Sure, let's complete the equation step-by-step:
The equation we need to complete is:
[tex]\[
\frac{7}{3} = 7 \div \square
\][/tex]
### Step 1: Understand the Equation
The fraction [tex]\(\frac{7}{3}\)[/tex] represents dividing 7 by 3. Our goal is to find which number, when used to divide 7, gives us the same result as [tex]\(\frac{7}{3}\)[/tex].
### Step 2: Rewrite the Equation
To make it clearer, let’s rewrite the equation using basic division notation:
[tex]\[
\frac{7}{3} = 7 \div x
\][/tex]
Here, we need to determine the value of [tex]\( x \)[/tex].
### Step 3: Relate the Fraction to the Division
In a fraction, the numerator (the top part) is divided by the denominator (the bottom part). So, if we have:
[tex]\[
\frac{7}{3}
\][/tex]
We need to find out what number [tex]\( x \)[/tex] makes the equation true:
[tex]\[
\frac{7}{3} = 7 \div x
\][/tex]
### Step 4: Equate the Denominators
Since [tex]\(\frac{7}{3}\)[/tex] simplifies to the same value, for the equation to hold true:
[tex]\[
7 \div x = \frac{7}{3}
\][/tex]
### Step 5: Find the Value of [tex]\( x \)[/tex]
To isolate [tex]\( x \)[/tex], we understand that dividing by a number is the same as multiplying by its reciprocal. In other words:
[tex]\[
7 \div x = 7 \times \frac{1}{x}
\][/tex]
Thus, setting these equal gives:
[tex]\[
\frac{7}{3} = 7 \times \frac{1}{x}
\][/tex]
### Step 6: Compare Fractions
To solve for [tex]\( x \)[/tex], we equate the fraction:
[tex]\[
\frac{7}{3} = 7 \times \frac{1}{x}
\][/tex]
Divide both sides by 7:
[tex]\[
\frac{1}{3} = \frac{1}{x}
\][/tex]
### Step 7: Equate and Solve for [tex]\( x \)[/tex]
From [tex]\(\frac{1}{3} = \frac{1}{x}\)[/tex], we can see that [tex]\( x = 3 \)[/tex].
### Final Answer
Therefore, the value of [tex]\( x \)[/tex] that completes the equation [tex]\(\frac{7}{3} = 7 \div \square\)[/tex] is:
[tex]\[
\boxed{3}
\][/tex]
