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Simplify each algebraic expression.

  1. 2 3 y 2 ( 4 3 y + z )
  2. 5 t 2 3 t + 1
  3. 4 p ( q 1 ) + q ( 1 p )
  4. 9 r ( s + 2 r ) + ( 6 s )
  1. −2 y −2 z  or  −2 ( y + z ) ;
  2. 2 t −1 ;
  3. 3 p q −4 p + q ;
  4. 7 r −2 s + 6
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Simplifying a formula

A rectangle with length L and width W has a perimeter P given by P = L + W + L + W . Simplify this expression.

P = L + W + L + W P = L + L + W + W Commutative property of addition P = 2 L + 2 W Simplify P = 2 ( L + W ) Distributive property
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If the amount P is deposited into an account paying simple interest r for time t , the total value of the deposit A is given by A = P + P r t . Simplify the expression. (This formula will be explored in more detail later in the course.)

A = P ( 1 + r t )

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Access these online resources for additional instruction and practice with real numbers.

Key concepts

  • Rational numbers may be written as fractions or terminating or repeating decimals. See [link] and [link] .
  • Determine whether a number is rational or irrational by writing it as a decimal. See [link] .
  • The rational numbers and irrational numbers make up the set of real numbers. See [link] . A number can be classified as natural, whole, integer, rational, or irrational. See [link] .
  • The order of operations is used to evaluate expressions. See [link] .
  • The real numbers under the operations of addition and multiplication obey basic rules, known as the properties of real numbers. These are the commutative properties, the associative properties, the distributive property, the identity properties, and the inverse properties. See [link] .
  • Algebraic expressions are composed of constants and variables that are combined using addition, subtraction, multiplication, and division. See [link] . They take on a numerical value when evaluated by replacing variables with constants. See [link] , [link] , and [link]
  • Formulas are equations in which one quantity is represented in terms of other quantities. They may be simplified or evaluated as any mathematical expression. See [link] and [link] .

Verbal

Is 2 an example of a rational terminating, rational repeating, or irrational number? Tell why it fits that category.

irrational number. The square root of two does not terminate, and it does not repeat a pattern. It cannot be written as a quotient of two integers, so it is irrational.

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What is the order of operations? What acronym is used to describe the order of operations, and what does it stand for?

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What do the Associative Properties allow us to do when following the order of operations? Explain your answer.

The Associative Properties state that the sum or product of multiple numbers can be grouped differently without affecting the result. This is because the same operation is performed (either addition or subtraction), so the terms can be re-ordered.

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Numeric

For the following exercises, simplify the given expression.

10 + 2 × ( 5 3 )

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6 ÷ 2 ( 81 ÷ 3 2 )

−6

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−2 × [ 16 ÷ ( 8 4 ) 2 ] 2

−2

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4 6 + 2 × 7

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3 12 × 2 + 19

4

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14 × 3 ÷ 7 6

0

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9 ( 3 + 11 ) × 2

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6 + 2 × 2 1

9

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64 ÷ ( 8 + 4 × 2 )

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( 12 ÷ 3 × 3 ) 2

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( 15 7 ) × ( 3 7 )

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2 × 4 9 ( −1 )

17

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4 2 25 × 1 5

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Algebraic

For the following exercises, solve for the variable.

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
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While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
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Not really sure
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to drain extracellular fluid all over the body.
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The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
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Anatomy is the identification and description of the structures of living things
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Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
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Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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