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Study Guides > Prealgebra

Translating Words to Equations That Contain Decimals

Learning Outcomes

  • Translate phrases that contain decimals into algebraic equations and solve
  Now that we have solved equations with decimals, we are ready to translate word sentences to equations and solve. Remember to look for words and phrases that indicate the operations to use.

example

Translate and solve: The difference of nn and 4.34.3 is 2.12.1. Solution
Translate. .
Add 4.34.3 to both sides of the equation. n−4.3−4.3=2.1+4.3n-4.3\color{red}{- 4.3}=2.1\color{red}{+ 4.3}
Simplify. n=6.4n=6.4
Check: Is the difference of nn and 4.34.3 equal to 2.12.1?
Let n=6.4n=6.4 : Is the difference of 6.46.4 and 4.34.3 equal to 2.12.1?
Translate. 6.4−4.3=?2.16.4-4.3\stackrel{?}{=}2.1
Simplify. 2.1=2.12.1=2.1
 
 

try it

[ohm_question]146384[/ohm_question]
The following video contains more examples of using the language of algebra to translate a statement containing subtraction. Not that it does not contain decimal specific examples. https://youtu.be/vtnAdQHCt5s

example

Translate and solve: The product of −3.1-3.1 and xx is 5.275.27.

Answer: Solution

Translate. .
Divide both sides by −3.1-3.1 . −3.1x−3.1=5.27−3.1\frac{-3.1x}{\color{red}{-3.1}}=\frac{5.27}{\color{red}{-3.1}}
Simplify. x=−1.7x=-1.7
Check: Is the product of −3.1−3.1 and xx equal to 5.275.27 ?
Let x=−1.7x=-1.7 : Is the product of −3.1-3.1 and −1.7-1.7 equal to 5.275.27 ?
Translate. −3.1(−1.7)=?5.27-3.1(-1.7)\stackrel{?}{=}5.27
Simplify. 5.27=5.275.27=5.27

 

try it

[ohm_question]146386[/ohm_question]
The video that follows contains examples of how to use the language of algebra to translate an expression that contains multiplication. Note that the examples do not contain decimals. https://youtu.be/KavmzEwvh1g

example

Translate and solve: The quotient of pp and −2.4-2.4 is 6.56.5.

Answer: Solution

Translate. .
Multiply both sides by −2.4-2.4 . −2.4(p−2.4)=−2.4(6.5)\color{red}{-2.4}(\frac{p}{-2.4})=\color{red}{-2.4}(6.5)
Simplify. p=−15.6p=-15.6
Check: Is the quotient of pp and −2.4-2.4 equal to 6.56.5 ?
Let p=−15.6:p=-15.6: Is the quotient of −15.6-15.6 and −2.4-2.4 equal to 6.56.5 ?
Translate. −15.6−2.4=?6.5\frac{\color{red}{-15.6}}{-2.4}\stackrel{?}{=}6.5
Simplify. 6.5=6.56.5=6.5

 

try it

[ohm_question]146387[/ohm_question]
The video that follows gives examples of how to use the language of algebra to translate an expression that contains division. Note that the examples do not contain decimals. https://youtu.be/WxJxY4aJ9Vk

example

Translate and solve: The sum of nn and 2.92.9 is 1.71.7.

Answer: Solution

Translate. .
Subtract 2.92.9 from each side. n+2.9−2.9=1.7−2.9n+2.9\color{red}{- 2.9}=1.7\color{red}{- 2.9}
Simplify. n=−1.2n=-1.2
Check: Is the sum nn and 2.92.9 equal to 1.71.7 ?
Let n=−1.2:n=-1.2: Is the sum −1.2-1.2 and 2.92.9 equal to 1.71.7 ?
Translate. −1.2+2.9=?1.7-1.2+2.9\stackrel{?}{=}1.7
Simplify. 1.7=1.71.7=1.7

 

TRY it

[ohm_question]146385[/ohm_question]
The video that follows gives examples of how to use the language of algebra to translate an expression that contains addition. Note that the examples do not contain decimals. https://youtu.be/sFbNgjxdf1A

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