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Chapter 1: Problem 98

In the following exercises, determine if each is an expression or an equation. $$7 路 9 = 63$$

Short Answer

Expert verified
Equation.

Step by step solution

01

Identify the given statement

Look at the provided mathematical statement: $$7 路 9 = 63$$.
02

Understand the definitions

Recall the definitions of expressions and equations. An expression is a combination of numbers, variables, and operations without an equality sign. An equation is a mathematical statement that asserts the equality of two expressions and includes an equality sign.
03

Analyze the statement

Examine the statement $$7 路 9 = 63$$. Notice it includes an equality sign ($$=$) separating two expressions. $$7 \times 9$$ is on the left side, and $$63$$ is on the right side.
04

Conclusion

Since the statement includes an equality sign and asserts that two expressions are equal, it is an equation.

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Key Concepts

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

Understanding Expressions
An expression in mathematics is a combination of numbers, variables, and operations (such as addition, subtraction, multiplication, and division) that are combined to represent a particular value.
An important characteristic of expressions is that they do not include an equality sign (=).
Here are some key points to remember about expressions:
  • They can include operations like +, -, *, /.
  • They can have variables (such as x, y).
  • They do not state that two things are equal.

For example, the expression 3 + 5 or x - 2 are both valid expressions. Note that there's no assertion of equality in these examples.
Understanding Equations
An equation is a mathematical statement that shows the equality of two expressions.
Equations always include an equality sign (=), which separates the two expressions.
  • Equations state that what鈥檚 on the left side is equal to what鈥檚 on the right side.
  • They include an equality sign.
  • They can be solved to find the value of a variable.

For example, consider the equation 7 路 9 = 63. In this equation:
  • The left side is 7 路 9.
  • The right side is 63.
  • The equality sign shows that 7 路 9 equals 63.
The Importance of the Equality Sign
The equality sign (=) is a fundamental part of an equation.
It indicates that the value on the left side of the sign is equal to the value on the right side.
Without this sign, you wouldn鈥檛 have an equation, and it could just be an expression.
Here鈥檚 what to keep in mind:
  • The equality sign connects two expressions.
  • It asserts that both sides have the same value.
  • It is essential for forming equations.

In the example provided, 7 路 9 = 63, it is the equality sign that turns the statement into an equation.
It reflects the relationship that the product of 7 and 9 is equal to 63.

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