Basic Math , Real Numbers And Their Basic Properties

Front 1

A. Operations and their basic properties
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B. Order of operations

Back 1

Commutative property
Associative property
Distributive property

Front 2

Number Systems
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Back 2

Number Systems


Natural (counting) numbers: ordinary whole numbers generally used to express size
of a finite set, or to assign order in a finite sequence
(1,2,3…)

Whole numbers: includes all the natural numbers as well as zero
(0,1,2,3…)

Integers: all natural numbers (including zero), together with the negatives of non-zero
natural numbers
(… -3,-2,-1,0,1,2,3 …)

Rational numbers: any number that can be expressed as the quotient or fraction a/b
of two integers (b≠0); so it includes all the integers as well as fractions

Irrational numbers: any real number that is not rational. It includes pi, non-repeating,
Non-terminating decimals and square roots
(√2, π, e ….)

Real numbers: includes both rational and irrational numbers; can be thought of as points on an infinitely long number line

Front 3

Operations on real numbers:

Addition:

Like signs


Unlike signs

Back 3

Like signs;
KEEP THE SAME SIGN
5 + 2 = 7
-4 + (-7) = -11

Unlike signs;
**In addition of unlike signed numbers: find absolute value of each, subtract smaller
Number from larger value, write sign of the number with larger value
5 + (-3) = 2

Front 4

Subtraction:

Back 4

Subtraction:

Change subtraction symbol to addition
Write additive inverse of number being subtracted
Use addition rules

6 – 11 =
6 + (-11) = -5

(-3) – 7 = -10

Front 5

Multiplication:

Back 5

2 (3) = (3 + 3) = (2 + 2 + 2) = 6
-4 (2) = - (4 + 4) = - (2 + 2 + 2+ 2) = -8

Same signs  (+) product vs. different signs  (-) product

** If there are even number of negative factors  (+) product
** If there are odd number of negative factors  (-) product

(-2)(-1) = 2 vs. 3(-2)(-5)(-1) = -30