Understanding the Algebraic Phrase

Oct 13, 2025 by wbrum.org 118 views

Algebraic Expressions: Translating Words into Math

When it comes to algebra, being able to translate words into mathematical expressions is a crucial skill. It's not just about solving equations, but also about understanding the language of mathematics. In this article, we'll explore how to translate the algebraic phrase "nine times a number plus thirteen" into a mathematical expression.

Understanding the Algebraic Phrase

The phrase "nine times a number plus thirteen" can be broken down into two parts: "nine times a number" and "plus thirteen." The first part, "nine times a number," can be represented by the variable $y$ , where $y$ is the unknown number. The second part, "plus thirteen," is a constant value that is added to the product of nine and the unknown number.

Analyzing the Options

Now that we have a clear understanding of the algebraic phrase, let's analyze the options:

A. $9 - y + 13$ B. $9 + y - 13$ C. $9y + 13$ D. $13y + 9$

Breaking Down Each Option

Let's break down each option to see which one matches the algebraic phrase:

Option A: $9 - y + 13$ . This option subtracts the unknown number $y$ from nine and then adds thirteen. This is not the correct translation of the phrase.
Option B: $9 + y - 13$ . This option adds the unknown number $y$ to nine and then subtracts thirteen. This is not the correct translation of the phrase.
Option C: $9y + 13$ . This option multiplies the unknown number $y$ by nine and then adds thirteen. This is the correct translation of the phrase.
Option D: $13y + 9$ . This option multiplies the unknown number $y$ by thirteen and then adds nine. This is not the correct translation of the phrase.

Conclusion

Based on our analysis, the correct answer is option C: $9y + 13$ . This expression accurately represents the algebraic phrase "nine times a number plus thirteen." When translating words into mathematical expressions, it's essential to understand the language of mathematics and break down the phrase into its individual parts. By doing so, we can ensure that we arrive at the correct solution.

Tips for Translating Words into Math

Here are some tips for translating words into mathematical expressions:

Read the phrase carefully and identify the key words and phrases.
Break down the phrase into its individual parts.
Use variables to represent unknown values.
Use mathematical operations to represent the relationships between the variables and constants.
Check your work by plugging in values and testing the expression.

Common Algebraic Phrases

Here are some common algebraic phrases and their corresponding mathematical expressions:

"Two times a number plus three": $2x + 3$
"Five times a number minus two": $5x - 2$
"Three times a number plus four": $3x + 4$
"Four times a number minus one": $4x - 1$

Practice Problems

Here are some practice problems to help you improve your skills in translating words into mathematical expressions:

Translate the phrase "six times a number minus two" into a mathematical expression.
Translate the phrase "eight times a number plus five" into a mathematical expression.
Translate the phrase "nine times a number minus three" into a mathematical expression.

Conclusion

Translating words into mathematical expressions is a crucial skill in algebra. By understanding the language of mathematics and breaking down phrases into their individual parts, we can ensure that we arrive at the correct solution. With practice and patience, you can become proficient in translating words into math and solve a wide range of algebraic problems.
Algebraic Expressions: Translating Words into Math - Q&A

In our previous article, we explored how to translate the algebraic phrase "nine times a number plus thirteen" into a mathematical expression. We also provided some tips and common algebraic phrases to help you improve your skills in translating words into math. In this article, we'll answer some frequently asked questions (FAQs) about algebraic expressions and provide additional practice problems to help you reinforce your understanding.

Q&A

Q: What is an algebraic expression?

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. It's a way to represent a relationship between variables and constants using mathematical symbols.

Q: How do I translate words into a mathematical expression?

A: To translate words into a mathematical expression, follow these steps:

Read the phrase carefully and identify the key words and phrases.
Break down the phrase into its individual parts.
Use variables to represent unknown values.
Use mathematical operations to represent the relationships between the variables and constants.
Check your work by plugging in values and testing the expression.

Q: What are some common algebraic phrases?

A: Here are some common algebraic phrases and their corresponding mathematical expressions:

"Two times a number plus three": $2x + 3$
"Five times a number minus two": $5x - 2$
"Three times a number plus four": $3x + 4$
"Four times a number minus one": $4x - 1$

Q: How do I simplify an algebraic expression?

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

Combine like terms.
Remove any parentheses.
Combine any constants.
Check your work by plugging in values and testing the expression.

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

A: An algebraic expression is a mathematical expression that contains variables, constants, and mathematical operations. An equation is a statement that says two expressions are equal. For example, $2x + 3 = 5$ is an equation, while $2x + 3$ is an algebraic expression.

Q: How do I solve an equation?

A: To solve an equation, follow these steps:

Isolate the variable by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
Check your work by plugging in values and testing the equation.

Practice Problems

Here are some practice problems to help you reinforce your understanding of algebraic expressions:

Translate the phrase "seven times a number minus four" into a mathematical expression.
Simplify the algebraic expression $3x + 2x - 1$ .
Solve the equation $2x + 3 = 7$ .
Translate the phrase "nine times a number plus two" into a mathematical expression.
Simplify the algebraic expression $4x - 2x + 1$ .

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and being able to translate words into math is a crucial skill. By understanding the language of mathematics and breaking down phrases into their individual parts, we can ensure that we arrive at the correct solution. With practice and patience, you can become proficient in translating words into math and solve a wide range of algebraic problems.

Additional Resources

Here are some additional resources to help you improve your skills in algebraic expressions:

Khan Academy: Algebraic Expressions
Mathway: Algebraic Expressions
IXL: Algebraic Expressions

Common Algebraic Phrases

Here are some common algebraic phrases and their corresponding mathematical expressions:

"Two times a number plus three": $2x + 3$
"Five times a number minus two": $5x - 2$
"Three times a number plus four": $3x + 4$
"Four times a number minus one": $4x - 1$

Tips for Translating Words into Math

Here are some tips for translating words into mathematical expressions:

Read the phrase carefully and identify the key words and phrases.
Break down the phrase into its individual parts.
Use variables to represent unknown values.
Use mathematical operations to represent the relationships between the variables and constants.
Check your work by plugging in values and testing the expression.