Messmer High School
CHAPTER One -Introduction to Algebra
Subtraction as Distributive, Commutative and Associative properties.
Consider 935 Ð 786
935 = 900 + 30 + 5
786 = 700 + 80 + 6
935 Ð 786 = 900 + 30 + 5 Ð (700 + 80 + 6)
= 900 + 30 + 5 Ð 700 Ð 80 Ð 6 This is the distributive property
= 900 Ð 700 + 30 Ð 80 + 5 Ð 6 Commutative property
|
935 |
= |
900 |
+ |
30 |
+ |
5 |
|
- 786 |
= |
-700 |
- |
-80 |
- |
-6 |
|
_______ |
|
_______ |
|
________ |
|
________ |
|
|
|
|
|
|
|
|
Set up the stealing ( borrowing if you do not like to use the word ÒstealingÓ)
= 900 Ð 100 Ð 700 +100+ 30 Ð10 Ð 80 +10+ 5 Ð 6
Notice here we add subtract 100 and add it back, then we
subtract 10 and add it back. Maybe ÒborrowingÓ isnÕt such a bad term at all!
Borrowing uses the additive identity, commutative and associative properties.
|
935 |
= |
800 |
+ |
120 |
+ |
15 |
|
-786 |
= |
-700 |
+ |
-80 |
+ |
-6 |
|
_______ |
|
_______ |
|
________ |
|
________ |
|
|
|
100 |
|
40 |
|
9 |
100 + 40 + 9 = 149
Break apart the number into its composite pieces.
Apply distributive property to the parts of the number being
subtracted.
Subtract the like units from the like units. Set up any necessary ÒborrowingÓ.
Carry out the subtractions and add the results.
You should get the same result as if you had subtracted
using the methods you used in grade school.
This example shows how we use distributive property, how we can
alter the order of addition ( commutative property ) and the groupings ( associative
property ) and the additive identity to carry out whole number subtraction.
Think about this: How does you knowledge of arithmetic help
you understand the properties of algebra?
Write about it.