To convert 1/4 of an inch (in) to millimeters (mm), we will need to use the conversion factor that relates these two units. The conversion factor for converting inches to millimeters is 25.4 mm/in.

Step 1: Write down the given value

In this case, the given value is 1/4 of an inch.

Step 2: Use the conversion factor

Now, we will use the conversion factor 25.4 mm/in to convert inches to millimeters.

Step 3: Set up the conversion equation

The conversion equation for converting inches (in) to millimeters (mm) using the conversion factor is:

1/4 in x 25.4 mm/in = ? mm

Step 4: Simplify the equation

We can simplify the equation by dividing both sides by the unit we want to convert from, which is 1/4 in.

1/4 in รท (1/4 in) x 25.4 mm/in = 1/4 in x ? mm

1 x 25.4 mm = 1/4 ? mm

Step 5: Solve for the unknown value

To solve for the unknown value (? mm), we will multiply both sides by the numerator of the fraction, which is 1 in.

25.4 mm x 1 = 1/4 ? mm x 1 in

25.4 mm = ? mm

Step 6: The conversion is complete

Therefore, 1/4 of an inch is equal to 25.4 millimeters. We can also write it as: 1/4 in = 25.4 mm.

Step 7: Check your answer

To double check our answer, we can use a calculator to convert 1/4 in to mm. By inputting 1/4 in into a calculator and converting it to mm, we should get the same result as our answer above, which is 25.4 mm.

In conclusion, to convert 1/4 of an inch to millimeters, we used the conversion factor 25.4 mm/in and set up a conversion equation to solve for the unknown value. The final answer is 25.4 mm. Make sure to always check your answer to ensure accuracy.