Question

1. solve the equation for a:

$ac = \frac{r}{d}$
a $a = \frac{-cd}{r}$
b $a = \frac{-r}{cd}$
c $a = \frac{r}{cd}$
d $a = -r + cd$

Explanation:

Step1: Isolate \( a \)

To solve \( ac = \frac{r}{d} \) for \( a \), divide both sides by \( c \) (assuming \( c
eq 0 \)) and multiply numerator and denominator appropriately. First, rewrite the right - hand side and then divide by \( c \).
We have the equation \( ac=\frac{r}{d} \). Divide both sides of the equation by \( c \):
\( a=\frac{\frac{r}{d}}{c} \)

Step2: Simplify the division of fractions

Recall that dividing by a number \( c \) is the same as multiplying by its reciprocal \( \frac{1}{c} \). So, \( \frac{\frac{r}{d}}{c}=\frac{r}{d}\times\frac{1}{c} \)
When we multiply two fractions \( \frac{r}{d} \) and \( \frac{1}{c} \), we multiply the numerators together and the denominators together. So \( \frac{r}{d}\times\frac{1}{c}=\frac{r}{cd} \)

Answer:

C. \( a = \frac{r}{cd} \)