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Basic algebra and algebraic manipulation - Coggle Diagram
Basic algebra and algebraic manipulation
terms
unknown
In the equation, a+28 = 60, "a" is referred to as an unknown instead of a variable as "a" has only one possible value
variable
constant
when a number constantly remains the same, for example the difference in age between mother and grandpa is always 28, the constant is 28
equation
if mothers age is "a" and grandpa's age is "b", then b=a+28. This is called an equation as it states the value of 2 mathematical expressions are equal (indicated by the sign =)
expression
e.g. mother is "a" years old, grandpa is 28 years older than mother, hence we can use a+28 (expression) for grandpa's age
exponent
the exponent is the power which the variable is raised to. For exmaple, in "a" to the power of 3, the exponent is 3
root of the equation
since a+28 = 60, "a" must be 32, hence 32 is the solution of the equation or the root of the equation
coefficient
it is the number which appears immediately in front of a variable or unknown. For example, when we multiple p by 3, we will get 3p and 3 is the coefficient of p. When we multiply q by 1, we usually write q and not 1q or q1, the coefficient of q is 1
monomial
solution
since a+28 = 60, "a" must be 32, hence 32 is the solution of the equation or the root of the equation
polynomial
they are algebraic expressions that consists of variables and coefficients. The terms in polynomials are written in decreasing order, with the highest exponent first, it is usually called the leading term
3 laws
associative law
an operation is associative if a change in grouping does not change the results, this means the parenthesis (or brackets) can be moved
eg. (2×3)×4 = 2×(3×4)
commutative law
an operation is commutative if a change in the order of the numbers does not change the results, this means the numbers can be swapped
e.g. 2+3 = 3+2
distributive law
distributive laws allows you to remove the parenthesis (or brackets) in an expression. Multiply the value outside the brackets with each of the terms in the brackets
e.g. 2 (3+4) = 2×3+2×4
