OpenStax-CNX module: m43274
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Addition, Subtraction,
Multiplication and Division of
∗
Whole Numbers
ProgressiveQuest
This work is produced by OpenStax-CNX and licensed under the
†
Creative Commons Attribution License 3.0
1 About - Operation
1.1 Insight
• Components
·
·
·
Operation: 2 + 3
Operator: + (plus)
Operands: 2 and 3
• Properties
·
·
Commutative: a $ b = b $ a
Associative: (a $ b) $ c = a $ (b $ c)
2 About - Addition
2.1 Insight
• Plus
• Sum or Summation
• Totalling
• Counting
• Properties
· Commutative: a + b = b + a
· Associative: (a + b) + c = a + (b + c)
∗ Version
1.1: Feb 20, 2012 8:14 pm -0600
† http://creativecommons.org/licenses/by/3.0/
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OpenStax-CNX module: m43274
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3 About - Subtraction
3.1 Insight
• Minus
• Dierence
Properties
• Not Commutative: a - b 6= b - a
• Not Associative: (a - b) - c 6= a - (b - c)
4 About - Multiplication
4.1 Insight
• Product
• Shortcut of repeated addition
• a X b = a times b's = b + b +
• Properties
b + ... a times
· Commutative: a X b = b X a
· Associative: (a X b) X c = a X (b X c)
4.2 Exercises
Exercise 1
Why is a X b always equal to b X a?
Exercise 2
If a X b = c then why is c ÷ a = b and c ÷ b = a?
(Solution on p. 4.)
(Solution on p. 4.)
5 About - Division
5.1 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 6= b ÷ a
• Not Associative: (a ÷ b) ÷ c 6= a ÷ (b ÷ c)
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OpenStax-CNX module: m43274
5.2 Exercises
Exercise 3
(Solution on p. 4.)
If t chocolates are distributed among n students, how many choclates each student will get?
Exercise 4
(Solution on p. 4.)
If each student should get n chocolates. How many students will get chocolates if there are t
chocolates?
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OpenStax-CNX module: m43274
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Solutions to Exercises in this Module
Solution to Exercise (p. 2)
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.
Solution to Exercise (p. 2)
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.
Solution to Exercise (p. 3)
Visualization: Distributing equally.
Visualization: Repeatedly subtracting n chocolates from t chocolates so that each student gets one.
t ÷ n.
Solution to Exercise (p. 3)
Visualization: Repeatedly subtracting
chocolates.
t ÷ n.
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n chocolates from t chocolates because each student should get n