Final answer:
To solve the fill-in-the-blank puzzle with the digits 0 to 9, we need to create two equivalent fractions considering each digit can be used only once. This involves using properties of numbers, such as reciprocity and significance, and may require some trial and error.
Step-by-step explanation:
To solve the puzzle Fill in the blanks using the digits 0 to 9 no more than once each. Use the space below to record any of your thinking as you experiment. □ / □ of □ = □ /□ of □, we need to consider the constraints given: each digit from 0 to 9 can be used no more than once, and we need to form two equivalent fractions.
Let's begin by understanding that we are essentially looking for three pairs of numbers (a, b, c) and (d, e, f) such that (a/b) of c equals (d/e) of f. 'Of' typically means multiplication in mathematics, so our equivalent statement is: (a/b) * c = (d/e) * f.
Now, we should choose numbers that make the equation true while adhering to the rules. Let's consider the number 1 first. It is neutral in multiplication, so typically it's a good choice for a denominator to simplify our search. Also, we can use the property that if two fractions are equal, their cross-products are also equal: a*f = d*c. This gives us a good starting point to experiment with different combinations.
The solution to this question will likely involve trial and error, experimenting with different digit combinations and using properties of numbers, such as reciprocals and the idea that significant digits are important in expressing the precision of our result.