i need help on properties of arithmetic
https://www.khanacademy.org/math/arithmetic/order-of-operations
you have study island ? practice there
http://www.khanacademy.org/math/arithmetic/order-of-operations
Of course! I'd be happy to help with properties of arithmetic. Arithmetic is the branch of mathematics that deals with operations like addition, subtraction, multiplication, and division. There are several important properties that govern these operations. Let me explain each property and how to apply them:
1. Commutative Property:
The commutative property states that the order of numbers does not affect the result of addition or multiplication. In simpler terms, it means that you can add or multiply numbers in any order and still get the same answer.
Example for addition: a + b = b + a
Example for multiplication: a × b = b × a
2. Associative Property:
The associative property states that the grouping of numbers does not affect the result of addition or multiplication. This means that you can group or regroup numbers and still get the same answer.
Example for addition: (a + b) + c = a + (b + c)
Example for multiplication: (a × b) × c = a × (b × c)
3. Distributive Property:
The distributive property relates addition and multiplication. It states that multiplying a number by a sum is the same as multiplying the number by each term of the sum and then adding the results together.
Example: a × (b + c) = (a × b) + (a × c)
4. Identity Property:
The identity property states that the sum of any number and zero is equal to the original number, and the product of any number and one is equal to the original number. In other words, zero is the identity element for addition, and one is the identity element for multiplication.
Example for addition: a + 0 = a
Example for multiplication: a × 1 = a
5. Inverse Property:
The inverse property states that every number has an additive inverse and a multiplicative inverse. The additive inverse of a number is the number that, when added to the original number, gives a sum of zero. The multiplicative inverse of a number is the number that, when multiplied by the original number, gives a product of one.
Example for addition: a + (-a) = 0
Example for multiplication: a × (1/a) = 1
By understanding and applying these properties, you can simplify arithmetic expressions, perform calculations more easily, and manipulate numbers efficiently.