Solve for a variable using properties of multiplication

Learning Objectives Identify variables and coefficients within formulas for two-dimensional figures. Apply the Multiplication Property of Equality to isolate a variable in an equation. Apply the Division Property of Equality to isolate a variable in an equation. Rearrange common geometric formulas (e.g., area, perimeter) to solve for a specific dimension. Solve real-world problems involving two-dimensional figures by isolating an unknown variable. Explain the relationship between inverse operations and solving equations involving multiplication. Ever wondered how architects calculate the exact length of a wall needed for a specific room area? 📐 Or how much fabric you need for a triangular flag? In this lesson, you'll learn how to use the powerful properties of multipl...

TermDefinitionExample VariableA letter or symbol (like $x$, $y$, $A$, $l$) that represents an unknown numerical value in an equation or formula.In the formula $A = lw$, $A$, $l$, and $w$ are variables. EquationA mathematical statement that shows two expressions are equal, typically containing an equals sign (=).$2x = 10$ or $A = lw$ are examples of equations. CoefficientA numerical factor that multiplies a variable.In $5x$, $5$ is the coefficient. In $rac{1}{2}bh$, $rac{1}{2}$ is the coefficient of $bh$. Inverse OperationsOperations that undo each other. Multiplication and division are inverse operations.To undo multiplication by 3, you use division by 3. Multiplication Property of EqualityStates that if you multiply both sides of an equation by the same non-zero number, the equation re...

Multiplication Property of Equality If $a = b$, then $ac = bc$ (where $c \neq 0$). Use this property to eliminate a divisor or a fractional coefficient by multiplying both sides of the equation by the same non-zero number. Division Property of Equality If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$. Use this property to eliminate a coefficient that is multiplying a variable by dividing both sides of the equation by the same non-zero number. Area of a Rectangle $A = lw$ This formula relates the Area ($A$) of a rectangle to its length ($l$) and width ($w$). You can use multiplication and division properties to solve for $l$ or $w$ if $A$ is known. Area of a Triangle $A = \frac{1}{2}bh$ This formula relates the Area ($A$) of a triangle to its base (...