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Chapter 2: Problem 71

Write each phrase as an algebraic expression. Twice the sum of \(c\) and \(d\)

Short Answer

Expert verified
2(c + d)

Step by step solution

01

- Identify the Phrase

The phrase to be translated into an algebraic expression is 'Twice the sum of c and d'.
02

- Identify the Sum of c and d

The phrase 'the sum of c and d' translates to the mathematical expression \(c + d\).
03

- Apply 'Twice'

To apply 'twice' to the sum, you need to multiply the sum of \(c + d\) by 2. This can be written as \(2 \times (c + d)\) or simply \(2(c + d)\).

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Key Concepts

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

translating phrases to algebra
Translating phrases to algebra involves converting words into mathematical symbols and expressions. This process is essential in solving word problems. Start by identifying what the phrase means in mathematical terms. For example, 'twice' suggests multiplication by 2, and 'sum' indicates addition.
Use the following steps to translate phrases to algebra:
  • Identify key mathematical operations (such as sum, difference, product, or quotient).
  • Determine the variables involved in the phrase.
  • Translate the words into algebraic expressions step by step.
For example, if the phrase is 'Twice the sum of c and d', you first identify 'sum' (which means addition), and then apply 'twice' (which means multiplying by 2). As a result, you write the expression as 2(c + d).
sum
In mathematics, the 'sum' refers to the result of adding two or more numbers or expressions together. When translating phrases involving sums, you use the addition operator (+).
Consider the phrase 'the sum of c and d'. Here, you simply add the variables c and d together, which gives you the expression c + d.
It's important to remember:
  • The variable names (like c and d) represent quantities that can vary.
  • Addition is a commutative operation, meaning c + d is the same as d + c.
Understanding these basics will help you break down more complex algebraic expressions in the future.
multiplication in algebra
Multiplication in algebra involves scaling one number or variable by another. This is often indicated by phrases like 'twice', 'thrice', or 'times'.
When dealing with phrases like 'twice the sum of c and d', you are instructed to multiply the entire sum by 2. Mathematically, this is represented as 2(c + d).
Here are key points to remember:
  • Use parentheses to group variables and operations before applying multiplication.
  • Multiplication distributes over addition, so 2(c + d) can also be written as 2c + 2d after distribution.
  • The symbol for multiplication in algebraic expressions can be represented by juxtaposition (2n) or with parentheses (2(n)).
Understanding how multiplication interacts with other operations is vital for creating and simplifying algebraic expressions accurately.

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