Basic Math Formulas

Find here a comprehensive list of basic math formulas commonly used when doing basic math computation

1. Arithmetic Operations

1.1 Whole Numbers

Operation	Symbol	Formula
Addition	+	a + b = sum
Subtraction	-	a - b = difference
Multiplication	×	a × b = product
Division	÷	a ÷ b = quotient

1.2 Fractions

Operation	Formula
Addition	$\frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd}$
	Example: $\frac{1}{2}+\frac{1}{3}=\frac{1\times 3+2\times 1}{2\times 3}=\frac{5}{6}$
Subtraction	$\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$
	Example: $\frac{1}{2}-\frac{1}{3}=\frac{1\times 3-2\times 1}{2\times 3}=\frac{1}{6}$
Multiplication	$\frac{a}{b}\times \frac{c}{d}=\frac{ac}{bd}$
	Example: $\frac{1}{2}\times \frac{1}{3}=\frac{1\times 1}{2\times 3}=\frac{1}{6}$
Division	$\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}=\frac{ad}{bc}$
	Example: $\frac{1}{2}÷\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}=\frac{1\times 3}{2\times 1}=\frac{3}{2}$

Note: For addition and subtraction of fractions with different denominators, find a common denominator first.

1.3 Converting Between Improper Fractions and Mixed Numbers

Conversion	Formula
Improper Fraction to Mixed Number	$\frac{a}{b}=q\frac{r}{b}$ where q = a ÷ b (quotient), r = remainder
	Example: $\frac{7}{3}=2\frac{1}{3}$
Mixed Number to Improper Fraction	$a\frac{b}{c}=\frac{a\times c+b}{c}$
	Example: $2\frac{1}{3}=\frac{2\times 3+1}{3}=\frac{7}{3}$

1.4 Consumer Math

Calculation	Formula
Discount	Discount = list price × discount rate
Sale price	Sale price = list price − discount
Discount rate	Discount rate = discount ÷ list price
Sales tax	Sales tax = price of item × tax rate
Interest	Interest = principal × rate of interest × time
Tips	Tips = cost of meals × tip rate
Commission	Commission = cost of service × commission rate

Note: Rates (discount rate, tax rate, interest rate, tip rate, commission rate) are typically expressed as decimals in these formulas. For example, 20% would be 0.20.

2. Geometry

2D Shapes

Shape	Area	Perimeter
Rectangle	A = l × w	P = 2l + 2w
Square	A = s²	P = 4s
Circle	A = πr²	C = 2πr
Triangle	A = (1/2) × b × h	P = a + b + c
Trapezoid	A = (1/2)(b1 + b2)h	P = a + b1 + b2 + c

3D Shapes

Shape	Volume	Surface Area
Cube	V = s³	SA = 6s²
Rectangular Prism (Box)	V = l × w × h	SA = 2(lw + lh + wh)
Sphere	V = (4/3)πr³	SA = 4πr²
Cylinder	V = πr²h	SA = 2πr² + 2πrh
Triangular Prism	V = (1/2)bhl	SA = bh + (s1 + s2 + s3)l

Note: For the triangular prism, b and h are the base and height of the triangular face, l is the length of the prism, and s₁, s₂, s₃ are the sides of the triangular face.

3. Percentages

Calculation	Formula
Percentage	$\text{Percentage}=\frac{\text{Part}}{\text{Whole}}\times 100$
	Calculates what percent one number is of another
Finding the Part	$\text{Part}=\frac{\text{Percentage}\times \text{Whole}}{100}$
	Calculates a specific percentage of a whole number
Finding the Whole	$\text{Whole}=\frac{\text{Part}\times 100}{\text{Percentage}}$
	Calculates the total when you know a part and its percentage

Additional Percentage Calculations

• Percentage increase: $\text{Increase}=\frac{\text{New Value}-\text{Original Value}}{\text{Original Value}}\times 100$
• Percentage decrease: $\text{Decrease}=\frac{\text{Original Value}-\text{New Value}}{\text{Original Value}}\times 100$

Note: When using these formulas, make sure to express the percentage as a number (e.g., 25 for 25%) and not as a decimal.

4. Basic Statistics

• Let a₁,a₂,a₃,......,a_n be a set of numbers, average = (a₁ + a₂ + a₃,+......+ a_n)/n
• Median: Middle value when the data is arranged in order
• Mode: Most frequently occurring value in a dataset(there can be more than 1!)

5. Simple Finance

Simple Interest: I = P × r × t

Where:

• I = Interest
• P = Principal
• r = rate (as a decimal)
• t = time (usually in years)