Verified Answer :
- The total amount of snack mix is the sum of the quantities of its components: \(P\) (pretzels), \(\frac{3}{4}\) (peanuts), and \(\frac{2}{3}\) (chocolate chips).
- To add the fractions, use a common denominator of 12, resulting in \(\frac{9}{12} + \frac{8}{12} = \frac{17}{12} = 1 \frac{5}{12}\).
- The final total quantity of the snack mix is \(\boxed{P + 1 \frac{5}{12}}\) cups.
Explanation
- Analyzing the Ingredients and Defining the Total Volume
The problem asks for the total quantity of snack mix made by combining mini pretzels, peanuts, and chocolate chips. We are given the following quantities:
- Peanuts: \(\frac{3}{4}\) cup
- Chocolate chips: \(\frac{2}{3}\) cup
- Mini pretzels: The quantity is not explicitly provided in the prompt. We will represent the number of cups of mini pretzels as \(P\).
The total volume of the snack mix is the sum of these individual ingredient quantities:
\[\text{Total} = P + \frac{3}{4} + \frac{2}{3}\]
- Adding the Fractional Ingredients
To sum the fractions \(\frac{3}{4}\) and \(\frac{2}{3}\), we must find a common denominator. The least common multiple of the denominators 4 and 3 is 12.
- Convert \(\frac{3}{4}\) to twelfths: \(\frac{3 \times 3}{4 \times 3} = \frac{9}{12}\).
- Convert \(\frac{2}{3}\) to twelfths: \(\frac{2 \times 4}{3 \times 4} = \frac{8}{12}\).
Now, add these two values:
\[\frac{9}{12} + \frac{8}{12} = \frac{17}{12}\]
Converting the improper fraction \(\frac{17}{12}\) to a mixed number, we get \(1 \frac{5}{12}\).
- Calculating the Final Total
Combining the variable amount of pretzels \(P\) with the sum of the other ingredients, the total amount of snack mix is:
\[\text{Total} = P + 1 \frac{5}{12} \text{ cups}\]
If the quantity of pretzels \(P\) were provided, you would simply add it to \(1 \frac{5}{12}\) to find the final total. Without a specific value for \(P\), the total is expressed as the sum of \(P\) and \(1 \frac{5}{12}\) cups.
Final answer is \(\boxed{P + 1 \frac{5}{12}}\).
Examples
Adding fractions is a fundamental skill used in everyday life, such as in cooking or baking. For example, if a recipe calls for specific portions of different ingredients, you need to find a common denominator to determine the total volume of the mixture. Understanding how to handle these combined measurements helps in adjusting recipes for more or fewer people, ensuring your final dish turns out perfectly.