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A b = b a is an example of the property called
A b = b a is an example of the property called the [B]commutative property of multiplication[/B].

Addition and Multiplication Multiples
Shows all addition and multiplication multiples up to 20 for a positive integer

Addition and Multiplication Tables (Times Tables)
Shows the color coded addition or multiplication table entries and answer for any 2 numbers 1-15.

Associative Property
Demonstrates the associative property using 3 numbers. Covers the Associative Property of Addition and Associative Property of Multiplication. Also known as the Associative Law of Addition and Associative Law of Multiplication Numerical Properties

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

Commutative Property
Demonstrates the commutative property of addition and the commutative property of multiplication using 3 numbers. Numerical Properties

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

Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of
Currently 16 out of every 25 American adults drink coffee every day. In a town with a population of 7900 adults, how many of these adults would you expect to drink coffee ever We'd multiply 16/25 times 7900: Using our [URL='https://www.mathcelebrity.com/fraction.php?frac1=7900&frac2=16/25&pl=Multiply']fraction multiplication calculator by type 16/25 of 7900[/URL], we get: [B]5056[/B]

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]

Every 6 customers receive a soda, every 8 a hot dog there are 329 customers . how many received both
This is a least common multiple problem. [URL='http://www.mathcelebrity.com/gcflcm.php?num1=6&num2=8&num3=&pl=LCM']The least common multiple of 6 and 8 is 24[/URL] So every 24th person, less than or equal to 329 receives both a soda [U]and[/U] a hot dog. Using our multiples calculator, we find there are [URL='http://www.mathcelebrity.com/multiple.php?num=24&pl=Multiplication+Multiples']13 multiples of 24 less than or equal to 329[/URL]. 24,48,72,96,120,144,168,192,216,240,264,288,312

Expand Master and Build Polynomial Equations
This calculator is the ultimate expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.
Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)x
* Polynomial Expansions c(d + e + f)x
* FOIL Expansions (a + b)(c + d)
* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)


Finite Field
Demonstrates the addition table and multiplication table for a finite field (Galois Field) of n denoted GF(n).

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

Lattice Multiplication
Performs Lattice Multiplication or the Napiers Bones (Napier Rods) method of multiplication

Multiplication Array
This allows you to enter pictorials using * symbols to represent multiplication

Multiplication Comparison
Evaluates a multiplication comparison

Multiplication Equality Property
Demonstrates the Multiplication Equality Property Numerical Properties

Multiplication Property Of Inequality
Demonstrates the Multiplication Property Of Inequality Numerical Properties

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

Zero Multiplication Property
Demonstrates the Zero Multiplication property using a number. Also called the Zero Product Property. Numerical Properties