3.8 Summary of key concepts

Elementary algebra Page 1 / 1

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] )

- (- a) = a

Absolute value (geometric) ( [link] )

The absolute value of a number

a

, denoted

| a |

, is the distance from

a

to 0 on the number line.

Absolute value (algebraic) ( [link] )

| a | = {\begin{matrix} a & if a \geq 0 \\ - a & if a < 0 \end{matrix}

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] )

0 + any number = that particular number

, that is,

0 + a = a

for any real number

a

Additive identity ( [link] )

Since adding 0 to a real number leaves that number unchanged, 0 is called the additive identity.

Definition of subtraction ( [link] )

a - b = a + (- b)

Subtraction of signed numbers ( [link] )

To perform the subtraction

a - b

, add the opposite of

b

a

, that is, change the sign of

b

and add.

Multiplication and division of signed numbers ( [link] )

\begin{array}{l} (+) (+) = + & \frac{(+)}{(+)} = + & \frac{(+)}{(-)} = - \\ (-) (-) = + \\ (+) (-) = - \\ (-) (+) = - & \frac{(-)}{(-)} = + & \frac{(-)}{(+)} = - \end{array}

Reciprocals ( [link] )

Two numbers are reciprocals of each other if their product is 1. The numbers 4 and

\frac{1}{4}

are reciprocals since

(4) (\frac{1}{4}) = 1

Negative exponents ( [link] )

n

is any natural number and

x

is any nonzero real number, then

x^{- n} = \frac{1}{x^{n}}

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

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Ewa Reply

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Moses

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Fredrick Reply

the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement

AI-Robot

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Is the ship moving at a constant velocity?

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The full note of modern physics

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introduction to applications of nuclear physics

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aluet

Show that the equal masses particles emarge from collision at right angle by making explicit used of fact that momentum is a vector quantity

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Isaac

A wave is described by the function D(x,t)=(1.6cm) sin[(1.2cm^-1(x+6.8cm/st] what are:a.Amplitude b. wavelength c. wave number d. frequency e. period f. velocity of speed.

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A body is projected upward at an angle 45° 18minutes with the horizontal with an initial speed of 40km per second. In hoe many seconds will the body reach the ground then how far from the point of projection will it strike. At what angle will the horizontal will strike

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Suppose hydrogen and oxygen are diffusing through air. A small amount of each is released simultaneously. How much time passes before the hydrogen is 1.00 s ahead of the oxygen? Such differences in arrival times are used as an analytical tool in gas chromatography.

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the science concerned with describing the interactions of energy, matter, space, and time; it is especially interested in what fundamental mechanisms underlie every phenomenon

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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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3.8 Summary of key concepts

Summary of key concepts

Positive and negative numbers ( [link] )

Opposites ( [link] )

Double-negative property ( [link] )

Absolute value (geometric) ( [link] )

Absolute value (algebraic) ( [link] )

Addition of signed numbers ( [link] )

Addition with 0 ( [link] )

Additive identity ( [link] )

Definition of subtraction ( [link] )

Subtraction of signed numbers ( [link] )

Multiplication and division of signed numbers ( [link] )

Reciprocals ( [link] )

Negative exponents ( [link] )

Writing a number in scientific notation ( [link] )

Converting from scientific notation: Positive exponent ( [link] )

Negative exponent ( [link] )

Questions & Answers

Read also:

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Converting from scientific notation:
Positive exponent ( [link] )