Basic Theory of Mathematics
Adjacent - Next to each other.
Area - Total Outer area is the total area of an object.
Fractions:
o “Fractions with fractions”
o Golden Rule - “you can multiply or divide by the same number at the
bottom without changing the value”
o Three ways to write a fraction
integer 1
As a :
integer 2
As a decimal fraction: 0.5
As a negative force: 2−1
o Change to a Decimal: Use ʼn Calculator
o Change to a Percentage: Multiply by 100 by ʼn Calculator: 7/8 x 100 =
87.5%
Division: * Opposite of multiply * Answer is called the quotient
1 1 1 3
Divide by: The number by which it is divided is “reversed” ÷ = ×
2 3 2 1
Decimals:
o Change to ʼn fraction: the number of decimal places gives the number
17
of zeros in the denominator of the fraction: 0.17 =
100
o Change to a percentage: multiply by 100
o ʼn Finite decimal is ʼn decimal which “stops”
o ʼn Repeating decimal is a decimal with “repeating digits”
Exponents:
o Terminology 25 Exponent = 2 x 2 x 2 x 2 x 2
Base or base number
o In 4.32the 4 is the coefficient (fixed to the power - elevation is preferred)
2
4.3 = 4.9 = 36
o In 〖(4.3)2brackets MUST be worked out first: ( 4.3)2= 122= 144
, o Act 1: When powers are multiplied by the same base, add exponents:
m n m+n
a xa =a
o Act 2: If forces are divided by the same basis, subtract exponents:
m n m−n
a ÷ a =a
o Act 3: If a power is elevated to a further power , multiply exponents (
(a ¿¿ m)n=amn ¿
o Act 4: If a product is elevated to a power, each factor must be elevated
to the same power:
(ab)n =an bn of ¿
EQUIVALENT: Changes what something looks like but retains the same
value
PARALLEL: Lines that are always equidistant from each other
FACTORS: Factors are linked by multiplication to make one term.
FACTOR RING:
o The purpose of factorization is to change many terms to one term
Step 1: Remove a Common factor if there is one
Step 2: If two terms are separated by ʼn minus, try “difference of
quadates”
1. Write two sets of open brackets next to each other, put a + in
one and a - in the other one
2. √❑of the first term and write it before the + and - in the two
sets of brackets
3. √❑ of the second term and write the after the + and - in the
two sets of brackets
EQUAL ∆:
o Two equal sides and two angles
o Elevation lines: 2 elevation lines halve the sides to which they were
drawn
2 elevation lines halve the angles from which they are
drawn
EQUAL ∆: All angles and all sides are equal
COMMON FACTOR
Adjacent - Next to each other.
Area - Total Outer area is the total area of an object.
Fractions:
o “Fractions with fractions”
o Golden Rule - “you can multiply or divide by the same number at the
bottom without changing the value”
o Three ways to write a fraction
integer 1
As a :
integer 2
As a decimal fraction: 0.5
As a negative force: 2−1
o Change to a Decimal: Use ʼn Calculator
o Change to a Percentage: Multiply by 100 by ʼn Calculator: 7/8 x 100 =
87.5%
Division: * Opposite of multiply * Answer is called the quotient
1 1 1 3
Divide by: The number by which it is divided is “reversed” ÷ = ×
2 3 2 1
Decimals:
o Change to ʼn fraction: the number of decimal places gives the number
17
of zeros in the denominator of the fraction: 0.17 =
100
o Change to a percentage: multiply by 100
o ʼn Finite decimal is ʼn decimal which “stops”
o ʼn Repeating decimal is a decimal with “repeating digits”
Exponents:
o Terminology 25 Exponent = 2 x 2 x 2 x 2 x 2
Base or base number
o In 4.32the 4 is the coefficient (fixed to the power - elevation is preferred)
2
4.3 = 4.9 = 36
o In 〖(4.3)2brackets MUST be worked out first: ( 4.3)2= 122= 144
, o Act 1: When powers are multiplied by the same base, add exponents:
m n m+n
a xa =a
o Act 2: If forces are divided by the same basis, subtract exponents:
m n m−n
a ÷ a =a
o Act 3: If a power is elevated to a further power , multiply exponents (
(a ¿¿ m)n=amn ¿
o Act 4: If a product is elevated to a power, each factor must be elevated
to the same power:
(ab)n =an bn of ¿
EQUIVALENT: Changes what something looks like but retains the same
value
PARALLEL: Lines that are always equidistant from each other
FACTORS: Factors are linked by multiplication to make one term.
FACTOR RING:
o The purpose of factorization is to change many terms to one term
Step 1: Remove a Common factor if there is one
Step 2: If two terms are separated by ʼn minus, try “difference of
quadates”
1. Write two sets of open brackets next to each other, put a + in
one and a - in the other one
2. √❑of the first term and write it before the + and - in the two
sets of brackets
3. √❑ of the second term and write the after the + and - in the
two sets of brackets
EQUAL ∆:
o Two equal sides and two angles
o Elevation lines: 2 elevation lines halve the sides to which they were
drawn
2 elevation lines halve the angles from which they are
drawn
EQUAL ∆: All angles and all sides are equal
COMMON FACTOR
