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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

-2

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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

if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
Syamthanda Reply
hey , can you please explain oxidation reaction & redox ?
Boitumelo Reply
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
the value of V1 and V2
Tumelo Reply
advantages of electrons in a circuit
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we're do you find electromagnetism past papers
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what a normal force
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it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
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what is physics?
Petrus Reply
what is the half reaction of Potassium and chlorine
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how to calculate coefficient of static friction
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how to calculate static friction
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How to calculate a current
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how to calculate the magnitude of horizontal component of the applied force
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How to calculate force
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a structure of a thermocouple used to measure inner temperature
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a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
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How is energy being used in bonding?
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what is acceleration
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a rate of change in velocity of an object whith respect to time
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how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
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t =r×f
Khuthadzo
how to calculate tension by substitution
Precious Reply
hi
Shongi
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Leago
use fnet method. how many obects are being calculated ?
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Hulisani
how to calculate acceleration and tension force
Lungile Reply
you use Fnet equals ma , newtoms second law formula
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how to calculate normal force
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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