Question

a fraction, 1, 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.
choose the correct equation below.
a. \\( \frac{1}{7}f = \frac{1}{6} \\)
b. \\( \frac{1}{6}f = 7 \\)
c. \\( 7f = \frac{1}{6} \\)
d. \\( \frac{1}{6}f = \frac{1}{7} \\)
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Explanation:

Step1: Translate the problem into an equation

The problem states "A fraction, \( t \), multiplied by 7 equals \( \frac{1}{6} \)". So the equation is \( 7t = \frac{1}{6} \). To solve for \( t \), we divide both sides by 7. Dividing by 7 is the same as multiplying by \( \frac{1}{7} \), so \( t = \frac{1}{6} \times \frac{1}{7} \)? Wait, no, wait. Wait, the equation is \( 7t=\frac{1}{6} \), so to solve for \( t \), we do \( t=\frac{1}{6}\div7 \), which is \( t = \frac{1}{6} \times \frac{1}{7} \)? Wait, no, that's not right. Wait, let's re - express the original problem. Wait, the problem says "a fraction \( t \) multiplied by 7 equals \( \frac{1}{6} \)", so \( 7t=\frac{1}{6} \). Then, to solve for \( t \), we divide both sides by 7: \( t=\frac{1}{6}\div7=\frac{1}{6}\times\frac{1}{7}=\frac{1}{42} \)? Wait, but the options are about the equation. Wait, let's look at the options. The options are:

A. \( \frac{1}{7}t=\frac{1}{6} \)

B. \( \frac{1}{6}t = 7 \)

C. \( 7t=\frac{1}{6} \)

D. \( \frac{1}{6}t=\frac{1}{7} \)

The correct equation for "a fraction \( t \) multiplied by 7 equals \( \frac{1}{6} \)" is \( 7t = \frac{1}{6} \), which is option C.

Step2: Verify the equation

We know that "multiplied by 7" means \( 7\times t \) or \( 7t \), and it equals \( \frac{1}{6} \). So the equation \( 7t=\frac{1}{6} \) is the correct translation of the problem statement.

Answer:

C. \( 7t=\frac{1}{6} \)