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- Elementary algebra
- Basic operations with real
- Summary of key concepts
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
The basic operations with real numbers are presented in this chapter. The concept of absolute value is discussed both geometrically and symbolically. The geometric presentation offers a visual understanding of the meaning of |x|. The symbolic presentation includes a literal explanation of how to use the definition. Negative exponents are developed, using reciprocals and the rules of exponents the student has already learned. Scientific notation is also included, using unique and real-life examples.This module contains a summary of the key concepts in the chapter "Basic Operations with Real Numbers".
Summary of key concepts
Positive and negative numbers
(
[link] )
A number is denoted as
positive if it is directly preceded by a "
" sign or no sign at all. A number is denoted as negative if it is directly preceded by a "
" sign.
Opposites
(
[link] )
Opposites are numbers that are the same distance from zero on the number line but have opposite signs.
Double-negative property
(
[link] )
Absolute value (geometric)
(
[link] )
The absolute value of a number
, denoted
, is the distance from
to 0 on the number line.
Absolute value (algebraic) (
[link] )
Addition of signed numbers
(
[link] )
To add two numbers with
like signs , add the absolute values of the numbers and associate the common sign with the sum.
unlike signs , subtract the smaller absolute value from the larger absolute value and associate the sign of the larger absolute value with the difference.
Addition with 0
(
[link] )
, that is,
for any real number
.
Additive identity
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[link] )
Since adding 0 to a real number leaves that number unchanged, 0 is called the additive identity.
Definition of subtraction
(
[link] )
Subtraction of signed numbers
(
[link] )
To perform the subtraction
, add the opposite of
to
, that is, change the sign of
and add.
Multiplication and division of signed numbers
(
[link] )
Reciprocals
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[link] )
Two numbers are reciprocals of each other if their product is 1. The numbers 4 and
are reciprocals since
.
Negative exponents
(
[link] )
If
is any natural number and
is any nonzero real number, then
.
Writing a number in scientific notation
(
[link] )
To write a number in scientific notation:
- Move the decimal point so that there is one nonzero digit to its left.
- Multiply the result by a power of 10 using an exponent whose absolute value is the number of places the decimal point was moved. Make the exponent positive if the decimal point was moved to the left and negative if the decimal point was moved to the right.
Converting from scientific notation:
Positive exponent
(
[link] )
To convert a number written in scientific notation to a number in standard form when there is a
positive exponent as the power of 10, move the decimal point to the
right the number of places prescribed by the exponent on the 10.
Negative exponent
(
[link] )
To convert a number written in scientific notation to a number in standard form when there is a
negative exponent as the power of 10, move the decimal point to the
left the number of places prescribed by the exponent on the 10.
Questions & Answers
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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