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33 results for “arithmetic”

Formulae (33)

Percentage

\% = \frac{\text{part}}{\text{whole}} \times 100

What fraction of a whole a part represents, out of 100.

Arithmetic & BasicsBasic

Percent of a Number

\text{value} = \frac{p}{100} \times N

Find p percent of a number N.

Arithmetic & BasicsBasic

Percentage Change

\% \text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Increase or decrease of a value as a percentage.

Arithmetic & BasicsBasic

Fraction to Decimal

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

Convert a fraction into a decimal by dividing.

Arithmetic & BasicsBasic

Adding Fractions

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

Add two fractions using a common denominator.

Arithmetic & BasicsBasic

Multiplying Fractions

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

Multiply numerators and denominators straight across.

Arithmetic & BasicsBasic

Dividing Fractions

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

Divide by multiplying by the reciprocal (flip and multiply).

Arithmetic & BasicsBasic

Average (Mean)

\text{average} = \frac{\text{sum of values}}{\text{number of values}}

Add all values and divide by how many there are.

Arithmetic & BasicsBasic

Ratio

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

Compares two quantities by division.

Arithmetic & BasicsBasic

Proportion (Cross Multiply)

\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc

Two equal ratios; solve using cross multiplication.

Arithmetic & BasicsBasic

Unit Rate

\text{unit rate} = \frac{\text{total}}{\text{quantity}}

Cost or amount for a single unit.

Arithmetic & BasicsBasic

Speed = Distance ÷ Time

s = \frac{d}{t}

How fast something moves.

Arithmetic & BasicsBasic

Distance = Speed × Time

d = s \times t

How far something travels.

Arithmetic & BasicsBasic

Rounding Rule

5\text{ or more} \uparrow, \ 4\text{ or less} \downarrow

Round up if the next digit is 5+, otherwise round down.

Arithmetic & BasicsBasic

Order of Operations (PEMDAS)

P \to E \to (M \div D) \to (A \div S)

Parentheses, Exponents, Multiply/Divide, Add/Subtract.

Arithmetic & BasicsBasic

Place Value

N = \sum d_i \times 10^{i}

Each digit’s value depends on its position.

Arithmetic & BasicsBasic

Even and Odd

n \bmod 2 = 0 \Rightarrow \text{even}

A number is even if it divides by 2 with no remainder.

Arithmetic & BasicsBasic

Discount Price

\text{price} = N \left(1 - \frac{p}{100}\right)

Final price after a percentage discount.

Arithmetic & BasicsBasic

Sales Tax Total

\text{total} = N \left(1 + \frac{t}{100}\right)

Price after adding a percentage tax.

Arithmetic & BasicsBasic

Tip Amount

\text{tip} = \frac{p}{100} \times \text{bill}

Gratuity as a percentage of the bill.

Arithmetic & BasicsBasic

Percent Increase

new = old(1 + p)

Value after a percentage increase.

Arithmetic & BasicsBasic

Percent Decrease

new = old(1 - p)

Value after a percentage decrease.

Arithmetic & BasicsBasic

Mixed Number to Fraction

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

Convert a mixed number to an improper fraction.

Arithmetic & BasicsBasic

Reciprocal

\frac{1}{x}

The multiplicative inverse of a number.

Arithmetic & BasicsBasic

Square of a Number

n^2 = n\times n

A number multiplied by itself.

Arithmetic & BasicsBasic

Cube of a Number

n^3 = n\times n\times n

A number multiplied by itself three times.

Arithmetic & BasicsBasic

Square Root

\sqrt{n}

The value that squares to n.

Arithmetic & BasicsBasic

Divisibility by 3

\text{digit sum divisible by 3}

A number is divisible by 3 if its digit sum is.

Arithmetic & BasicsBasic

Divisibility by 9

\text{digit sum divisible by 9}

A number is divisible by 9 if its digit sum is.

Arithmetic & BasicsBasic

Percent to Fraction

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

Convert a percentage to a fraction.

AlgebraBasic

Arithmetic Series Sum

S_n = \frac{n}{2}(a_1 + a_n)

Sum of the first n terms of an arithmetic sequence.

AlgebraBasic

Arithmetic nth Term

a_n = a_1 + (n-1)d

The nth term of an arithmetic sequence.

Statistics & ProbabilityBasic

Arithmetic Mean

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i

The average of a data set.