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Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign (+).
Subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with. Subtraction is denoted by a minus sign(-).The traditional names for the parts of the: c − b = a are minuend (c) − subtrahend (b) = difference (a).
Multiplication ( cross symbol “×”) is the mathematical operation of scaling one number by another. Because the result of scaling by whole numbers can be thought of as consisting of some number of copies of the original, whole-number products greater than 1 can be computed by repeated addition; for example, 3 multiplied by 4 (often said as “3 times 4”) can be calculated by adding 4 copies of 3 together:
Here 3 and 4 are the “factors” and 12 is the “product”.
Division The operation of determining how many times one quantity is contained in another ; the inverse of multiplication. Specifically, if c times b equals a, written:
where b is not zero, then a divided by b equals c, written:
In the above expression, a is called the dividend, b the divisor and c the quotient. Dividing two integers may result in a remainder.
Exponents and Powers An expression like 64 is called a power. The exponent 4 represents the number of times the base 6 is used as factor
Order of operations
- First do operations that occur within grouping symbols.
- Then evaluate powers.
- Then do multiplications and divisions from left to right.
- Additions and subtractions from left to right.
Properties of addition and multiplication
Commutative property
The order in which number are added does not change the sum.
a + b = b + a
The order in which number are added does not change the product.
a ∙ b = b ∙ a
Associative property
The way you group three numbers when adding does not change the sum.
(a + b) + c = a + (b + c)
The way you group three numbers when multiplying does not change the product.
(a ∙ b) ∙ c = a ∙ (b ∙ c)
The distributive property
a ∙ (b + c) = a ∙ b + a ∙ c
(b + c) ∙ a = b ∙ a + c ∙ a
a ∙ (b – c) = a ∙ b – a ∙ c
(b – c) ∙ a = b ∙ a – c ∙ a
