Generating Equivalent Algebraic Expressions Module Quiz B Answer Key

Learning Outcomes

• Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 2016
• Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 11 7
• Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 2017
• Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 14 18
• Generating Equivalent Algebraic Expressions Module Quiz B Answer Key Pltw
• Generating Equivalent Algebraic Expressions Module Quiz B Answer Key Chapter 10

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• Translate word phrases into algebraic expressions
• Write an algebraic expression that represents the relationship between two measurements such as length and width or the amount of different types of coins

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.

Operation	Phrase	Expression
Addition	[latex]a[/latex] plus [latex]b[/latex] the sum of [latex]a[/latex] and [latex]b[/latex] [latex]a[/latex] increased by [latex]b[/latex] [latex]b[/latex] more than [latex]a[/latex] the total of [latex]a[/latex] and [latex]b[/latex] [latex]b[/latex] added to [latex]a[/latex]	[latex]a+b[/latex]
Subtraction	[latex]a[/latex] minus [latex]b[/latex] the difference of [latex]a[/latex] and [latex]b[/latex] [latex]b[/latex] subtracted from [latex]a[/latex] [latex]a[/latex] decreased by [latex]b[/latex] [latex]b[/latex] less than [latex]a[/latex]	[latex]a-b[/latex]
Multiplication	[latex]a[/latex] times [latex]b[/latex] the product of [latex]a[/latex] and [latex]b[/latex]	[latex]acdot b[/latex] , [latex]ab[/latex] , [latex]aleft(bright)[/latex] , [latex]left(aright)left(bright)[/latex]
Division	[latex]a[/latex] divided by [latex]b[/latex] the quotient of [latex]a[/latex] and [latex]b[/latex] the ratio of [latex]a[/latex] and [latex]b[/latex] [latex]b[/latex] divided into [latex]a[/latex]	[latex]adiv b[/latex] , [latex]a/b[/latex] , [latex]frac{a}{b}[/latex] , [latex]boverline{)a}[/latex]

Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 2016

Look closely at these phrases using the four operations:

• the sum of [latex]a[/latex] and [latex]b[/latex]
• the difference of [latex]a[/latex] and [latex]b[/latex]
• the product of [latex]a[/latex] and [latex]b[/latex]
• the quotient of [latex]a[/latex] and [latex]b[/latex]

Each phrase tells you to operate on two numbers. Look for the words of and and to find the numbers.

Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 11 7

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:

Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 2017

1. How old will you be in eight years? What age is eight more years than your age now? Did you add [latex]8[/latex] to your present age? Eight more than means eight added to your present age.
2. How old were you seven years ago? This is seven years less than your age now. You subtract [latex]7[/latex] from your present age. Seven less than means seven subtracted from your present age.

Show Solution

Solution:

1. Eight more than [latex]y[/latex]
2. Seven less than [latex]9z[/latex]

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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. 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:

Generating Equivalent Algebraic Expressions Module Quiz B Answer Key 14 18

1. five times the sum of [latex]m[/latex] and [latex]n[/latex]
2. the sum of five times [latex]m[/latex] and [latex]n[/latex]

Show Solution

Generating Equivalent Algebraic Expressions Module Quiz B Answer Key Pltw

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 Chapter 10

Show Solution

Solution

Write a phrase about the height.	[latex]6[/latex] less than the width
Substitute [latex]w[/latex] for the width.	[latex]6[/latex] less than [latex]w[/latex]
Rewrite ‘less than’ as ‘subtracted from’.	[latex]6[/latex] subtracted from [latex]w[/latex]
Translate the phrase into algebra.	[latex]w - 6[/latex]

example

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.

Show Solution

Solution

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Write a phrase about the number of dimes.	two less than five times the number of quarters
Substitute [latex]q[/latex] for the number of quarters.	[latex]2[/latex] less than five times [latex]q[/latex]
Translate [latex]5[/latex] times [latex]q[/latex] .	[latex]2[/latex] less than [latex]5q[/latex]
Translate the phrase into algebra.	[latex]5q - 2[/latex]

in the following video we show more examples of how to write basic algebraic expressions from words, and simplify.