2006-06-18 23:49:49 · 14 answers · asked by forgetfulpcspice 3 in Science & Mathematics ➔ Mathematics
a/a = 1 (axiom: any thing except zero divided by the same yields 1 all the time)
so, a/a = 1
now multiplying everyside by (a/1) we get,
a/a * (a/1) = 1* (a/1)
or a^2/a = a/1
or a = a/1 (axiom: anything except zero multiplied by 1 yields the same number)
so it is proved that a = a/1
2006-07-02 17:36:09 · answer #1 · answered by TJ 5 · 2⤊ 0⤋
a/1=a <=> a= a*1 <=> a=a
2006-06-18 23:54:01 · answer #2 · answered by denis_gk 1 · 0⤊ 0⤋
OK, a/1 = a. Begin by removing the fraction. This is done by multiplying both sides of the equation by "1": (a/1)*1 = a *1=> a*(1/1) = a => a*1 = a => a = a (applying the multiplicative identity).
2006-07-02 12:30:33 · answer #3 · answered by flyfisher_20750 3 · 0⤊ 0⤋
If u times 1 by 1, then a times 1.
Then ur conclusion will be a=a which means a equals a
2006-07-02 10:49:03 · answer #4 · answered by jagger7@verizon.net 1 · 0⤊ 0⤋
Proof of a/1=a using direct proof (deduction)
a/1=a (Given)
a*1/1=a*1 ("Golden rule of mathematics, what is done to one side of an equation must be done to the other)
a*1=a*1 (1/1=1 Substitution property of equality)
a=a (1*a=a Identity property of equality)
2006-06-28 17:05:13 · answer #5 · answered by sonicfan2006 1 · 0⤊ 0⤋
1 is the identity element for multiplication,
thus a = a * 1 by definition.
divide both sides by 1, and you have a/1 = a
2006-07-02 19:26:42 · answer #6 · answered by noshyuz 4 · 0⤊ 0⤋
You divide both sides by a so you have a/a = a/a = 1
2006-07-02 19:11:42 · answer #7 · answered by Joseph Binette 3 · 0⤊ 0⤋
If you split a into 1 group, you will have 1 group equaling a.
Hence,
a/1=a
2006-07-01 18:19:58 · answer #8 · answered by _anonymous_ 4 · 0⤊ 0⤋
By definition using the identity property for division: a/1=a.
Identity property for multiplication: a*1=a.
Identity property for addition: a+0=a.
Identity property for subtraction: a-0=a.
Identity property for exponents: a^1=a.
2006-07-02 19:22:34 · answer #9 · answered by slobberknocker_usa 7 · 0⤊ 0⤋
a/1=a•1^(-1)=a•1=a (1 is its own inverse since 1•1=1)
2006-06-19 00:01:57 · answer #10 · answered by Eulercrosser 4 · 0⤊ 0⤋