Simplifying Expressions With Decimals and Fractions

Learning Outcomes

  • Use the order of operations to simplify expressions that contain decimals

The order of operations introduced in an earlier lesson also applies to decimals. Do you remember what the phrase “Please excuse my dear Aunt Sally” stands for?

example

Simplify the expressions:
1.   [latex]7\left(18.3 - 21.7\right)[/latex]
2.   [latex]{\Large\frac{2}{3}}\left(8.3 - 3.8\right)[/latex]

Solution

1.
[latex]7\left(18.3 - 21.7\right)[/latex]
Simplify inside parentheses. [latex]7\left(-3.4\right)[/latex]
Multiply. [latex]-23.8[/latex]
2.
[latex]{\Large\frac{2}{3}}\left(8.3 - 3.8\right)[/latex]
Simplify inside parentheses. [latex]{\Large\frac{2}{3}}\left(4.5\right)[/latex]
Write [latex]4.5[/latex] as a fraction. [latex]{\Large\frac{2}{3}}\left({\Large\frac{4.5}{1}}\right)[/latex]
Multiply. [latex]{\Large\frac{9}{3}}[/latex]
Simplify. [latex]3[/latex]

 

try it

For more examples similar to the ones above, watch the following video

example

Simplify each expression:
1.   [latex]6\div 0.6+\left(0.2\right)4-{\left(0.1\right)}^{2}[/latex]
2.   [latex]{\left({\Large\frac{1}{10}}\right)}^{2}+\left(3.5\right)\left(0.9\right)[/latex]

 

try it

The following two videos contain more examples of how to use the order of operations to simplify expressions with decimals.