Division Property of Equality
The Division Property of Equality states that if you divide both sides of an equation by the same nonzero number, the equation remains balanced. It is used to solve multiplication equations: if 4x = 24, divide both sides by 4 to get x = 6. This is the inverse of multiplication and is one of the four basic equation-solving tools (addition, subtraction, multiplication, division properties of equality). This 6th grade algebra skill from enVision Mathematics Grade 6 is foundational to isolating variables in all algebraic equations.
Key Concepts
Property For any numbers $a$, $b$, and $c$, and $c \neq 0$, if $a = b$, then $\frac{a}{c} = \frac{b}{c}$. When you divide both sides of an equation by any non zero number, you still have equality. The goal in solving an equation is to 'undo' the operation on the variable. If a variable is multiplied by a number, we divide both sides by that number to 'undo' the multiplication.
Examples To solve $9x = 72$, we divide both sides by 9. This gives $\frac{9x}{9} = \frac{72}{9}$, which simplifies to $x = 8$. To solve $6y = 48$, we divide both sides by $6$. This gives $\frac{6y}{6} = \frac{48}{6}$, which simplifies to $y = 8$. To solve $5p = 15$, we divide both sides by 5. This gives $\frac{5p}{5} = \frac{15}{5}$, which simplifies to $p = 3$.
Explanation Think of this as fair sharing. If two sides of an equation are balanced, dividing both by the same non zero amount keeps them balanced. This is how we isolate a variable that's being multiplied by a number.
Common Questions
What is the Division Property of Equality?
The Division Property of Equality states that dividing both sides of an equation by the same nonzero number preserves equality. If 4x = 24, then 4x/4 = 24/4, so x = 6.
How do you use the Division Property of Equality to solve an equation?
Identify the coefficient multiplying the variable, then divide both sides by that coefficient. For 5y = 35: divide both sides by 5 to get y = 7.
Why can you not divide by zero?
Division by zero is undefined. The Division Property of Equality only applies to division by nonzero numbers. Dividing by zero produces an invalid result.
What grade learns the Division Property of Equality?
The Division Property of Equality is a 6th grade algebra concept in enVision Mathematics Grade 6, used throughout the chapter on one-step equations.
How does the Division Property of Equality relate to the Multiplication Property?
They are inverse properties. The Division Property undoes multiplication; the Multiplication Property undoes division. Together they handle all one-step equations involving multiplication or division.
What is a common mistake when using the Division Property?
Dividing only one side of the equation. You must divide both sides by the same number to maintain equality. The scale must stay balanced.