What is Division Property of Equality?
At times we refer to algebra as generalized arithmetic. Algebraic thinking plants seeds for many higher-order concepts as well helps in understanding the other domains of science.
The equation is a mathematical sentence with an equal sign, and it is one of the essential elements Algebra.
The operations of addition, subtraction, multiplication and division do not change the truth value of any equation.
The division property of equality states that when we divide both sides of an equation by the same non-zero number, the two sides remain equal.
That is, if a, b, and c are real numbers such that a = b and c ≠0, then a c =a c .
Example: Consider the equation 12 = 12.
Divide both sides by 4.
12 4 =12 4
3 = 3
That is, the equation still remains true.
Note, that the divisor cannot be zero as the division by zero is not defined.
This property is used in solving equations.
Example: 6x = 24
Divide both sides by 6.
6x 6 =24x 6
To check we can substitute the value of x in the original equation.
24 = 24
Example: Rhea bought 7 notebooks for $21. What is the cost of each notebook?
Let a be the cost of each notebook. Then, 7 times a is the total cost, $21.
That is, 7a = 21.
By the division property of equality, if you divide both sides by the same non-zero number, the equality still holds true. So, divide both sides by 7.
17a 7 =21 7
Therefore, the cost of each notebook is $3.
– Another form of the property is if a, b, c, and d are real numbers such that a = b, c = d and c, d ≠0, then a c =b d .