Study Guide: 7-2-7. One-Step Equations with Rational Numbers
Method
Use inverse operations to issolate the variable on one side of the equation and move all other values to the other side.
Example 1: Subtraction and Addition
\begin{align} y - 17.5 &= 11 &&\textit{Given} \\[2ex] y - 17.5 {\color{teal} ; + ; 17.5} &= 11 {\color{teal} ; + ; 17.5 } &&\textit{Add 17.5 to both sides} \\[2ex] y &= 28.5 &&\textit{Solution} \\\ \end{align}
Example 2: Multiplication and Division
\begin{align} -4.2p &= 12.6 &&\textit{Given} \\[2ex] \frac{-4.2p}{{\color{red} -4.2}} &= \frac{12.6}{{\color{red} -4.2}} &&\textit{Divide both sides by -4.2} \\[2ex] p &= -3 &&\textit{Solution} \\\ \end{align}
Example 3: Multiplication and Division of Fractions
\begin{align} \frac{3}{5}w &= \frac{3}{16} &&\textit{Given} \\[2ex] \frac{3}{5}w ; {\color{red}\div \frac{3}{5}} &= \frac{3}{16} ; {\color{red}\div \frac{3}{5}} &&\textit{Divide both sides by } \frac{3}{5} \\[2ex] \frac{3}{5}w ; {\color{red}\times \frac{5}{3}} &= \frac{3}{16} ; {\color{red}\times \frac{5}{3}} &&\textit{Multiply by the reciprocal } \frac{5}{5} \\[2ex] w &= \frac{5}{16} &&\textit{Cross-cancel and simplify} \\\ \end{align}
Vocabulary
| Term | Description |
|---|---|
| Equation | A statement that two mathematical expressions are equal |
| Issolate a variable | Move all other values to the other sides of the equation. |
| Inverse operations | Two operations that undo each other, such as + and - |
| Reciprocal | The inverse of a fraction, such as $\frac{1}{2}$ and $\frac{2}{1}$. Inverse fractions always multiply to 1. |
| Cross-cancel | When multiplying fractions, simplify numerators and denominators that have common factors. |
| Simplify | Solve |