Prove (ab)/b=a

Proof 1. (ab)/b=(ab)x 1/b

Is this property of reciprocal?
or definition of division

To prove that (ab)/b = a, you can use either the property of reciprocals or the definition of division.

Proof 1 using the property of reciprocals:
1. Start with the expression (ab)/b.
2. According to the property of reciprocals, we can rewrite this expression as (ab) * (1/b), where 1/b is the reciprocal of b.
3. Simplify the expression by multiplying (ab) and (1/b), resulting in ab/b.
4. Since b/b = 1 (any number divided by itself equals 1), we can simplify further to ab/1.
5. Any number divided by 1 is equal to the number itself, so ab/1 is equal to ab.
6. Therefore, (ab)/b = ab = a.

Proof 2 using the definition of division:
1. Start with the expression (ab)/b.
2. By the definition of division, dividing by b is the same as multiplying by the reciprocal of b. So, we can rewrite this expression as (ab) * (1/b).
3. Simplify the expression by multiplying (ab) and (1/b), resulting in ab/b.
4. Since b/b = 1, we can simplify further to ab/1.
5. Any number divided by 1 is equal to the number itself, so ab/1 is equal to ab.
6. Therefore, (ab)/b = ab = a.

Both proofs demonstrate that (ab)/b is equal to a, regardless of using the property of reciprocals or the definition of division.