Which Of The Following Phrases Are Expressions? Choose 2 Answers: Choose 2 Answers: (Choice A) 6 − 1 > ℓ {6-1>\ell} 6 − 1 > ℓ A 6 − 1 > ℓ {6-1>\ell} 6 − 1 > ℓ (Choice B) − 6 K = − 8 {-6k=-8} − 6 K = − 8 B − 6 K = − 8 {-6k=-8} − 6 K = − 8 (Choice C) J 9 {j^9} J 9 C J 9 {j^9} J 9 (Choice D, Checked) 1 4 < 3 8 {\dfrac{1}{4}<\dfrac{3}{8}} 4 1 ​ < 8 3 ​ D

In mathematics, an expression is a combination of numbers, variables, and mathematical operations that can be evaluated to produce a value. Expressions are used to represent mathematical relationships and can be used to solve equations, inequalities, and other mathematical problems. In this article, we will explore which of the given phrases are expressions and why.

What is an Expression?

An expression is a mathematical phrase that can be evaluated to produce a value. It consists of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. Expressions can be simple or complex, and they can be used to represent a wide range of mathematical relationships.

Types of Expressions

There are several types of expressions, including:

• Algebraic expressions: These are expressions that contain variables and constants, and are used to represent mathematical relationships.
• Arithmetic expressions: These are expressions that contain numbers and mathematical operations, and are used to represent simple mathematical relationships.
• Trigonometric expressions: These are expressions that contain trigonometric functions such as sine, cosine, and tangent, and are used to represent relationships between angles and side lengths of triangles.

Evaluating Expressions

To evaluate an expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Analyzing the Given Phrases

Now that we have a good understanding of what an expression is and how to evaluate it, let's analyze the given phrases:

Choice A: ${6-1>\ell}$

This phrase is an expression because it contains a mathematical operation (subtraction) and a variable (\ell). However, it is an inequality, not an equation, and it is not a complete expression because it is missing a value for \ell.

Choice B: ${-6k=-8}$

This phrase is an equation, not an expression. An equation is a statement that says two expressions are equal, whereas an expression is a single mathematical phrase that can be evaluated to produce a value.

Choice C: ${j^9}$

This phrase is an expression because it contains a variable (j) and an exponential operation. However, it is a simple expression and does not contain any mathematical operations other than exponentiation.

Choice D: ${\dfrac{1}{4}<\dfrac{3}{8}}$

This phrase is an inequality, not an expression. An inequality is a statement that says one expression is greater than, less than, or equal to another expression, whereas an expression is a single mathematical phrase that can be evaluated to produce a value.

Conclusion

In conclusion, the two phrases that are expressions are:

• Choice A: ${6-1>\ell}$ (although it is an inequality and not a complete expression)
• Choice C: ${j^9}$

The other two phrases are not expressions because they are either equations (Choice B) or inequalities (Choice D).

Discussion

This problem requires the reader to understand the difference between expressions, equations, and inequalities, and to be able to identify which phrases are expressions and why. It also requires the reader to be able to evaluate expressions and to understand the order of operations.

Additional Resources

For more information on expressions and other mathematical concepts, please see the following resources:

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

Final Answer

The final answer is:

• Choice A: ${6-1>\ell}$
• Choice C: ${j^9}$
  Frequently Asked Questions (FAQs) About Expressions =====================================================

In our previous article, we discussed what expressions are and how to identify them. In this article, we will answer some frequently asked questions about expressions to help you better understand this mathematical concept.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical phrase that can be evaluated to produce a value, whereas an equation is a statement that says two expressions are equal. For example, the expression "2x + 3" can be evaluated to produce a value, but the equation "2x + 3 = 5" says that the expression "2x + 3" is equal to the value 5.

Q: Can an expression be a single number?

A: Yes, an expression can be a single number. For example, the expression "5" is a single number and can be evaluated to produce the value 5.

Q: Can an expression contain variables?

A: Yes, an expression can contain variables. For example, the expression "2x + 3" contains the variable x.

Q: Can an expression contain mathematical operations?

A: Yes, an expression can contain mathematical operations such as addition, subtraction, multiplication, and division. For example, the expression "2x + 3" contains the addition operation.

Q: How do I evaluate an expression?

A: To evaluate an expression, you need to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate any expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can an expression be a fraction?

A: Yes, an expression can be a fraction. For example, the expression "1/2" is a fraction and can be evaluated to produce the value 1/2.

Q: Can an expression contain trigonometric functions?

A: Yes, an expression can contain trigonometric functions such as sine, cosine, and tangent. For example, the expression "sin(x)" contains the sine function.

Q: Can an expression contain logarithmic functions?

A: Yes, an expression can contain logarithmic functions such as log and ln. For example, the expression "log(x)" contains the logarithmic function.

Q: Can an expression contain absolute value?

A: Yes, an expression can contain absolute value. For example, the expression "|x|" contains the absolute value function.

Q: Can an expression contain square roots?

A: Yes, an expression can contain square roots. For example, the expression "√x" contains the square root function.

Conclusion

In conclusion, expressions are mathematical phrases that can be evaluated to produce a value. They can contain variables, mathematical operations, and other mathematical concepts such as fractions, trigonometric functions, logarithmic functions, absolute value, and square roots. By understanding expressions, you can better evaluate mathematical problems and solve equations.

Additional Resources

For more information on expressions and other mathematical concepts, please see the following resources:

• Khan Academy: Algebra
• Mathway: Algebra
• Wolfram Alpha: Algebra

Final Answer

The final answer is:

• An expression is a mathematical phrase that can be evaluated to produce a value.
• An expression can contain variables, mathematical operations, and other mathematical concepts.
• To evaluate an expression, you need to follow the order of operations (PEMDAS).
• Expressions can be single numbers, fractions, trigonometric functions, logarithmic functions, absolute value, and square roots.