Question

a fraction, f, multiplied by 7 equals \\(\frac{1}{6}\\). write an equation to show the algebraic sentence. then solve the equation and explain how you solved it.\
\
\\(\bigcirc\\) b. \\(\frac{1}{6}f = 7\\)\
\\(\bigcirc\\) c. \\(7f = \frac{1}{6}\\)\
\\(\bigcirc\\) d. \\(\frac{1}{6}f = \frac{1}{7}\\)\
solve for f.\
f = \\(\square\\)\
(type a whole number, fraction, or mixed number.)

Explanation:

Step1: Identify the correct equation

The problem states a fraction \( f \) multiplied by 7 equals \( \frac{1}{6} \). Translating this into an equation, we get \( 7f=\frac{1}{6} \), which corresponds to option C.

Step2: Solve for \( f \)

To solve for \( f \), we need to isolate \( f \). We can do this by dividing both sides of the equation \( 7f = \frac{1}{6} \) by 7. Dividing by 7 is the same as multiplying by \( \frac{1}{7} \), so:

$$ f=\frac{1}{6}\times\frac{1}{7} $$

$$ f = \frac{1}{42} $$

Answer:

The correct equation is C. \( 7f=\frac{1}{6} \) and \( f = \frac{1}{42} \)