Arithmetic operations (addition, subtraction, multiplication, division)

Arithmetic operations (addition, subtraction, multiplication, division)

Arithmetic Operations

Addition

  • Joining or combining numbers is referred to as addition. The sum of two numbers is derived from combining the two numbers. For instance, the sum of 6 and 3 is 9.

  • Associative property of addition: When adding more than two numbers, the order of the numbers does not matter. For example, (4 + 3) + 2 = 4 + (3 + 2).

  • Commutative property of addition: When two numbers are added together, their order doesn’t matter. For example, 6 + 3 = 3 + 6.

Subtraction

  • Subtraction is used to calculate the difference between two numbers. For instance, the difference between 9 and 6 is 3.

  • Subtraction does not demonstrate the associative property. For example, (10 - 3) - 2 ≠ 10 - (3 - 2).

  • Subtraction also does not show the commutative property. For example, 6 - 3 ≠ 3 - 6.

Multiplication

  • Multiplication is the process of combining multiples of numbers. For example, 5 multiplied by 3 is 15 (5 groups of 3).

  • Associative property of multiplication: When more than two numbers are multiplied, the groupings do not matter. For example, (2 * 3) * 4 = 2 * (3 * 4).

  • Commutative property of multiplication: When two numbers are multiplied, the order does not matter. For example, 6 * 3 = 3 * 6.

Division

  • Division is the process of distributing a total equally. For example, if 15 is divided by 3, the result is 5.

  • Division does not exhibit the associative property. For example, (10 ÷ 2) ÷ 5 ≠ 10 ÷ (2 ÷ 5).

  • Division does not exhibit the commutative property either. For example, 10 ÷ 2 ≠ 2 ÷ 10.

Importance of Arithmetic Operations

  • Mastery of addition, subtraction, multiplication, and division is crucial in solving problems and understanding more complex mathematical operations.

  • Understanding the properties of these operations can be useful in making computations simpler and faster.

  • These four operations form the foundation from which other mathematical topics are derived. Whether it’s algebra, geometry, trigonometry, or calculus, arithmetic operations play a significant role.

Exercise Practice

  • Build confidence in arithmetic operations by solving as many practice problems as possible.

  • Learn and understand the use of these operations in different problem types such as word problems, puzzles, and equations.

  • Practice makes you proficient. Keep testing your skills with problems that require combining operations. Always revisit ones you found difficult.