Multiplication and Division Properties of Equality
Multiplication and division properties of equality is a Grade 6 algebra skill in Big Ideas Math Advanced 1, Chapter 13: Expressions and Equations. These properties state that multiplying or dividing both sides of an equation by the same non-zero number keeps the equation balanced, enabling students to isolate variables and solve one-step equations.
Key Concepts
Multiplication Property of Equality: Multiplying both sides of an equation by the same non zero number maintains the equality. If $a=b$ and $c \neq 0$, then $ac = bc$.
Division Property of Equality: Dividing both sides of an equation by the same non zero number maintains the equality. If $a=b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. These properties are used to isolate variables in equations.
Common Questions
What is the multiplication property of equality?
If a = b, then a x c = b x c for any number c. You can multiply both sides of an equation by the same number and it remains balanced. This is used to solve equations where a variable is divided, like x/4 = 5 — multiply both sides by 4 to get x = 20.
What is the division property of equality?
If a = b, then a / c = b / c for any non-zero number c. You can divide both sides of an equation by the same number. This is used to solve equations where a variable is multiplied, like 3x = 12 — divide both sides by 3 to get x = 4.
How do these properties help solve equations?
They allow you to undo operations applied to a variable. To isolate the variable, apply the inverse operation to both sides — multiplication undoes division, and division undoes multiplication.
Where is this skill taught in Big Ideas Math Advanced 1?
Multiplication and division properties of equality are covered in Chapter 13: Expressions and Equations of Big Ideas Math Advanced 1, the Grade 6 math textbook.