Division Property of Equality

When two things have the same value, we call them equal. In math, we use the ‘=’ sign to show that both sides are equal. For example, 2 + 3 = 5. Here, the left-hand side (LHS) is equal to the right-hand side (RHS). 
 

According to the division property of equality, when both sides of an equation are divided by the same non-zero number, the equality stays true. In other words, if a = b, and c  0, then ac = bc.
Example:
Start with the equation 10 = 10
Now divide both sides by 5
105 = 105
2 = 2
LHS = RHS. So both sides are equal.
 

The properties of equality are basic rules in math that explain how we can work with equations while keeping both sides equal. They help us perform basic operations like addition, subtraction, multiplication, and division without altering the meaning of the equation. Some of the properties of equality are given below:

• Reflexive Property of Equality
• Symmetric Property of Equality
• Transitive Property of Equality
• Substitution Property of Equality
• Addition Property of Equality
• Subtraction Property of Equality
• Multiplication Property of Equality
• Division Property of Equality
   

The multiplication property of equality states that if two values are equal, we can multiply both sides of the equation by the same number, and they’ll still be equal. In other words, if a = b, and c is any real number, then: 
a × c = b × c.  
Example:
Consider an equation 2 = 2
Now multiply both sides by 4:
2 × 4 = 2 × 4
8 = 8.
 

We use the division property of equality in various mathematical fields. It is often used in algebra when solving for the unknowns. This property also plays a crucial role while learning how logical steps keep equations balanced. For example, let’s say the given equation is 4x = 20. To isolate and solve for x, we have to divide both sides by 4:
4x/4 = 20/4
x = 5.
 

Whenever we want to split or share something equally, or when we need to find the value of one part of a whole, we use the division property of equality. We often use this in our daily lives without even realizing it, especially when dealing with sharing, measuring, or calculating costs. Given below are some real-life applications of the division property of equality

• Education: Teachers use division property of equality when dividing the resources equally among the students. If a teacher has 40 chocolates for 8 students. Dividing 40 by 8 gives 5 chocolates each.
• Business: In business, shopkeepers use the divisibility rule for finding the price of one item if they know the total price for many items. For example, if 10 books cost $500, dividing 500 by 10 gives $50 per book.
• Travel: Drivers use division property to find the speed or time by dividing distance by time or vice versa. If a car covers 300 km in 5 hours, we can find the kilometers it covered in an hour by dividing 300 by 5.