a = b then ac = bc
This statement is not true. In mathematics, if a = b, it does not necessarily mean that ac = bc. This is because the equation a = b only establishes equality between the values of a and b, not their product with another variable c. To determine if ac = bc, more information or equations involving a, b, and c would be needed.
To prove that if a = b, then ac = bc, we can use the commutative property of multiplication.
1. Given: a = b
To prove: ac = bc
Proof:
Step 1: Multiply both sides of the equation a = b by c.
a * c = b * c
Step 2: Apply the commutative property of multiplication.
c * a = c * b
Step 3: Rearrange the order of multiplication using the commutative property.
ac = bc
Therefore, we have successfully proven that if a = b, then ac = bc.
The equation you have stated is: a = b.
To prove that ac = bc, we need to multiply both sides of the equation "a = b" by the same value, which is c in this case.
So, multiply both sides of the equation by c:
a * c = b * c
By the commutative property of multiplication, we can rearrange the order of multiplication:
c * a = c * b
Since multiplication is commutative, the order doesn't matter. Therefore, we can switch the order:
ac = bc
Hence, if a = b, then ac = bc.