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Algebra Master (Polynomials)
Given 2 polynomials this does the following:
1) Polynomial Addition
2) Polynomial Subtraction

Also generates binomial theorem expansions and polynomial expansions with or without an outside constant multiplier.

Balancing Equations
Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.

Basic m x n Matrix Operations
Given 2 matrices |A| and |B|, this performs the following basic matrix operations
* Matrix Addition |A| + |B|
* Matrix Subtraction |A| - |B|
* Matrix Multiplication |A| x |B|
* Scalar multiplication rA where r is a constant.

Basic Math Operations
Given 2 numbers, this performs the following arithmetic operations:
* Addition (Adding) (+)
* Subtraction (Subtracting) (-)
* Multiplication (Multiplying) (x)
* Long division (Dividing) with a remainder (÷)
* Long division to decimal places (÷)
* Partial Sums (Shortcut Sums)
* Short Division
* Duplication and Mediation

Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign
Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation [LIST=1] [*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition. [*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication [/LIST] So we have the start equation: 3x - 7 If the answer was x = -4, then we plug this in to get our number on the right side of the equation: 3(-4) - 7 -12 - 7 -19 This means our original equation was: [B]3x - 7 = -19[/B] And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get: x = -4

Complex Number Operations
Given two numbers in complex number notation, this calculator:
1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.
2) Determines the Square Root of a complex number denoted as √a + bi
3) Absolute Value of a Complex Number |a + bi|
4) Conjugate of a complex number a + bi

Counting on a Number Line
Shows addition or subtraction by moving left or right on a number line.

Danny's mom ate 1/6 of an ice cream cake. Danny and his sister want to split the remainder of it. Ho
Danny's mom ate 1/6 of an ice cream cake. Danny and his sister want to split the remainder of it. How much of the cake would each get? If Danny's mom ate 1/6 of the cake, then we have: 1 - 1/6 of the cake left. We [URL='https://www.mathcelebrity.com/fraction.php?frac1=1&frac2=1%2F6&pl=Subtract']use our fraction subtraction calculator[/URL] for 1 - 1/6 to get: 5/6 If Danny and his sister split the remainder, then we divide 5/6 by 2. It's also the same as multiplying 5/6 by 1/2: We [URL='https://www.mathcelebrity.com/fraction.php?frac1=5%2F6&frac2=1%2F2&pl=Multiply']use our fraction multiplication calculator[/URL] to get: [B]5/12 for Danny and his sister[/B]

Fractions and Mixed Numbers
Given (improper fractions, proper fraction, mixed numbers, or whole numbers), this performs the following operations:
* Addition (Adding)
* Subtraction (Subtracting)
* Positive Difference (Absolute Value of the Difference)
* Multiplication (Multiplying)
* Division (Dividing: complex fraction division is included)
* Compare Fractions
* Simplifying of proper and improper fractions as well as mixed numbers. Fractions will be reduced down as far as possible (Reducing Fractions).
* Reciprocal of a Fraction
* Find all fractions between two fractions
* reduce a fraction

Given: BC = EF AC = EG AB = 10 BC = 3 Prove FG = 10
Given: BC = EF AC = EG AB = 10 BC = 3 Prove FG = 10 [LIST] [*]AC = AB + BC (Segment Addition Postulate) [*]AB = 10, BC = 3 (Given) [*]AC = 10 + 3 (Substitution Property of Equality) [*]AC = 13 (Simplify) [*]AC = EG, BC = EF (Given) [*]EG = 13, EF = 3 (Segment Equivalence) [*]EG = EF + FG (Segment Addition Postulate) [*]13 = 3 + FG (Substitution Property of Equality) [*]FG = 10 (Subtraction Property) [/LIST]

Percent Math
Simplifies expressions involving numbers and percents with respect to addition and subtraction

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.
Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7. Collinear means on the same line. By segment subtraction, we have: AB = AC - BC AB = 15 - 7 AB = [B]8[/B]

Signed Integer Operations
This performs a string of signed integer operations, either all addition and subtraction, or all multiplication and division.

Subtraction Equality Property
Demonstrates the Subtraction Equality Property Numerical Properties

Subtraction Property Of Inequality
Demonstrates the Subtraction Property Of Inequality Numerical Properties

True False Equations
Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent. Also known as true or false equations

Vectors
Given 2 vectors A and B, this calculates:
* Length (magnitude) of A = ||A||
* Length (magnitude) of B = ||B||
* Sum of A and B = A + B (addition)
* Difference of A and B = A - B (subtraction)
* Dot Product of vectors A and B = A x B
A ÷ B (division)
* Distance between A and B = AB
* Angle between A and B = θ
* Unit Vector U of A.
* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).
* Cauchy-Schwarz Inequality
* The orthogonal projection of A on to B, projBA and and the vector component of A orthogonal to B → A - projBA
Also calculates the horizontal component and vertical component of a 2-D vector.