7.2: Solve for the Unknown
Solve for the Unknown  Apply Order of Operations
Teacher Notes
Presented with an equation with one unknown, students follow the rule for the order of operations to solve for the value of the unknown. In all equations, unknowns are presented alone as one of the expressions of the equation. All computations are performed on the other expression. The operations to be performed are those in parentheses first, followed, from left to right, by multiplication and division, and then by addition and subtraction.
Solutions

\begin{align*}e =18\end{align*}
e=18 
\begin{align*}a = 1\end{align*}
a=1 
\begin{align*}c = 15\end{align*}
c=15 
\begin{align*}b = 19\end{align*}
b=19 
\begin{align*}d = 9\end{align*}
d=9
\begin{align*}(3 + 5) \div 2 + 4 \times 6 = a\end{align*}
\begin{align*}\mathbf{What's \ the \ value \ of} \ a?\end{align*}
\begin{align*}& \mathbf{Describe:} && \text{The equation has parentheses and three operations, addition, division, and}\\ &&& \text{multiplication. The variable is} \ a.\\ & \mathbf{My \ Job:} && \text{Do the operations to figure out the value of} \ a.\\ & \mathbf{Plan:} && \text{Follow the rule for the order of operations: parentheses first, then multiplication}\\ &&& \text{and division from left to right, and then addition and subtraction from left to right.}\\ & \mathbf{Solve} && \text{Equation} \qquad \qquad \qquad \qquad (3 + 5) \div 2 + 4 \times 6 = a\\ &&& \text{Parentheses} \qquad \qquad \qquad \quad 8 \div 2 + 4 \times 6 = a\\ &&& \text{Multiplication and} \qquad \qquad 4 + 24 = a\\ &&& \text{Division (left to right)}\\ &&& \text{Addition and} \qquad \qquad \qquad \ 28 = a\\ &&& \text{Subtraction (left to right)}\\ & \mathbf{Check:} && \text{Replace} \ a \ \text{with its value in the equation. Check that the two expressions are the}\\ &&& \text{same.}\\ &&& (3 + 5) \div 2 + 4 \times 6 = 28\\ &&& 8 \div 2 + 4 \times 6 = 28\\ &&& 4 + 24 = 28\\ &&& 28 = 28\end{align*}
Figure out the value of each variable.
Follow the order of operations:
Parenthesis first
Multiplication and division (left to right)
Addition and subtraction (left to right)
\begin{align*}1. \quad 8  (3  1) + 6 \times 2 = e\!\\ \!\\ {\;} \quad \ e = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\!\\ \!\\ 2. \quad (4 + 6) \div 5  3 \div 3 = a\!\\ \!\\ {\;} \quad \ a = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\!\\ \!\\ 3. \quad 6 \times 7 \div 6 + 8 = c\!\\ \!\\ {\;} \quad \ c = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\!\\ \!\\ 4. \quad (10  2) \div 2 + 5 \times 3 = b\!\\ \!\\ {\;} \quad \ b = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\!\\ \!\\ 5. \quad 4 + (9 + 6) \div 3 = d\!\\ \!\\ {\;} \quad \ d = \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}