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Chapter 1: Problem 10

Classify each of the following as either an expression or an equation. $$ 12-4 x y $$

Short Answer

Expert verified
Expression.

Step by step solution

01

Identify the given mathematical content

Look at the given content: \(12 - 4xy\).
02

Understand the difference between an expression and an equation

An equation will have an equals sign \(=\), indicating that two expressions are equal. An expression does not include an equals sign.
03

Check for the equals sign

Examine \(12 - 4xy\) and see if there is an equals sign. Since there is no equals sign present, it means this is not an equation.
04

Classify the given content

Since \(12 - 4xy\) does not have an equals sign, classify it as an expression.

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Key Concepts

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

Mathematical Expression
A mathematical expression consists of numbers, variables, and operators (like +, -, *, and /) arranged in a meaningful way. It does not include an equal sign.
An example of an expression is: \( 12 - 4xy \)
This expression can be simplified or evaluated, but it never states that one segment is equal to another.
In our exercise, the term \(12 - 4xy\) is classified as an expression because it lacks an equals sign.
Mathematical Equation
A mathematical equation consists of two expressions set equal to each other, connected by an equal sign (\(=\)). This equality states that the two expressions on either side of the equals sign are equivalent under certain conditions.
An example of an equation is: \(12 - 4xy = 8\)
In contrast to expressions, equations can often be solved to find the values of the variables that make the equality true.
Equals Sign
The equals sign (\(=\)) is a fundamental symbol in mathematics, used to denote equality. It is a crucial component in equations, serving as the bridge that links two expressions.
For example, in the equation \(12 - 4xy = 8\), the equals sign asserts that the expression \(12 - 4xy\) has the same value as 8.
In our given problem \(12 - 4xy\), the absence of an equals sign helps us determine that it is a mathematical expression, not an equation.
Algebraic Classification
Algebraic classification involves determining whether a given mathematical content is an expression or an equation. This process usually involves looking for the presence of an equals sign.
In our example exercise:
  • We identified the content: \(12 - 4xy\)
  • We understood that an equation must include an equals sign
  • We verified the absence of an equals sign in \(12 - 4xy\)
  • We classified \(12 - 4xy\) as an expression
Using these steps, you can classify any given mathematical content accurately.

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Most popular questions from this chapter

Evaluate using a calculator. $$ 3(m+2 n) \div m, \text { for } m=1.6 \text { and } n=5.9 $$

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$5.5 \overline{5}$$

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