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Chapter 2: Problem 25

Determine if each is an expression or an equation. \(5 \cdot 4+3\)

Short Answer

Expert verified
Expression

Step by step solution

01

Identify the Components

Look at the problem: the expression given is \(5 \times 4 + 3\). Identify the different parts of the statement.
02

Check for Equal Signs

Notice if there is an equal sign '=' in the statement. An equation will have an '=' sign, whereas an expression will not.
03

Determine the Category

Since there is no '=' sign in \(5 \times 4 + 3\), this indicates it is an expression and not an equation.

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Key Concepts

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

math expressions
A math expression is a combination of numbers, variables, and operators (such as +, -, *, /) that represent a value. Unlike equations, expressions do not contain equal signs. An example of a math expression is\(5 \times 4 + 3\) from the exercise. Expressions can be as simple as a single number or as complex as a polynomial.
Here are some key points about math expressions:
  • They do not have an equal sign.
  • They can be simplified or evaluated (i.e., we can perform the arithmetic operations).
  • They represent a single value once simplified.
For instance, in the expression \(5 \times 4 + 3\), you can simplify it to \(20 + 3 = 23\). The meaning remains the same: a single value calculated from the given numbers and operations.
math equations
Math equations are statements that show the equality between two expressions by using an equal sign '='. They are like a balance, where what is on one side of the '=' must be equal to what is on the other side. Equations are used to find unknown values by solving them.
Consider some characteristics of math equations:
  • They always include an equal sign.
  • They can have one or more variables.
  • Solving an equation means finding the value(s) of the variable(s) that make the equation true.
For example, the equation \(2x + 3 = 7\) can be solved by isolating x, giving us \(x = 2\). This process involves logical steps to keep the balance on both sides of the equation.
identifying expressions
Identifying expressions involves looking at a mathematical statement and determining whether it contains an equal sign or not. To decide if a given statement is an expression or an equation, you can follow these simple steps:
Step 1: Identify the Components
  • Look at the statement and identify the parts like numbers, variables, and operators.
  • In our exercise example, look at \(5 \times 4 + 3\).
Step 2: Check for Equal Signs
  • Scan the statement for an '='.
  • An absence of '=' indicates an expression. In our example, there is no '=', so it's an expression.
These steps help differentiate whether you are working with expressions or equations, simplifying your understanding of math problems.

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Most popular questions from this chapter

In the following exercises, find the prime factorization of each number. $$ 84 $$

In the following exercises, translate each English sentence into an algebraic equation and then solve it. Find the prime factorization of 1080 .

In the following exercises, using the divisibility tests, determine whether each number is divisible by \(2,\) by \(3,\) by \(5,\) by \(6,\) and by 10. $$ 420 $$

In the following exercises, solve each equation using the addition property of equality. $$ f-55=123 $$

In the following exercises, solve each equation using the subtraction property of equality. $$ 116=q+79 $$
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