Simplifying Expressions With Decimals and Fractions

Learning Outcomes

Simplify expressions containing decimals using the order of operations

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? For a review on how to perform order of operations, you can go to this page.

example

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

Solution

1.
	$7\left(18.3 - 21.7\right)$
Simplify inside parentheses.	$7\left(-3.4\right)$
Multiply.	$-23.8$

2.
	${\Large\frac{2}{3}}\left(8.3 - 3.8\right)$
Simplify inside parentheses.	${\Large\frac{2}{3}}\left(4.5\right)$
Write $4.5$ as a fraction.	${\Large\frac{2}{3}}\left({\Large\frac{4.5}{1}}\right)$
Multiply.	${\Large\frac{9}{3}}$
Simplify.	$3$

try it

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

example

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

Show Solution

Solution

1.
	$6\div 0.6+\left(0.2\right)4-{\left(0.1\right)}^{2}$
Simplify exponents.	$6\div 0.6+\left(0.2\right)4 - 0.01$
Multiply and divide from left to right.	$10+0.8 - 0.01$
Add and subtract from left to right.	$10.79$

2.
	${\left({\Large\frac{1}{10}}\right)}^{2}+\left(3.5\right)\left(0.9\right)$
Simplify exponents.	${\Large\frac{1}{100}}+\left(3.5\right)\left(0.9\right)$
Multiply.	${\Large\frac{1}{100}}+3.15$
Convert $\frac{1}{100}$ to a decimal.	$0.01+3.15$
Add.	$3.16$

try it

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

Module 5: Decimals

Simplifying Expressions With Decimals and Fractions

Learning Outcomes

example

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example

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