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Basic Arithmetic

Module by: ProgressiveQuest. E-mail the author

Summary: Understanding the Basics of Arithmetic.

About - Numbers

Insight

  • Components
    • Digit
    • Place-value
  • Sequence of digits.
  • Quantity or Count of something.
  • How much? How many?

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

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

About - Subtraction

Insight

  • 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 = atimesb'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

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

(Visualization: Check it using a grid with a rows and b columns.)

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.

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.

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

About - Division

Insight

  • Equal distribution or sharing
  • 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

t ÷ n.

(Visualization: n choclates are subtracted each time so that everyone gets one chocolate each time.)

Exercise 4

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

Solution

t ÷ n.

(Visualization: n chocolates are subtracted repeatedly from t chocolates because each student has to get n chocolates.)

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