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Questions and Answers
What is the result of evaluating the expression $3x + 5$ when $x = 4$?
What is the result of evaluating the expression $3x + 5$ when $x = 4$?
- 15
- 17 (correct)
- 14
- 12
When comparing the expressions $5x + 2$ and $3x + 8$, what value of $x$ would indicate $5x + 2$ is greater?
When comparing the expressions $5x + 2$ and $3x + 8$, what value of $x$ would indicate $5x + 2$ is greater?
- 3 (correct)
- 1
- 2
- 4
What does the expression $2(x + 5)$ equal when $x = 3$?
What does the expression $2(x + 5)$ equal when $x = 3$?
- 10
- 14
- 12
- 16 (correct)
The expression $4x - 6$ is equal to what when $x = 2$?
The expression $4x - 6$ is equal to what when $x = 2$?
Which of the following keywords indicates subtraction when translating a word problem?
Which of the following keywords indicates subtraction when translating a word problem?
What is the first step in evaluating the expression $x^2 + 2$ for $x = 3$?
What is the first step in evaluating the expression $x^2 + 2$ for $x = 3$?
In the expression $x + 7$ compared to $2x + 3$, what condition must be met for $x + 7$ to be greater?
In the expression $x + 7$ compared to $2x + 3$, what condition must be met for $x + 7$ to be greater?
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Study Notes
Writing Expressions - 5th Grade Study Notes
Evaluating Expressions
- Definition: Finding the value of an expression by substituting numbers for variables.
- Steps to Evaluate:
- Identify the expression and the values of the variables.
- Substitute the values into the expression.
- Follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
- Example: For the expression (3x + 5) with (x = 2):
- Substitute: (3(2) + 5)
- Calculate: (6 + 5 = 11)
Comparing Expressions
- Definition: Determining which expression has a greater value or if they are equal.
- Methods:
- Evaluate both expressions: Substitute the same values for any variables and compute the results.
- Analyze the structure: Look for similarities or differences in the expressions' terms.
- Example: Compare (2x + 3) and (x + 7) for (x = 4):
- Evaluate (2(4) + 3 = 8 + 3 = 11)
- Evaluate (4 + 7 = 11)
- Conclusion: (2x + 3 = x + 7)
Translating Word Problems
- Definition: Converting a word problem into a mathematical expression or equation.
- Common Keywords:
- Addition: sum, more than, increased by
- Subtraction: difference, less than, decreased by
- Multiplication: product, times, of
- Division: quotient, divided by, per
- Steps to Translate:
- Read the problem carefully.
- Identify the quantities involved and the operations required.
- Write the corresponding expression or equation.
- Example: "Twice a number decreased by 5":
- Let the number be (x):
- Expression: (2x - 5)
Evaluating Expressions
- Finding the value of an expression by substituting in variables.
- Steps to evaluate:
- Identify the expression and variable values.
- Substitute values into the expression.
- Follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).
- Example for (3x + 5) when (x = 2):
- Substitute: (3(2) + 5)
- Calculate: (6 + 5 = 11)
Comparing Expressions
- Determining the greater value or equality of expressions.
- Methods to compare:
- Evaluate both expressions by substituting the same variable values.
- Analyze the structure for similarities or differences in terms.
- Example comparing (2x + 3) and (x + 7) when (x = 4):
- Evaluate (2(4) + 3 = 11)
- Evaluate (4 + 7 = 11)
- Conclusion: (2x + 3 = x + 7)
Translating Word Problems
- Converting word problems into mathematical expressions or equations.
- Common keywords:
- Addition: sum, more than, increased by.
- Subtraction: difference, less than, decreased by.
- Multiplication: product, times, of.
- Division: quotient, divided by, per.
- Steps to translate:
- Read the problem carefully.
- Identify the quantities and required operations.
- Write the corresponding expression or equation.
- Example: "Twice a number decreased by 5."
- Let the number be (x).
- Expression: (2x - 5)
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