Mathematics Handbook/Multiplication: Difference between revisions
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==Rules== | |||
#a x 0 = 0 | |||
#a x 1 = a | |||
#a x a = a<sup>2</sup> | |||
#a x -a = -a<sup>2</sup> | |||
==Properties== | ==Properties== | ||
'''Commutative property''' | '''Commutative property''' | ||
'' | '''''Addition''''' | ||
a + b = b + a | a + b = b + a | ||
a + b + c = a + c + b | a + b + c = a + c + b | ||
| Line 19: | Line 25: | ||
= 10 | = 10 | ||
''' | '''''Multiplication''''' | ||
a x b = b x a | a x b = b x a | ||
a x b x c = a x c x b | a x b x c = a x c x b | ||
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(a - b)(c + d) = a(c + d) - b(c + d) | (a - b)(c + d) = a(c + d) - b(c + d) | ||
[[Category:Mathematics Handbook]] | |||
Latest revision as of 02:37, 12 June 2011
Rules
- a x 0 = 0
- a x 1 = a
- a x a = a2
- a x -a = -a2
Properties
Commutative property
Addition
a + b = b + a
a + b + c = a + c + b
= b + a + c
= b + c + a
= c + a + b
= c + b + a
To add two, three or more numbers the order of their arrangement in the sum does no matter.
Example:
2 + 3 + 5 = 2 + 5 + 3
= 3 + 2 + 5
= 3 + 5 + 2
= 5 + 2 + 3
= 5 + 3 + 2
= 10
Multiplication
a x b = b x a
a x b x c = a x c x b
= b x a x c
= b x c x a
= c x a x b
= c x b x a
To multiply two, three or more numbers the order of their arrangement in the product does no matter.
Example:
2 x 3 x 5 = 2 x 5 x 3
= 3 x 2 x 5
= 3 x 5 x 2
= 5 x 2 x 3
= 5 x 3 x 2
= 30
Associative property:
- (a x b) x c = a x (b x c)
To multiply a x b x c; it does not matter whether to first associate a and b, then associate the result with c or to first associate b and c, then associate the result with a associate
Distributive property
- a(b + c) = ab + ac → a is distributed over b and c
(a + b)(c + d) = a(c + d) + b(c + d) (a + b)(c - d) = a(c - d) + b(c - d) (a - b)(c + d) = a(c + d) - b(c + d)