First we show that:
(a / b) ⋅ c ⋅ b = a ⋅ (1 / b) ⋅ c ⋅ b (step 3)
Then we use the Commutative and Associative properties to reorder some of the terms:
a ⋅ (1 / b)) ⋅ c ⋅ b = (1 / b) ⋅ b ⋅ a ⋅ c (step 4)
Then we show that:
(1 / b) ⋅ b ⋅ a ⋅ c = 1 ⋅ a ⋅ c (step 7)
Then we simplify the right side as follows:
1 ⋅ a ⋅ c = a ⋅ c (step 9)
Finally, we use the Transitive Property a few times to reach our conclusion.
Quiz (1 point)
- a / b = a ⋅ (1 / b)
- ((a ⋅ b) ⋅ c) ⋅ d = ((b ⋅ d) ⋅ a) ⋅ c
- 1 ⋅ a = a
if a = b, then a ⋅ c = b ⋅ c
if a = b, then a ⋅ c = b ⋅ c
if not (a = 0), then (1 / a) ⋅ a = 1
if a = b, then a ⋅ c = b ⋅ c
if a = b, then a ⋅ c = b ⋅ c
if a = b, then a ⋅ c = b ⋅ c
if the following are true:
- a = b
- b = c
then a = c
if the following are true:
- a = b
- b = c
then a = c
if the following are true:
- a = b
- b = c
then a = c
Please write your proof in the table below. Each row should contain one claim. The last claim is the statement that you are trying to prove.