Question

1. use patterns and structure a fraction, f, multiplied by 5 equals \\(\frac{1}{8}\\). write an algebraic sentence to show the equation. then solve the equation and explain how you solved it.

Explanation:

Step1: Write the algebraic equation

A fraction \( f \) multiplied by 5 is \( 5f \), and this equals \( \frac{1}{8} \). So the equation is \( 5f=\frac{1}{8} \).

Step2: Solve for \( f \)

To solve for \( f \), we divide both sides of the equation by 5. Dividing by 5 is the same as multiplying by \( \frac{1}{5} \). So \( f = \frac{1}{8}\times\frac{1}{5} \).

Step3: Calculate the product

\( \frac{1}{8}\times\frac{1}{5}=\frac{1\times1}{8\times5}=\frac{1}{40} \).

Answer:

The algebraic equation is \( 5f = \frac{1}{8} \). The solution for \( f \) is \( \frac{1}{40} \). We solved it by dividing both sides of the equation \( 5f=\frac{1}{8} \) by 5 (or multiplying both sides by \( \frac{1}{5} \)) to isolate \( f \), and then calculated the product of \( \frac{1}{8} \) and \( \frac{1}{5} \) to find the value of \( f \).