https://file.aiquickdraw.com/mathbot/file/1725377628708qcxwsdq2.jpg

The equation provided in the image is:

\[
12 \times \frac{5}{16} = \frac{\square}{1} \times \frac{5}{\square}
\]

We need to determine the values that will fill in the squares.

### Step 1: Simplify the left-hand side
Let's first simplify \(12 \times \frac{5}{16}\):

\[
12 \times \frac{5}{16} = \frac{12 \times 5}{16} = \frac{60}{16} = \frac{15}{4}
\]

So, the equation becomes:

\[
\frac{15}{4} = \frac{\square}{1} \times \frac{5}{\square}
\]

### Step 2: Determine the missing values
Let the first blank be \(x\) and the second blank be \(y\). The equation can now be written as:

\[
\frac{15}{4} = \frac{x}{1} \times \frac{5}{y} = \frac{5x}{y}
\]

This implies:

\[
\frac{15}{4} = \frac{5x}{y}
\]

Cross-multiply to get:

\[
15y = 20x
\]

Dividing both sides by 5:

\[
3y = 4x
\]

Thus:

\[
\frac{y}{x} = \frac{4}{3}
\]

To satisfy this equation, \(x\) must be 3 and \(y\) must be 4. Substituting these into the equation gives:

\[
\frac{5 \times 3}{4} = \frac{15}{4}
\]

Which matches the original expression on the left-hand side.

### Final Answer
The completed equation is:

\[
12 \times \frac{5}{16} = \frac{3}{1} \times \frac{5}{4}
\]

Would you like more details on any of the steps, or do you have any questions?

Here are 5 related questions you might explore:
1. How would the equation change if the left side was \(12 \times \frac{7}{16}\)?
2. What is the general form of the equation if the fractions were different?
3. How can we check if an equation like this is balanced?
4. What are the steps to simplify complex fractions?
5. How would the solution process differ if the multiplication was on the right-hand side?

**Tip:** When simplifying fractions, always look for the greatest common divisor (GCD) to reduce the fraction to its simplest form efficiently.

Solve the equation 12 × 5/16 = □/1 × 5/□, where □ represents unknown values.

Explore the solution to the equation 12 × 5/16 = □/1 × 5/□. This problem covers key concepts such as simplifying fractions, cross multiplication, and solving equations with unknown variables. Suitable for students in Grades 6-8.

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