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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

differentiate between demand and supply giving examples
Lambiv Reply
differentiated between demand and supply using examples
Lambiv
what is labour ?
Lambiv
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Venny Reply
how is the graph works?I don't fully understand
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information
Eliyee
devaluation
Eliyee
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WARKISA
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Lambiv
multiple choice question
Aster Reply
appreciation
Eliyee
explain perfect market
Lindiwe Reply
In economics, a perfect market refers to a theoretical construct where all participants have perfect information, goods are homogenous, there are no barriers to entry or exit, and prices are determined solely by supply and demand. It's an idealized model used for analysis,
Ezea
What is ceteris paribus?
Shukri Reply
other things being equal
AI-Robot
When MP₁ becomes negative, TP start to decline. Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of lab
Kelo
Extuples Suppose that the short-run production function of certain cut-flower firm is given by: Q=4KL-0.6K2 - 0.112 • Where is quantity of cut flower produced, I is labour input and K is fixed capital input (K-5). Determine the average product of labour (APL) and marginal product of labour (MPL)
Kelo
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Shukri
Can I ask you other question?
Shukri
what is monopoly mean?
Habtamu Reply
What is different between quantity demand and demand?
Shukri Reply
Quantity demanded refers to the specific amount of a good or service that consumers are willing and able to purchase at a give price and within a specific time period. Demand, on the other hand, is a broader concept that encompasses the entire relationship between price and quantity demanded
Ezea
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Shukri
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what is the difference between economic growth and development
Fiker Reply
Economic growth as an increase in the production and consumption of goods and services within an economy.but Economic development as a broader concept that encompasses not only economic growth but also social & human well being.
Shukri
production function means
Jabir
What do you think is more important to focus on when considering inequality ?
Abdisa Reply
any question about economics?
Awais Reply
sir...I just want to ask one question... Define the term contract curve? if you are free please help me to find this answer 🙏
Asui
it is a curve that we get after connecting the pareto optimal combinations of two consumers after their mutually beneficial trade offs
Awais
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Asui
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities, where neither p
Cornelius
In economics, the contract curve refers to the set of points in an Edgeworth box diagram where both parties involved in a trade cannot be made better off without making one of them worse off. It represents the Pareto efficient allocations of goods between two individuals or entities,
Cornelius
Suppose a consumer consuming two commodities X and Y has The following utility function u=X0.4 Y0.6. If the price of the X and Y are 2 and 3 respectively and income Constraint is birr 50. A,Calculate quantities of x and y which maximize utility. B,Calculate value of Lagrange multiplier. C,Calculate quantities of X and Y consumed with a given price. D,alculate optimum level of output .
Feyisa Reply
Answer
Feyisa
c
Jabir
the market for lemon has 10 potential consumers, each having an individual demand curve p=101-10Qi, where p is price in dollar's per cup and Qi is the number of cups demanded per week by the i th consumer.Find the market demand curve using algebra. Draw an individual demand curve and the market dema
Gsbwnw Reply
suppose the production function is given by ( L, K)=L¼K¾.assuming capital is fixed find APL and MPL. consider the following short run production function:Q=6L²-0.4L³ a) find the value of L that maximizes output b)find the value of L that maximizes marginal product
Abdureman
types of unemployment
Yomi Reply
What is the difference between perfect competition and monopolistic competition?
Mohammed
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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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