A metal fabricator checked the placement of a 2 7/8 inch diameter hole relative to the edge of the part she was building. Calculate the edge-to-centre distance for the hole. State your answer as a mixed number in lowest terms.
Answer (2)
The edge-to-center distance of a hole with a diameter of 2 8 7 inches is 1 16 7 inches. This distance is found by first converting the diameter to an improper fraction, calculating the radius, and then converting back to a mixed number. Accurate measurements ensure the integrity of the part being fabricated.
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Convert the diameter from a mixed number to an improper fraction: 2 8 7 = 8 23 .
Divide the diameter by 2 to find the radius: 8 23 ÷ 2 = 16 23 .
Convert the radius from an improper fraction back to a mixed number: 16 23 = 1 16 7 .
State the edge-to-center distance: 1 16 7 inches .
Explanation
Problem Analysis The problem asks us to find the edge-to-center distance of a hole, given its diameter is 2 8 7 inches. The edge-to-center distance is simply the radius of the hole.
Convert mixed number to improper fraction To find the radius, we need to divide the diameter by 2. First, let's convert the mixed number 2 8 7 to an improper fraction.
Calculate improper fraction 2 8 7 = 8 2 × 8 + 7 = 8 16 + 7 = 8 23
Divide by 2 to find the radius Now, we divide the improper fraction by 2 to find the radius:
Calculate the radius radius = 8 23 ÷ 2 = 8 23 × 2 1 = 16 23
Convert back to mixed number Finally, we convert the improper fraction 16 23 back to a mixed number.
Calculate mixed number 16 23 = 1 16 7
Final Answer Therefore, the edge-to-center distance is 1 16 7 inches.
Examples
In manufacturing, knowing the edge-to-center distance of a hole is crucial for precise placement and structural integrity. For example, when attaching components with screws or bolts, the distance from the edge of the hole to the material's edge must be accurately calculated to prevent material failure or improper alignment. This calculation ensures that the fasteners are securely anchored and the assembly meets the required specifications.
