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Chapter 4: Problem 11

Write each algebraic expression as an English phrase. $$3(x+y)$$

Short Answer

Expert verified
The algebraic expression \(3(x+y)\) translates to 'Three times the sum of x and y' in English.

Step by step solution

01

Understand the given algebraic expression

The given algebraic expression is \(3(x+y)\). Here, the number '3' is being multiplied to the whole bracket 'x+y'. The '+' symbol inside the brackets represents addition. The 'x' and 'y' are algebraic variables.
02

Translate symbols to English

In English, the '+' symbol translates to 'plus' or 'and'. The brackets indicate that the operations inside should be done first, and situation where a number and a bracket are next to each other as in '3(x+y)' is understood as multiplication, which can be translated to 'times' or 'multiplied by'.
03

Write the full English phrase

Combine all these English translations of the algebraic symbols and write them in order. So, the expression \(3(x+y)\), could be translated to English as 'Three times the sum of x and y'.

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Key Concepts

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

Algebraic Expressions
Algebraic expressions are combinations of numbers, variables, and mathematical operations. They form the building blocks of algebra. In the expression \(3(x+y)\), we find the number '3', the variables 'x' and 'y', and the operation symbols enclosed in parentheses.
Variables are symbols that represent unknown or changeable values, commonly denoted by letters like 'x,' 'y,' or 'z'. These variables allow us to create general mathematical models that can adapt to different numerical values.
The importance of understanding algebraic expressions lies in the ability to translate them into real-world scenarios or other mathematical forms, offering great flexibility in problem-solving.
Mathematical Operations
Mathematical operations are actions performed on numbers and expressions. They include addition, subtraction, multiplication, and division, which are fundamental to understanding algebraic expressions.
In the expression \(3(x+y)\), multiplication and addition are the key operations used. Multiplication appears as '3' placed next to the parentheses, indicating that it multiplies the sum of the variables inside.
Addition is shown inside the parentheses with the '+' symbol, which combines the values of 'x' and 'y'. Parantheses dictate the order of operations, ensuring that whatever operations are inside them are completed first. Recognizing these operations is vital in translating mathematical expressions into English phrases accurately.
English Phrasing
English phrasing is the act of expressing mathematical symbols and operations using words. It involves transforming numbers, operations, and variables into a coherent sentence.
Translating \(3(x+y)\) into English helps interpret what the expression signifies in words. Starting with the number '3', which is already in English, this is followed by the term 'the sum of' to signify the addition inside the parentheses.
The phrase ends with 'x and y', representing the variables being added, concluded with an overall 'times' to indicate multiplication. Thus, learning to convert algebraic expressions into English phrases enhances comprehension and articulation across various contexts.
  • '+' is 'plus' or 'and'
  • Multiplication can be expressed as 'times' or 'multiplied by'
  • Parentheses suggest grouping as in 'the sum of'

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