Determine the value of $h$ in the equation $\frac{1}{7}+h=\frac{9}{7}$.
The problem requires solving the linear equation \(\frac{1}{7} + h = \frac{9}{7}\) for the unknown variable \(h\). We are dealing with basic fractional arithmetic where the denominators are equal, which simplifies the process of isolating the variable. Our goal is to determine the correct value of \(h\) from the given options.
To isolate \(h\), we subtract \(\frac{1}{7}\) from both sides of the equation. This gives:
\[h = \frac{9}{7} - \frac{1}{7}\]
Since the denominators of both fractions are identical, we can subtract the numerators directly:
\[h = \frac{9 - 1}{7}\]
\[h = \frac{8}{7}\]
The resulting value of \(h\) is \(\frac{8}{7}\).
Comparing our result of \(h = \frac{8}{7}\) to the provided options:
Our calculated value matches the third option. Thus, the value of \(h\) is \(\boxed{\frac{8}{7}}\).
Imagine you are following a recipe that calls for a total of \(\frac{9}{7}\) cups of flour. If you have already added \(\frac{1}{7}\) of a cup, you need to determine how much more flour to add to complete the mixture. By solving the equation \(\frac{1}{7} + h = \frac{9}{7}\), you find that you need exactly \(\frac{8}{7}\) cups of flour to reach the required amount. This is a practical example of how simple algebraic equations help in everyday tasks like cooking and measurement.