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 \(\quad c \neq 0\), then \(\frac{a}{c} = \frac{b}{c}\).


Example:


Start with the equation 10 = 10


Now divide both sides by 5


\(\frac{10}{5} = \frac{10}{5}\)


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 of 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:


\(\frac{4x}{4} = \frac{20}{4} \)


x = 5.
 

The Division Property of Equality means that if we divide both sides of an equation by the same number, it stays equal. This rule helps children learn how to solve equations step by step. With your help, they can understand it better through daily examples, like sharing things equally. The tips below will guide you in making this concept clear and fun for your child.

 

• If you divide one side of an equation, make sure to divide the other side by the same number to keep it balanced.
  
   
• Dividing by zero is not allowed, it makes the equation meaningless.
  
   
• If a variable is being multiplied, use division to find its value.
  
   
• Once you find the value of x, plug it back into the original equation to see if both sides match.
  
   
• Draw two sides of a balance with weights or stickers to show that equality means both sides are the same even after dividing.

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

Architecture: Architects use the Division Property of Equality to scale drawings, divide spaces equally, and maintain balance and symmetry in designs.


Robotics: In robotics, programmers and engineers divide values equally to balance motion and power. In an example, If a motor’s total torque must be shared equally among 4 robot arms, they divide the torque by 4 to maintain balance and equal performance.


Animation and Graphics: Animators and graphic designers often divide frames, movements, or pixels equally to keep scenes smooth and proportionate.

 

Physics: In physics, almost every formula involves balancing both sides of an equation.
Example: From \(v = \frac{d}{t}\), if d = vt, dividing both sides by t helps find v.


Engineering: Engineers often use the Division Property of Equality to solve equations when calculating force, pressure, speed, or resistance.