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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

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

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 .

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

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

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

Visualization: Distributing equally.

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

t ÷ n .

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

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

t ÷ n .

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Source:  OpenStax, Math. OpenStax CNX. Feb 18, 2012 Download for free at http://cnx.org/content/col11409/1.12
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