#8 Translating Algebraic Expressions

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#8 Translating Algebraic Expressions

Table of Contents

  1. Introduction
  2. Translating Algebraic Expressions
    • Additions
    • Subtractions
    • Multiplications
    • Divisions
  3. Translating Verbal Phrases into Expressions
    • Less Than
    • Sum of
    • Quotient of
    • Product of
  4. Translating Real-Life Situations into Expressions
    • Number of Pages Left to Read
    • Amount Spent on Clothing
    • Conversion from Minutes to Hours
    • And More
  5. Translating Equations
    • Simple Equations
    • Two-Step Equations
  6. Checking Possible Solutions
    • Using Coordinate Points
    • True and False Statements

Translating Algebraic Expressions

In algebra, translating verbal phrases into expressions is a fundamental skill. It involves converting words or phrases into mathematical symbols and operations. By understanding the keywords associated with each operation, You can accurately write expressions that represent real-life situations.

Additions

Addition is one of the basic operations in algebra. It involves combining two or more numbers or variables. The keywords that indicate addition include "plus," "more than," "increased by," "sum," and "total."

For example, if you have the phrase "four plus a number," you would write it as "4 + x," where x represents the unknown variable. Similarly, if it is written as "five more than a number," the expression would be "x + 5."

Subtractions

Subtraction is the operation of taking away one quantity from another. The keywords associated with subtraction include "minus," "difference of," "less than," "decreased by," and "less."

For instance, if you have the phrase "a number y minus 5," the expression would be written as "y - 5." Similarly, if it is written as "three less than a number," the expression would be "x - 3."

Multiplications

Multiplication involves repeated addition or combining numbers to find a total. The keywords that indicate multiplication include "multiplied by," "product of," "times," "twice a number," "three times a number," and "50% of a number."

For example, the phrase "negative eight multiplied by a number" would be written as "-8x." And the phrase "the product of 7 and B" would be written as "7B," where B is the variable.

Divisions

Division is the operation of separating a quantity into equal parts. The keywords associated with division include "quotient of," "divided by," and "ratio of."

For instance, if you have the phrase "the quotient of a and B," it would be written as "a / B." Similarly, if it is written as "a number divided by 8," the expression would be "x / 8."

Translating Verbal Phrases into Expressions

Translating verbal phrases into expressions is an essential skill in algebra. It involves converting spoken or written words into mathematical expressions. By identifying the keywords and understanding their meaning, you can accurately represent real-life scenarios.

Less Than

When the phrase includes the words "less than," it indicates subtraction and requires the order of the expression to be switched. For example, if you have the phrase "less than 6 times a number," the expression would be "6x - 6".

Sum of

When the phrase includes the word "sum," it indicates addition and implies combining multiple quantities. For example, if you have the phrase "3 times the sum of 7 and Y," the expression would be "3(7 + Y)".

Quotient of

When the phrase includes the word "quotient," it implies division and requires writing the expression as a fraction. For example, if you have the phrase "the quotient of 10 plus a number divided by 2," the expression would be "(10 + x) / 2".

Product of

When the phrase includes the word "product," it indicates multiplication and involves multiplying multiple quantities. For example, if you have the phrase "the product of 3 and the sum of a number and 2," the expression would be "3(x + 2)".

Translating Real-Life Situations into Expressions

In algebra, we often encounter real-life situations that can be represented using mathematical expressions. By translating these situations into expressions, we can solve problems and analyze data more effectively.

Number of Pages Left to Read

Suppose you are reading an article with 15 pages, and you want to determine how many more pages you need to read. The expression for this situation would be "15 - P," where P represents the number of pages you have already read.

Amount Spent on Clothing

Consider buying a shirt for $20 and jeans for an unknown amount. In this case, the expression for the total amount spent would be "$20 + J," where J represents the cost of the jeans.

Conversion from Minutes to Hours

To convert minutes into hours, you can use the expression "M / 60," where M represents the number of minutes. For example, if you have 120 minutes, the expression would be "120 / 60 = 2 hours."

And so on...

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