Formula Sheet | Adriamics Study

Prerequisites

Arithmetic | 16 of 17

Prerequisites: Addition. Enables: None.

Place value and comparison

Expanded form:

$$ 4382.65 = 4000 + 300 + 80 + 2 + 0.6 + 0.05 $$

Absolute value:

|a| \ge 0

Distance between two numbers:

$$ |a-b| $$

Basic operation properties

Addition:

$$ a + b = b + a $$

$$ (a+b)+c = a+(b+c) $$

Multiplication:

$$ ab = ba $$

$$ (ab)c = a(bc) $$

Distributive property:

$$ a(b+c)=ab+ac $$

Additive identity:

$$ a+0=a $$

Multiplicative identity:

a\cdot1=a

Additive inverse:

$$ a+(-a)=0 $$

Subtraction and division

Subtraction as addition:

$$ a-b=a+(-b) $$

Division as a fraction:

a\div b=\frac{a}{b}

where

b \ne 0

Remainder form:

$$ a=bq+r $$

where

0 \le r < b

Signed numbers

Same signs in multiplication or division give a positive result:

$$ (+)(+) = + $$

$$ (-)(-) = + $$

Different signs in multiplication or division give a negative result:

$$ (+)(-) = - $$

$$ (-)(+) = - $$

Fractions

Equivalent fractions:

\frac{a}{b}=\frac{ak}{bk}

Multiplication:

\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}

Division:

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

Addition with common denominator:

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

Subtraction with common denominator:

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

Unlike denominators:

\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}

Decimals

Decimal to fraction:

0.75=\frac{75}{100}=\frac{3}{4}

Multiplying by powers of ten:

a\cdot10^n

Dividing by powers of ten:

a\div10^n

Ratios and proportions

Ratio:

a:b=\frac{a}{b}

Proportion:

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

Cross products:

$$ ad=bc $$

Scale factor:

\text{new length}=k(\text{old length})

Percents

Percent as decimal:

p\%=\frac{p}{100}

Percent of a number:

\frac{p}{100}N

Finding percent:

\frac{A}{B}\cdot100\%

Percent increase:

\frac{\text{new}-\text{old}}{\text{old}}\cdot100\%

Percent decrease:

\frac{\text{old}-\text{new}}{\text{old}}\cdot100\%

Simple interest:

$$ I=Prt $$

Total amount:

$$ A=P(1+rt) $$

Numerical powers and roots

See Numerical powers, roots, and scientific notation for computational examples. Symbolic exponent laws and radicals belong to Algebra.

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