Problem 7 Classify each of the following a... [FREE SOLUTION]

Chapter 1: Problem 7

Classify each of the following as either an expression or an equation. $$ 4 a-5 b $$

Short Answer

Expert verified

Expression.

Step by step solution

Identify Terms and Operators

Identify the different terms and operators given in the mathematical statement. In this case, the terms are 4a and -5b, and the operator is a minus sign (-).

Look for an Equal Sign

Check if there is an equal sign (=) present in the statement. This sign indicates that the mathematical statement is an equation, because it shows equality between two expressions.

Classify the Statement

Since there is no equal sign (=) in the given statement, it does not express equality. Therefore, the mathematical statement is an expression.

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Key Concepts

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

Classifying Equations and Expressions

Mathematical statements can either be equations or expressions. Understanding the difference between the two is crucial.

- **Expressions** are combinations of numbers, variables, and operators without an equal sign. For example, the statement $ 4a - 5b $ is an expression. It indicates a value but not a relation or equality.

- **Equations**, however, always contain an equal sign (=), indicating that two expressions are equal to each other. For instance, $ 4a - 5b = 10 $ is an equation because it shows that the expression $ 4a - 5b $ is equal to 10.

Remember, the presence of the equal sign is what differentiates an equation from an expression.

Terms and Operators

To break down any mathematical statement, it's essential to identify its components: terms and operators.

- **Terms** are the distinct parts of an expression or equation separated by + or - signs. In the expression $ 4a - 5b $, $ 4a $ and $-5b $ are the terms.

- **Operators** are the symbols that show the operations to be performed, such as +, -, *, and /. In $ 4a - 5b $, the minus sign (-) is the operator.

Understanding these components helps simplify and solve mathematical problems effectively.

Identifying Equal Signs

One of the most straightforward yet essential steps in classifying a mathematical statement is checking for an equal sign.

The equal sign (=) indicates that two expressions on either side are equivalent. For example:

- In the equation $ 3x + 2 = 14 $, the equal sign tells us that $ 3x + 2 $ is equal to 14.

- If the statement lacks an equal sign like $ 4a - 5b $, it is an expression, not an equation.

This simple check can help you quickly classify and understand the nature of any mathematical statement.

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91影视

Classify each of the following as either an expression or an equation. $$ 4 a-5 b $$

Short Answer

Step by step solution

Identify Terms and Operators

Look for an Equal Sign

Classify the Statement

Key Concepts

Classifying Equations and Expressions

Terms and Operators

Identifying Equal Signs

One App. One Place for Learning.

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