Arithmetic Numbers

Introduction to Arithmetic numbers

Sometimes people use the term arithmetic synonymously with math or working with numbers. But often, it is used more specifically to refer to the four basic math operations: Addition, Subtraction, Multiplication, and Division.

Addition

The addition operation instructs us to consider two numbers and combine the values of both the numbers.

Example: If we add the amount 5 to the amount 10, we end up with the amount 15. The example demonstrates the addition operation as it combines two amounts.

Symbol: A plus sign (+) shows that two numbers are being added. 

Examples: 2+3=5, 10+20=30 etc.

Sign rules of addition

• Whenever a positive value is combined with another positive value, the sum is always positive.
  Example: (+150) + (+150) =+300 

• Whenever a negative value is combined with another negative value; the sum is always negative.
  Example:(-150) +(-150) = -300

• Whenever we add a negative number with a positive number; we need to subtract the two numbers and the sign of the largest number is considered.
  Example: (+150) +(-100) = +50

Subtraction

The subtraction operation instructs us to take away/separate one number from the other number.

Example: If we start with the number 10 and take away or subtract the amount 5, we have 5 left over. The example demonstrates subtraction operation as it takes an amount away from another and yields a difference amount. 

Symbol: A minus sign (-) is used to show when a number is being subtracted from another. 

Examples:3-2=1, 10-9=1 etc.

Sign rules of Subtraction

• The difference is always positive, when a positive value is subtracted from another positive value.
  Example: (+200) -(+100) = +100

• When a negative value is subtracted from another negative value; the difference is always negative.
  Example:(-400) -(-200) = -200

• When one among the two values is positive, and the other is negative, then we subtract the two numbers and the sign of the larger of the two numbers is considered.
  Example: (+4) -(-2) = +6

Multiplication

The multiplication operation instructs us to consider one number and repeat it several times. It is thus considered as repeated addition.

Example: If we have the amount 12 and we multiply it by 2 that means, we combine 2 groups of 12 to get a product of 24. So, 12 multiplied by 2 is the same as 12 added to 12. Thus, multiplication is considered as repeated addition.

Symbol: A time symbol (×)/ dot (.)/ asterisk (*) is used to show the multiplication operation. 

Example:2*10=20, 2×4=8, etc.

Sign rules of multiplication

• When two positive numerals are multiplied, the product is always positive.
  Example: (+2) *(+3) = +6

• When two negative numerals are multiplied, the product is always positive.
  Example: (-2) *(-3) =-6

• When a positive value is multiplied with a negative value, the product is always negative.
  Example: (+2) *(-3) = -6

Division

The division operation instructs us to consider a number and divide it into a certain number of equal groups.

Example: If we start with the number 12 and divide it with the number 2, this means that we want to separate 12 into 2 groups that are of the same size. In this context, that would be 2 groups of 6. Thus, division takes an amount and separates it into several equally sized groups.

If you notice, you can observe that division is similar to repeated subtraction.

Symbol: A division sign (÷) shows the division operation. 

Example: 20÷2=10, 30÷3 =10 etc. 

Sign rules of division

• When two positive digits are divided, the result is always positive.
  Example: (+4) ÷ (+2) = +2

• When two negative digits are divided, the result is always positive.
  Example: (-4) ÷ (-2) = +2

• When a positive value is divided by a negative value, the result is always negative.
  Example: (-4) ÷ (+2) = -2

Properties of Arithmetic numbers

1. Commutative property
   This property applies only to addition and multiplication operations.
   The Commutative property state that “if P and Q are two numbers then according to commutative property”, P+Q=Q+P, and P*Q=Q*P.
   Example:
   Consider two numbers: 2 and 3
   2+3=3+2, which is equal to 5
   2*3=3*2, which is equal to 6
   
2. Associative property
   This property applies only for addition and multiplication operations, just like the commutative property.
   The Associative property states that “if P, Q, and Rare three numbers, then according to associative property”, P+ (Q+R) =(P+Q) +R and P*(Q*R) = (P*Q)
   Example:
   Consider three numbers: 2, 4, 1
   2+ (4+1) = (2+4) +1, which is equal to 7
   2* (4*1) = (2*4) *1, which is equal to 8
   
3. Distributive Property
   Distributive property states that, if P, Q, and R are three numbers, then according to distributive property, P*(Q+R) = P*Q+P*R
   Example:
   Consider three numbers: 2, 4, 1
   2*(4+1) =2*4+2*1, which is equal to 10