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Guides d'étude > Prealgebra

Simplifying Expressions With Decimals

Learning Outcomes

  • Use the order of operations to simplify expressions that contain decimals
The order of operations introduced in Use the Language of Algebra also applies to decimals. Do you remember what the phrase "Please excuse my dear Aunt Sally" stands for?  

example

Simplify the expressions: ⓐ 7(18.3−21.7)7\left(18.3 - 21.7\right) ⓑ 23(8.3−3.8)\frac{2}{3}\left(8.3 - 3.8\right) Solution
ⓐ
7(18.3−21.7)7\left(18.3 - 21.7\right)
Simplify inside parentheses. 7(−3.4)7\left(-3.4\right)
Multiply. −23.8-23.8
ⓑ
23(8.3−3.8)\frac{2}{3}\left(8.3 - 3.8\right)
Simplify inside parentheses. 23(4.5)\frac{2}{3}\left(4.5\right)
Write 4.54.5 as a fraction. 23(4.51)\frac{2}{3}\left(\frac{4.5}{1}\right)
Multiply. 93\frac{9}{3}
Simplify. 33
 

try it

[ohm_question]146295[/ohm_question] [ohm_question]146297[/ohm_question]
For more examples similar to the ones above, watch the following video https://youtu.be/xO1cjj_TqaY

example

Simplify each expression: ⓐ 6÷0.6+(0.2)4−(0.1)26\div 0.6+\left(0.2\right)4-{\left(0.1\right)}^{2} ⓑ (110)2+(3.5)(0.9){\left(\frac{1}{10}\right)}^{2}+\left(3.5\right)\left(0.9\right)

Answer: Solution

ⓐ
6÷0.6+(0.2)4−(0.1)26\div 0.6+\left(0.2\right)4-{\left(0.1\right)}^{2}
Simplify exponents. 6÷0.6+(0.2)4−0.016\div 0.6+\left(0.2\right)4 - 0.01
Divide. 10+(0.2)4−0.0110+\left(0.2\right)4 - 0.01
Multiply. 10+0.8−0.0110+0.8 - 0.01
Add. 10.8−0.0110.8 - 0.01
Subtract. 10.7910.79
ⓑ
(110)2+(3.5)(0.9){\left(\frac{1}{10}\right)}^{2}+\left(3.5\right)\left(0.9\right)
Simplify exponents. 1100+(3.5)(0.9)\frac{1}{100}+\left(3.5\right)\left(0.9\right)
Multiply. 1100+3.15\frac{1}{100}+3.15
Convert 1100\frac{1}{100} to a decimal. 0.01+3.150.01+3.15
Add. 3.163.16

 

try it

[ohm_question]146309[/ohm_question] [ohm_question]146310[/ohm_question]
The following two videos contain more examples of how to use the order of operations to simplify expressions with decimals. https://youtu.be/c-iknWD7piU https://youtu.be/CMQrctqdz6g

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