Quantities
Algebra Help: Section 1.2
What are algebraic quantities? Learn about known, unknown, literal, multiplication of literal quantities, coefficients, exponents, powers, roots, equations, and the first member or second member of an equation.
Algebraic Quantities
- Known & Unknown The algebraic quantities are of two kinds, known and unknown.
-
Known Quantities
are those whose values are
given; they are represented by the first
letters of the alphabet, as
a, b, c, d. -
Unknown Quantities
are those whose values are
to be determined; they are represented by
the final letters of the alphabet, as
u, x, y, z. - Literal Quantities are those which are expressed by letters.
-
Multiplication of Literal Quantities
is expressed by simply writing the factors together,
without the * sign; thus,
2 times
xis written2x; 3 timesxis written3x;atimesxis writtenax; andatimesbtimesyis writtenaby; and so on. -
Coefficient
is a number or quantity prefixed to another quantity,
to denote how many times the latter
is taken; thus, in
3
x, 3 is the coefficient ofx, and indicates that x is taken 3 times. In 3ax, 3 may be regarded as the coefficient ofax, or3aas the coefficient ofx. In 4(a + x), 4 is the coefficient of (a + x). When no coefficient is written, the unit 1 is understood. -
An Exponent is a number
written above, and to the right of a quantity,
to denote how many times
the quantity is used as a factor;
thus, the repetitions of the
same factor, as
xxxx, may be writtenx4, in which 4 is the exponent ofx, and indicates thatxis used 4 times as a factor.NOTE - To enable the student to discriminate between a coefficent and an exponent, the two may be contrasted, thus:
3xindicates thatxis multiplied by 3;x3indicates thatxis multiplied by itself till it is used 3 times as a factor. Again,3xis an abbreviation ofx + x + x;x3is an abbreviation ofx * x * x. -
A Power
of a quantity is the product of
factors each of which is equal to that quantity;
thus,
a2is the second power ofaoraa;a3the third power, oraaa;a4the fourth power, oraaaa. When no exponent is written, 1 is understood. -
A Root
is a factor repeated to form a power; thus,
in
m5,mis the root which is repeated to form the powerm5. -
An Equation
is an expression of equality between
two quantities; thus,
x = 4; 5x = 60; 30x = a + bare equations. - The First Member of an equation is the part on the left of the = sign.
- The Second Member of an equation is the part on the right of the = sign.
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Help with Algebra Homework
Free tutorials provide math help for math problems. Tutorials start with algebra 1. Algebra tutorials include word problems related to algebra topics, as they're introduced. See the menu, above for algebra math equations, and explanation, by section.
Windows algebra games, designed to help with classwork, coming soon!
Windows games, in progress, work with this set of free tutorials, modified
from the public domain text book titled,
New Elementary Algebra
containing the rudiments of the science for schools and academies.
By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
