Answer :
- Zachary incorrectly took the reciprocal of $\frac{3}{4}$ instead of $\frac{5}{6}$ in Step 1.
- The correct transformation should be $\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5}$.
- Therefore, Zachary made an error in Step 1.
- The final answer is: Zachary made an error in Step 1.$\boxed{Zachary made an error in Step 1.}$
### Explanation
1. Analyzing Zachary's Work
Let's analyze Zachary's work step by step to identify any errors in his calculation of $\frac{3}{4} \div \frac{5}{6}$.
2. Identifying the Error in Step 1
Step 1: Zachary wrote $\frac{3}{4} \div \frac{5}{6} = \frac{4}{3} \times$. When dividing by a fraction, you should multiply by its reciprocal. The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$, not $\frac{4}{3}$. Therefore, Step 1 is incorrect. The correct Step 1 should be $\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5}$.
3. Concluding the Analysis
Since we've identified an error in Step 1, we don't need to check the subsequent steps.
4. Final Answer
Zachary made an error in Step 1 by taking the reciprocal of the first fraction instead of the second.
### Examples
Dividing fractions is a common task in cooking. For example, if a recipe calls for $\frac{3}{4}$ cup of flour, but you only want to make half of the recipe, you would need to divide $\frac{3}{4}$ by 2 (or multiply by $\frac{1}{2}$). Understanding how to divide fractions allows you to scale recipes up or down as needed. This is also useful in other real-life situations, such as calculating distances on a map or determining proportions in construction projects.
- The correct transformation should be $\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5}$.
- Therefore, Zachary made an error in Step 1.
- The final answer is: Zachary made an error in Step 1.$\boxed{Zachary made an error in Step 1.}$
### Explanation
1. Analyzing Zachary's Work
Let's analyze Zachary's work step by step to identify any errors in his calculation of $\frac{3}{4} \div \frac{5}{6}$.
2. Identifying the Error in Step 1
Step 1: Zachary wrote $\frac{3}{4} \div \frac{5}{6} = \frac{4}{3} \times$. When dividing by a fraction, you should multiply by its reciprocal. The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$, not $\frac{4}{3}$. Therefore, Step 1 is incorrect. The correct Step 1 should be $\frac{3}{4} \div \frac{5}{6} = \frac{3}{4} \times \frac{6}{5}$.
3. Concluding the Analysis
Since we've identified an error in Step 1, we don't need to check the subsequent steps.
4. Final Answer
Zachary made an error in Step 1 by taking the reciprocal of the first fraction instead of the second.
### Examples
Dividing fractions is a common task in cooking. For example, if a recipe calls for $\frac{3}{4}$ cup of flour, but you only want to make half of the recipe, you would need to divide $\frac{3}{4}$ by 2 (or multiply by $\frac{1}{2}$). Understanding how to divide fractions allows you to scale recipes up or down as needed. This is also useful in other real-life situations, such as calculating distances on a map or determining proportions in construction projects.
