Step 1: Find the Equivalent Fraction
To find a rational number equivalent to 4/7 with a numerator of 32 and a denominator of 28, we need to first calculate the equivalent fraction.
We can do this by multiplying the numerator and denominator of the original fraction (4/7) by the same number. In this case, we can multiply both the numerator and denominator by 4 to get 16/28.

Step 2: Simplify the Equivalent Fraction
Once we have the equivalent fraction 16/28, we can simplify it by finding the greatest common divisor (GCD) of the numerator and denominator.
In this case, the GCD of 16 and 28 is 4. By dividing both the numerator and denominator by 4, we get the simplified fraction 4/7.

Step 3: Check for Equivalence
Now, we need to check if the fraction 4/7 is equivalent to the fraction with a numerator of 32 and a denominator of 28.
We can do this by multiplying the numerator and denominator of 4/7 by 4. This gives us 16/28, which is the same as the equivalent fraction we calculated in step 1.
Therefore, the rational number equivalent to 4/7 with a numerator of 32 and a denominator of 28 is 32/28.