Question

A client drank 24 ounces of water. How many cups did the client drink? ______ cups

Short answer

The client drank 3 cups of water.

Step-by-step solution

Understand the Conversion Factor

To solve the problem, we need to understand the unit conversion between ounces and cups. There are 8 ounces in 1 cup. This is crucial in setting up our conversion equation.

Set Up the Conversion Equation

We are given 24 ounces and need to find out how many cups that equals. Using the conversion factor from Step 1, we can set up the equation: \[\text{Cups} = \frac{\text{Ounces}}{\text{Ounces per Cup}} = \frac{24}{8} \]

Perform the Calculation

Now, we calculate the number of cups by dividing the total ounces by the number of ounces in one cup:\[\frac{24}{8} = 3\]Thus, 24 ounces is equal to 3 cups.

Key concepts

Understanding Unit Conversion

Unit conversion is a fundamental concept in math that allows us to understand and switch between different units of measurement. For this concept, you need to know the basic conversion factors, which are the numbers used to change one unit to another. In the exercise, the key conversion factor to consider is between ounces and cups. Here, it is essential to know that 1 cup equals 8 ounces. Understanding this is crucial because it forms the basis of solving the problem accurately. Without the correct conversion factor, it's easy to make mistakes. By applying this knowledge, you can solve not only this exercise but also similar ones, involving other units of measurement like liters to gallons or grams to pounds.

Exploring Different Measurement Systems

Measurement systems vary around the world, but understanding them is key to effective mathematical problem-solving. The United States primarily uses the Imperial system, which includes units like ounces, cups, and pounds. Other countries use the Metric system, which includes milliliters, liters, and kilograms. Knowing which system you're dealing with helps in setting up conversions correctly. In our exercise, we deal with ounces and cups from the Imperial system. Recognizing this system directs us towards using specific conversion factors. This knowledge helps universally, as converting between systems, like converting miles to kilometers, often involves an understanding of multiple conversion factors.

Approach to Mathematical Problem-Solving

Mathematical problem-solving is a structured process that involves understanding the problem, planning, executing, and checking the solution. Firstly, comprehend the problem you’re dealing with—what is being asked? In the exercise, we need to convert ounces to cups. Next is planning. Identify your conversion factor, which is 8 ounces per cup in this case. This step involves setting up an equation based on this factor. After planning, perform the calculations as set up during planning. Divide the total ounces by the number of ounces per cup: 24 ÷ 8 = 3. Finally, double-check your work. Verify that calculations are done correctly and that all conversion factors are applied accurately. These steps are repeatable and can be applied to many different mathematical challenges, enhancing both knowledge and confidence.