You are a carpenter and have a $\frac{3}{16}$ inch piece of wood and a $\frac{5}{16}$ inch piece of wood. If you glue the pieces together, what is the new measurement of the combined piece of wood in its lowest form? Type your answer as a fraction in simplest form: \_\_\_\_ inches
To find the total length of the wood when two pieces are glued together, we add their individual lengths. We have one piece measuring \(\frac{3}{16}\) inches and another piece measuring \(\frac{5}{16}\) inches. Adding these together, we get:
\[\frac{3}{16} + \frac{5}{16} = \frac{3 + 5}{16} = \frac{8}{16}\]
This calculation is straightforward since the two pieces have a common denominator.
Now that we have the sum \(\frac{8}{16}\) inches, we must simplify it to its lowest form. We look for the greatest common divisor (GCD) of the numerator (8) and the denominator (16).
Since \(16 = 8 \times 2\), the greatest common divisor is 8. Dividing both the numerator and the denominator by 8, we obtain:
\[\frac{8 \div 8}{16 \div 8} = \frac{1}{2}\]
Thus, the total length of the wood in its simplest form is \(\frac{1}{2}\) inches.
In carpentry and construction, precise measurements are crucial. When combining materials, you often deal with fractional lengths—such as pieces of wood, metal, or piping. By knowing how to add and simplify these fractions, a builder ensures the final assembly fits perfectly, reducing waste and errors. This is a fundamental skill used daily to maintain accuracy in various hands-on projects.