Emma

November 6, 2020

Chapters

Power Formulas

{ a }^{ 0 } = 1

{ a }^{ 1 } = a

{ a }^{ -n } = \frac { 1 }{ { a }^{ n } } \qquad a \neq 0

{ a }^{ \frac { m }{ n } } = \sqrt [ n ]{ { a }^{ m } }

{ a }^{ m } \times { a }^{ n } = { a }^{ m+n }

\frac { { a }^{ m } }{ { a }^{ n } } = { a }^{ m-n }

{ ({ a }^{ m }) }^{ n } = { a }^{ m \times n}

{ a }^{ n } \times { b }^{ n } = { (ab) }^{ n }

\frac { { a }^{ n } }{ { b }^{ n } } = { (\frac { a }{ b }) }^{ n }

Fractions Formulas

Mixed Fraction

a \times \frac { b }{ c } = \frac { (a \times c) + b }{ c }

Equivalent Fractions

\frac { a }{ b } = \frac { c }{ d } \quad if \quad a \times d = b \times c

With the Same Denominator

\frac { a }{ b } + \frac { c }{ b } = \frac { a + c }{ b }

\frac { a }{ b } - \frac { c }{ b } = \frac { a-c }{ b }

With Different Denominator

\frac { a }{ b } + \frac { c }{ d } = \frac { (a \times d) + (b \times c) }{ b \times d }

\frac { a }{ b } - \frac { c }{ d } = \frac { (a \times d) - (b \times c) }{ b \times d }

Multiplying Fractions

\frac { a }{ b } \times \frac { c }{ d } = \frac { a \times c}{ b \times d }

Dividing Fractions

\frac { a }{ b } : \frac { c }{ d } = \frac { a \times d }{ b \times c }

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Radical Formulas

\sqrt [ n ]{ { a }^{ m } } = { a }^{ \frac { m }{ n } }

\sqrt [ n - k ]{ { a }^{ m - k } } = \sqrt [ n ]{ { a }^{ m } }

a\sqrt [ n ]{ b } = \sqrt [ n ]{ { a }^{ n } b }

a \sqrt [ n ]{ k } + b \sqrt [ n ]{ k } + c \sqrt [ n ]{ k } = (a+b+c) \sqrt [ n ]{ k }

\sqrt { a } \times \sqrt { b } = \sqrt { a \times b }

\frac { \sqrt [ n ]{ a } }{ \sqrt [ n ]{ b } } = \sqrt [ n ]{ \frac { a }{ b } }

\sqrt [ n ]{ \sqrt [ m ]{ a } } = \sqrt [ nm ]{ a }

Rationalization

1 \frac { a }{ b \sqrt { c } }

\frac { a }{ b \sqrt { c } } = \frac { a \times \sqrt { c } }{ b \sqrt { c } \times \sqrt { c } } = \frac { a \times \sqrt { c } }{ b { \sqrt { c } }^{ 2 } } = \frac { a \times \sqrt { c } }{ b \times c }

 

2 \frac { a }{ b \sqrt [ n ]{ { c }^{ m } } }

\frac { a }{ b \sqrt [ n ]{ { c }^{ m } } } = \frac { a \times \sqrt [ n ]{ { c }^{ n-m } } }{ b \times \sqrt [ n ]{ { c }^{ m } } \times \sqrt [ n ]{ { c }^{ n-m } } } = \frac { a\times \sqrt [ n ]{ { c }^{ n-m } } }{ b\times \sqrt [ n ]{ { c }^{ m }\times { c }^{ n-m } } } = \frac { a\times \sqrt [ n ]{ { c }^{ n-m } } }{ b\times \sqrt [ n ]{ { c }^{ n } } } = \frac { a\sqrt [ n ]{ { c }^{ n-m } } }{ bc }

 

3 \frac { a }{ \sqrt { b } + \sqrt { c } }

\frac { a }{ \sqrt { b } + \sqrt { c } } = \frac { a(\sqrt { b } - \sqrt { c } ) }{ (\sqrt { b } + \sqrt { c })( \sqrt { b } - \sqrt { c } ) } = \frac { a(\sqrt { b } - \sqrt { c } ) }{ { ( \sqrt { b } ) }^{ 2 } - { ( \sqrt { c } ) }^{ 2 } } = \frac { a(\sqrt { b } - \sqrt { c } ) }{ b - c }

Ratio Formulas

Ratio

\frac { a }{ b }

where,

a is the antecedent(numerator),

and b is the consequent(denominator).

Proportion

\frac { a }{ b } = \frac { c }{ d }

where,

a, d are extremos,

and b, c are medios.

 

a \times d = b \times c

\frac { a }{ b } = \frac { c }{ d } = \frac { e }{ f } = \frac { a + c + e}{ b + d + f }

\frac { a }{ b } = \frac { c }{ d } \qquad \frac { d }{ c } = \frac { b }{ a }

Mean Proportional

\frac { a }{ b } = \frac { b }{ d } \qquad b = \sqrt { a \times d }

Third Proportional

\frac { a }{ b } = \frac { b }{ d } \qquad a = \frac { { b }^{ 2 } }{ d }

Fourth Proportional

\frac { a }{ b } = \frac { c }{ d } \qquad a = \frac { b \times c }{ d }

Arithmetic Tables

Addition Table

Multiplication Table

Roman numerals

Cardinal numbers

Ordinal numbers

Metric System

Arithmetic

Arithmetic Problems and Worksheets

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.