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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
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Opposites are numbers that are the same distance from zero on the number line but have opposite signs.
Double-negative property
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Absolute value (geometric)
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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
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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
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, that is,
for any real number
.
Additive identity
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Since adding 0 to a real number leaves that number unchanged, 0 is called the additive identity.
Definition of subtraction
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Subtraction of signed numbers
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To perform the subtraction
, add the opposite of
to
, that is, change the sign of
and add.
Multiplication and division of signed numbers
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Reciprocals
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Two numbers are reciprocals of each other if their product is 1. The numbers 4 and
are reciprocals since
.
Negative exponents
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If
is any natural number and
is any nonzero real number, then
.
Writing a number in scientific notation
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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
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[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
number of sport play by 50 student construct discrete data
width of the frangebany leaves on how to write a introduction
Solve the mean of variance
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ...
Step 2: Find each score's deviation from the mean. ...
Step 3: Square each deviation from the mean. ...
Step 4: Find the sum of squares. ...
Step 5: Divide the sum of squares by n – 1 or N.
kenneth
Is mistake done to something
Vutshila
What is the life teble
anas
statistics is the analyzing of data
how do you calculate mean
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
data collected all over the world
Shaynaynay
construct a less than and more than table
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400
a. what is the probability of getting more than 12,000 hits?
b. what is the probability of getting fewer than 9,000 hits?
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400.
a. What is the probability of getting more than 12,000 hits
Akshay
Sorry i want to learn more about this question
Bright
a= 0.20233
b=0.3384
Sufiyan
How do I interpret level of significance?
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
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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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