One Step Equations Multiplication and Division: in this lesson we will be looking at how to solve equations starting with the simplest equations, one-step equations. It includes Multiplicative Inverse Property, and how to solve equations with more than one variable.
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One Step Equations Multiplication and Division
Remember when solving equations
we want to get the variable we are solving for on one side of the equation and everything else on the other side of the equation.
To solve an equation of the form $ax=b$ for x,
we could think what is the inverse operation for multiplication?
Well that would be division, since $a\div a=1$.
So to solve an equation of the form $\frac{x}{c}=d$ for x,
we could think what is the inverse operation for division?
Well that would be multiplication, since $\frac{1}{c}* c=1$.
Example 1:
A carpenter purchases twenty-five 10-foot-long two-by-fours. The charge is $ \$105$. What is the price of one of the two-by-fours?
| Let $p=$ the price of one two by four. | |
| Write the equation | $25p=105$ |
| The inverse operation of multiplication is division | |
| Divide both sides of the equation by $25$. | $\frac{25p}{25} = 105$ |
| $p=4.2$ | |
| The price of one two-four is $ \$4.20$ |
Example 2:
The formula $I= \frac{v}{r}$ is used to find the current in an electrical circuit
where $I$ = current, $V$ = voltage, and $R$ = resistance. Find the voltage in a circuit when $R=25$ ohms and $I=4$ amperes.
| Write the equation | $4=\frac{V}{25}$ |
| The inverse operation of division is multiplication. | |
| Multiply both sides of the equation by $25$. | $4*25=\frac{V*25}{25}$ |
| Simplify. | $100=V$ |
| The voltage in the circuit is $100$ volts. |
Multiplicative Inverse Property:
any number times its reciprocal is equal to 1
| $a*\frac{1}{a}$ | $=$ | $1$ |
| $\frac{1}{a}*a$ | $=$ | $1$ |
