To solve the equation [tex]\( 6 \times \square = \frac{6}{7} \)[/tex], let's explore each of the given options one by one to see which one makes the equation true.
Given options are:
A. [tex]\( \frac{1}{7} \)[/tex]
B. [tex]\( \frac{1}{6} \)[/tex]
C. [tex]\( \frac{6}{7} \)[/tex]
D. [tex]\( \frac{7}{1} \)[/tex]
Let's test each option in the equation [tex]\( 6 \times \square = \frac{6}{7} \)[/tex].
Option A: [tex]\( \frac{1}{7} \)[/tex]
[tex]\[
6 \times \frac{1}{7} = \frac{6}{7}
\][/tex]
This calculation shows:
[tex]\[
6 \times \frac{1}{7} = \frac{6}{7}
\][/tex]
So, option A matches the right side of the equation.
Option B: [tex]\( \frac{1}{6} \)[/tex]
[tex]\[
6 \times \frac{1}{6} = 1
\][/tex]
This results in:
[tex]\[
1 \neq \frac{6}{7}
\][/tex]
So, option B is not correct.
Option C: [tex]\( \frac{6}{7} \)[/tex]
[tex]\[
6 \times \frac{6}{7} = \frac{36}{7}
\][/tex]
This results in:
[tex]\[
\frac{36}{7} \neq \frac{6}{7}
\][/tex]
So, option C is not correct.
Option D: [tex]\( \frac{7}{1} \)[/tex]
[tex]\[
6 \times 7 = 42
\][/tex]
This results in:
[tex]\[
42 \neq \frac{6}{7}
\][/tex]
So, option D is not correct.
From the tests above, we can conclude that the fraction which makes the number sentence [tex]\( 6 \times \square = \frac{6}{7} \)[/tex] true is:
A. [tex]\( \frac{1}{7} \)[/tex]
Hence, the correct answer is:
[tex]\[
\boxed{\frac{1}{7}}
\][/tex]
