Jan 19, 2017 Equivalent expressions examples Follow these rules to determine if two expressions are equal 1st - Use the distributive property on the left expression. 2nd - Combine all like terms on the left. Practice determining whether or not two algebraic expressions are equivalent by manipulating the expressions. These problems require you to combine like terms and apply the distributive property. Generating equivalent algebraic expressions: An algebraic expression is a mathematical sentence involving constants (any real number), variables and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). Let us consider the algebraic expression which is given below.
Learning Outcomes
Translate Words to Algebraic Expressions
In the previous section, we listed many operation symbols that are used in algebra, and then we translated expressions and equations into word phrases and sentences. Now we’ll reverse the process and translate word phrases into algebraic expressions. The symbols and variables we’ve talked about will help us do that. They are summarized below.
Look closely at these phrases using the four operations:
Each phrase tells you to operate on two numbers. Look for the words of and and to find the numbers.
example
Translate each word phrase into an algebraic expression:
1. The difference of [latex]20[/latex] and [latex]4[/latex]
2. The quotient of [latex]10x[/latex] and [latex]3[/latex]
Solution
1. The key word is difference, which tells us the operation is subtraction. Look for the words of and and to find the numbers to subtract. [latex]begin{array}{} text{the difference of }20text{ and }4hfill 20text{ minus }4hfill 20 - 4hfill end{array}[/latex] ![]()
2. The key word is quotient, which tells us the operation is division.
[latex]begin{array}{} text{the quotient of }10xtext{ and }3hfill text{divide }10xtext{ by }3hfill 10xdiv 3hfill end{array}[/latex] This can also be written as [latex]begin{array}{l}10x/3text{ or}frac{10x}{3}hfill end{array}[/latex] example
Translate each word phrase into an algebraic expression:
Solution:
1. Eight more than [latex]y[/latex]
2. Seven less than [latex]9z[/latex]
1. The key words are more than. They tell us the operation is addition. More than means “added to”.
[latex]begin{array}{l}text{Eight more than }y text{Eight added to }y y+8end{array}[/latex] 2. The key words are less than. Nfs carbon key generator download mac. They tell us the operation is subtraction. Less than means “subtracted from”. [latex]begin{array}{l}text{Seven less than }9z text{Seven subtracted from }9z 9z - 7end{array}[/latex] example
Translate each word phrase into an algebraic expression:
1. five times the sum of [latex]m[/latex] and [latex]n[/latex] Show Solution
2. the sum of five times [latex]m[/latex] and [latex]n[/latex]
Solution
1. There are two operation words: times tells us to multiply and sum tells us to add. Because we are multiplying [latex]5[/latex] times the sum, we need parentheses around the sum of [latex]m[/latex] and [latex]n[/latex]. five times the sum of [latex]m[/latex] and [latex]n[/latex]
[latex]begin{array}{} 5left(m+nright)hfill end{array}[/latex]
2. To take a sum, we look for the words of and and to see what is being added. Here we are taking the sum of five times [latex]m[/latex] and [latex]n[/latex]. the sum of five times [latex]m[/latex] and [latex]n[/latex]
[latex]begin{array}{} 5m+nhfill end{array}[/latex]
Notice how the use of parentheses changes the result. In part 1, we add first and in part 2, we multiply first.
Watch the video below to better understand how to write algebraic expressions from statements.
Later in this course, we’ll apply our skills in algebra to solving equations. We’ll usually start by translating a word phrase to an algebraic expression. We’ll need to be clear about what the expression will represent. We’ll see how to do this in the next two examples.
example
The height of a rectangular window is [latex]6[/latex] inches less than the width. Let [latex]w[/latex] represent the width of the window. Write an expression for the height of the window.
Generating Equivalent Algebraic Expressions Module Quiz B Answer Key Unit 3Show Solution
Solution
Generating Equivalent Algebraic Expressions Module Quiz B Answer Key Page 38example
Blanca has dimes and quarters in her purse. The number of dimes is [latex]2[/latex] less than [latex]5[/latex] times the number of quarters. Let [latex]q[/latex] represent the number of quarters. Write an expression for the number of dimes.
Generating Equivalent Algebraic Expressions Module Quiz B Answer Key AnswersShow Solution
Solution
Generating Equivalent Algebraic Expressions Module Quiz B Answer Key Chapter 10
in the following video we show more examples of how to write basic algebraic expressions from words, and simplify.
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