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Chapter 2: Problem 67

Translate each phrase into an algebraic expression. the sum of \(t\) and 9

Short Answer

Expert verified
The algebraic expression is \( t + 9 \).

Step by step solution

01

Identify Key Terms

First, identify the key terms in the phrase: 'the sum of'. This indicates we are dealing with an addition.
02

Define the Variables

Identify the variable represented by the letter in the phrase. Here, the letter 't' is a variable that represents an unknown number.
03

Translate the Expression

Using the identified operation ('sum' means addition), translate the phrase into an algebraic expression. The 'sum of t and 9' is written as the addition of the variable t and the number 9.
04

Formulate the Expression

Combine the variable and constant using the addition operation to write the final algebraic expression: \( t + 9 \).

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Key Concepts

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

Understanding Variables
Variables are symbols used to represent numbers in mathematical expressions and equations. They allow us to describe general rules and relationships. In our example, the letter \( t \) is used as a variable. It acts as a placeholder for an unknown or changeable number.

Variables make it easier to work with problems where specific numbers are not known at the start.
  • For instance, in 'the sum of \( t \) and 9', \( t \) can be any number.
  • Once \( t \) is substituted with a specific value, we can compute the final result.
Role of Addition
Addition is one of the basic operations in mathematics. It involves combining two or more numbers to get a total sum. In our exercise, the phrase 'the sum of' indicates addition.

Together with subtraction, multiplication, and division, addition forms the foundation of arithmetic operations.
  • Addition is commutative, which means \( a + b = b + a \).
  • It is also associative, meaning \( (a + b) + c = a + (b + c) \).
Understanding how addition works is crucial for solving problems and writing expressions.
Translation of Phrases into Expressions
Translating phrases into expressions is an important skill in algebra. It helps in converting verbal descriptions into mathematical forms. Let's break down how to translate our given phrase:

  • The phrase 'the sum of' leads directly to the addition operation.
  • The words 't and 9' indicate the two numbers or terms we are adding together.
Hence, 'the sum of \( t \) and 9' becomes \( t + 9 \). Learning to recognize keywords such as 'sum' helps in writing accurate algebraic expressions that reflect real-world problems.
Basic Prealgebra Concepts
Prealgebra lays the groundwork for algebra and focuses on fundamental mathematical concepts. It includes operations with whole numbers, understanding variables, and the basics of expression translation.

In the context of our exercise:
  • We learned how to identify variables which are crucial for developing algebraic thinking.
  • We explored basic operations like addition to form equations and expressions.
These basic ideas ensure that as we advance, we can handle more complex algebraic challenges.

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Most popular questions from this chapter

Find the values that complete the table below for \(y=-4 x\). $$\begin{array}{|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 \\ \hline y & ? & ? & ? & ? \\ \hline \end{array}$$

Evaluate each expression if \(a=6, b=10,\) and \(c=3\) $$2 b-6$$

Find the solution of each equation from the list given. (lesson \(1-5\) ) $$18-n=12 ; 3,6,30$$

Evaluate each expression if \(a=6, b=10,\) and \(c=3\) $$3 a-(b+c)$$

Find each product. $$5 \cdot 15$$
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