24\left(20 \cdot \frac{1}{60}\right)\). (C) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \((24 \cdot 20) \frac{1}{60}, \quad\) and \(\quad(b),\) where you multiplied \(24\left(20 \cdot \frac{1}{60}\right),\) should be equal?

Trader Joe's grocery stores sold a bottle of wine they called "Two Buck Chuck" for $$\$ 1.99 .\( They sold a case of 12 bottles for \)\$ 23.88\(. To find the cost of 12 bottles at \)\$ 1.99,\( notice that 1.99 is \)2-0.01\( (a) Multiply 12(1.99) by using the distributive property to multiply \)12(2-0.01)$$. (b) Was it a bargain to buy "Two Buck Chuck" by the case?

Convert the units. Lynn's cruise lasted 6 days and 18 hours. Convert the time to hours.

Simplify using the distributive property. $$ u(v-10) $$

Convert the units. Lynn's cruise lasted 6 days and 18 hours. Convert the time to hours.
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