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Basic Arithmetic Operations

Module by: ProgressiveQuest. E-mail the author

Summary: Understanding the basic arithmetic operations namely Addition, Subtraction, Multiplication and Division.

About - Operation

Insight

  • Components
    • Operation: 2 + 3
    • Operator: + (plus)
    • Operands: 2 and 3
  • Properties
    • Commutative: a $ b = b $ a
    • Associative: (a $ b) $ c = a $ (b $ c)

About - Addition

Insight

  • Plus
  • Sum
  • Summation
  • Totalling
  • Counting
  • Properties
    • Commutative: a + b = b + a
    • Associative: (a + b) + c = a + (b + c)

About - Subtraction

Insight

  • Minus
  • Difference

Properties

  • Not Commutative: a - b ≠ b - a
  • Not Associative: (a - b) - c ≠ a - (b - c)

About - Multiplication

Insight

  • Product
  • Shortcut of repeated addition
  • a X b = a times b's = b + b + b + ... a times
  • Properties
    • Commutative: a X b = b X a
    • Associative: (a X b) X c = a X (b X c)

Exercises

Exercise 1

Why is a X b always equal to b X a?

Solution

Visualization: Draw a grid with a rows and b columns and rotate the page 90 degress so that the rows appear as columns and columns appear as rows. Now we have b rows and a columns.

a X b = a times b's = b times a's = b X a.

Exercise 2

If a X b = c then why is c ÷ a = b and c ÷ b = a?

Solution

Note: a times b's = b times a's = c.

Visualization: Draw a grid with a rows and b columns, or; b rows and a columns.

If we repeatedly take away b's then that can be done a times. Therefore c ÷ b = a.

If we repeatedly take away a's then that can be done b times. Therefore c ÷ a = b.

About - Division

Insight

  • Sharing or Distributing equally
  • Shortcut of repeated subtraction
  • a ÷ b denotes b is repeatedly subtracted from a for maximum number of times.
  • Components
    • Quotient: How much each one will get? How many times a number can be repeatedly subtracted?
    • Remainder: How much will remain that can not be distributed?

Properties

  • Not Commutative: a ÷ b ≠ b ÷ a
  • Not Associative: (a ÷ b) ÷ c ≠ a ÷ (b ÷ c)

Exercises

Exercise 3

If t chocolates are distributed among n students, how many choclates each student will get?

Solution

Visualization: Distributing equally.

Visualization: Repeatedly subtracting n chocolates from t chocolates so that each student gets one.

t ÷ n.

Exercise 4

If each student should get n chocolates. How many students will get chocolates if there are t chocolates?

Solution

Visualization: Repeatedly subtracting n chocolates from t chocolates because each student should get n chocolates.

t ÷ n.

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