Multiplication with Algebra
Algebra Help: Section 2.12
Multiplication is the process of taking one quantity as many times as there are units in another quantity.
Case 1
When both factors are mononomials:
1. Multiply 4a by 3b.
OPERATION:
Multiplicand 4a
Multiplier 3b
_____
Product 12ab
ANALYSIS - It doesn't matter which order the factors are processed, in multiplication. The following steps demonstrate how to find the product.
- 3 times 4 are 12.
btimesaareab.- 12 times
abare 12ab.
2. Multiply a3 by
a2.
OPERATION:
Multiplicand a3
Multiplier a2
_____
Product a5
ANALYSIS - Since a3 equals aaa
and a2 equals aa, their product
equals aaaaa, which is a5.
Add the given exponents, to find the product of exponents. 3 plus 2 equals 5.
3. Multiply 3ab2 by 4b3.
OPERATION:
Multiplicand 3ab2
Multiplier 4b3
______
Product 12ab5
ANALYSIS - 4 times 3a equals 12a.
b2 times b3
equals b5.
In the examples given above, all the quntities are understood to be positive. It is necessary, however, to investigate the law of signs when one or both factors are negative. In arithmetic, multplication is restricted to the simple idea of repeating a number.
In algebra, quantities have two qualities, and are either positive or negative. Multiplication has the double province of repeating by addition and repeating by subtraction. The sign of the multiplier indicates whether to repeat by addition or subtraction. Concepts for multiplication follow.
- The plus sign of a multiplier shows that the multiplicand is to be added to zero.
- The minus sign of a multiplier shows that the multiplicand is to be subtracted from zero.
- The value of the multipiler shows how many times the multiplicand should be taken by either process.
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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.
