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Multiplying fractions is a crucial skill in mathematics, especially when calculating values like discounts or parts of a whole. The primary rule to remember is that multiplication of fractions involves multiplying the numerators together, and then multiplying the denominators together. However, things are slightly different when you multiply a whole number by a fraction.
For instance, in our problem, we are tasked to find \( \frac{2}{3} \) of the regular price. This requires multiplying the regular price \( 2757 \) by \( \frac{2}{3} \). Effectively, you approach this by multiplying the whole number by the numerator:

• First, multiply the whole number (2757) by the numerator (2): \( 2757 \times 2 = 5514 \).
• Next, divide the result by the denominator (3): \( 5514 \div 3 \).

This calculation results in the final sale price of \( 1838 \). Thus, this process shows how multiplication of fractions can efficiently determine parts of a whole number.

Division is often used in practical scenarios to split a value into equal parts, and it's an essential arithmetic operation for many real-world applications. In this problem, we have used division to find a fraction of a whole number.
After multiplying by 2 to get \( 5514 \), the next crucial step is dividing by 3. Here, division helps in distributing that multiplied value into three equal parts. Calculating \( 5514 \div 3 \) gives us 1838, assisting us in determining what two-thirds of 2757 is.
The key steps for executing division of numbers include:

• Identifying how many times the divisor fits into parts of the dividend progressively.
• Multiplying the divisor with the current quotient part.
• Subtracting to carry the remainder to the next part of the dividend.

This arithmetic division process allows us to unravel fractional segments of a number, grasping how large or small each portion is in relation to the whole.

Breaking down a math problem into manageable steps is crucial for finding an accurate solution. When faced with a question like finding the sale price of a cruise, a series of structured steps helps clarify and solve the problem efficiently.
Here’s a concise breakdown:

• **Understand the Problem:** Clearly identify what is being asked. Here, it's about finding \( \frac{2}{3} \) of a set price.
• **Write the Expression:** Construct the mathematical expression needed. This involves setting up the equation: \( \text{Sale Price} = \frac{2}{3} \times 2757 \).
• **Perform the Calculation:** Execute operations step-by-step. Start by multiplying, then divide to simplify.
• **Check Your Work:** Always review calculations for accuracy. Double-check math and confirm that answers make logical sense.

Following these problem-solving steps ensures you tackle each math problem systematically, avoiding mistakes and understanding each action's purpose in the solution process.