Common Algebraic Expressions

Oct 13, 2025 by miodeya.com 7 views

When it comes to simplifying algebraic expressions, it's essential to follow the correct order of operations. This ensures that we arrive at the correct solution. In this article, we'll delve into the expression $(7 \times 2) - 10$ and explore the different options that describe it.

The Order of Operations

The order of operations is a set of rules that dictate the order in which we perform mathematical operations when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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

Evaluating the Expression

Now that we've covered the order of operations, let's apply it to the expression $(7 \times 2) - 10$ . Following the order of operations, we first evaluate the expression inside the parentheses:

$7 \times 2 = 14$

Next, we subtract 10 from the result:

$14 - 10 = 4$

Therefore, the expression $(7 \times 2) - 10$ simplifies to 4.

Analyzing the Options

Now that we've evaluated the expression, let's examine the options:

A. The product of seven and two subtracted from ten This option is incorrect because the expression is not subtracted from ten, but rather ten is subtracted from the product of seven and two.

B. The product of seven and two and ten This option is also incorrect because the expression does not involve adding ten to the product of seven and two.

C. Ten less than the product of seven and two This option is correct because the expression involves subtracting ten from the product of seven and two.

D. Ten This option is incorrect because the expression does not simplify to ten.

Conclusion

In conclusion, the correct option that describes the expression $(7 \times 2) - 10$ is C. Ten less than the product of seven and two. This option accurately reflects the order of operations and the resulting value of the expression.

Common Algebraic Expressions

Here are some common algebraic expressions that involve the order of operations:

$(3 + 2) \times 4$
$(5 - 2) \div 3$
$(7 \times 2) + 10$
$(10 - 3) \times 2$

Tips for Simplifying Algebraic Expressions

Here are some tips for simplifying algebraic expressions:

Follow the order of operations (PEMDAS)
Evaluate expressions inside parentheses first
Simplify any exponential expressions
Evaluate multiplication and division operations from left to right
Finally, evaluate any addition and subtraction operations from left to right

Practice Problems

Here are some practice problems to help you reinforce your understanding of the order of operations:

$(2 + 3) \times 4$
$(5 - 2) \div 3$
$(7 \times 2) + 10$
$(10 - 3) \times 2$

Answer Key

Here are the answers to the practice problems:

$(2 + 3) \times 4 = 20$
$(5 - 2) \div 3 = 1$
$(7 \times 2) + 10 = 24$
$(10 - 3) \times 2 = 14$
Frequently Asked Questions (FAQs) about Algebraic Expressions ================================================================

In this article, we'll address some common questions and concerns about algebraic expressions, including the order of operations, simplifying expressions, and more.

Q: What is the order of operations in algebraic expressions?

A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

Evaluate any expressions inside parentheses.
Simplify any exponential expressions.
Evaluate any multiplication and division operations from left to right.
Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a product and a sum?

A: A product is the result of multiplying two or more numbers together, while a sum is the result of adding two or more numbers together.

Q: How do I evaluate an expression with multiple operations?

A: To evaluate an expression with multiple operations, follow the order of operations (PEMDAS). For example, if you have the expression $(2 + 3) \times 4$ , you would first evaluate the expression inside the parentheses (2 + 3 = 5), and then multiply 5 by 4.

Q: What is the value of the expression $(7 \times 2) - 10$ ?

A: To evaluate this expression, follow the order of operations (PEMDAS). First, evaluate the expression inside the parentheses (7 \times 2 = 14), and then subtract 10 from 14 (14 - 10 = 4).

Q: Can I simplify an expression with variables?

A: Yes, you can simplify an expression with variables. For example, if you have the expression $2x + 3$ , you can simplify it by combining like terms (2x + 3 = 2x + 3).

Q: How do I evaluate an expression with fractions?

A: To evaluate an expression with fractions, follow the order of operations (PEMDAS). For example, if you have the expression $\frac{1}{2} + \frac{1}{4}$ , you would first find a common denominator (4), and then add the fractions together.

Q: What is the value of the expression $\frac{1}{2} + \frac{1}{4}$ ?

A: To evaluate this expression, follow the order of operations (PEMDAS). First, find a common denominator (4), and then add the fractions together ( $\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$ ).

Q: Can I simplify an expression with decimals?

A: Yes, you can simplify an expression with decimals. For example, if you have the expression $2.5 + 1.2$ , you can simplify it by adding the decimals together (2.5 + 1.2 = 3.7).

Q: How do I evaluate an expression with negative numbers?

A: To evaluate an expression with negative numbers, follow the order of operations (PEMDAS). For example, if you have the expression $-2 + 3$ , you would first evaluate the expression (2 + 3 = 5), and then subtract 2 from 5 (-2 + 3 = 1).

Q: What is the value of the expression $-2 + 3$ ?

A: To evaluate this expression, follow the order of operations (PEMDAS). First, evaluate the expression (2 + 3 = 5), and then subtract 2 from 5 (-2 + 3 = 1).

Conclusion

In conclusion, algebraic expressions can be complex and require careful evaluation. By following the order of operations (PEMDAS) and simplifying expressions, you can arrive at the correct solution. Remember to evaluate expressions inside parentheses first, simplify any exponential expressions, and then evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.