Question

A client is instructed to drink 20 ounces of water within 1 hour. The client has only been able to drink 12 ounces. What portion of the water remains? (Express your answer as a fraction reduced to lowest terms.) ______

Short answer

The remaining water is \(\frac{2}{5}\) of the total.

Step-by-step solution

Calculate Total Water to Drink

The client is instructed to drink a total of 20 ounces of water. This is the complete amount that should be consumed within the time frame given.

Determine Amount Already Consumed

The client has already drunk 12 ounces of water. This needs to be subtracted from the total to find out how much remains.

Calculate Remaining Water

Subtract the amount of water the client has drunk from the total amount:\[20 - 12 = 8 \text{ ounces}\]This means there are 8 ounces of water remaining to be consumed.

Express Remaining Water as a Fraction

To express the remaining water as a fraction of the total initial amount:\[\frac{8}{20}\]Simplify this fraction by finding the greatest common divisor (GCD) of 8 and 20, which is 4:\[\frac{8 \div 4}{20 \div 4} = \frac{2}{5}\]

Conclusion

The fraction representing the remaining amount of water to be consumed is \(\frac{2}{5}\).

Key concepts

Problem Solving in Fraction Simplification

Problem solving involves applying a logical approach to tackle a mathematical problem, such as determining what portion of water remains undrunk when we are given certain amounts. It is important to break down the problem into manageable steps to ensure clarity.
In this case, the exercise guides us through a sequence of steps which illustrate a practical scenario.

• First, identify the total and consumed amounts of water.
• Then, calculate the remainder by subtracting the consumed amount from the total.
• Finally, express this remainder as a fraction of the total and simplify it.

These problems teach students not only to evaluate fractions but also enhance their logical thinking and arithmetic skills. The sequence of identifying, calculating, and simplifying is the core essence of the problem-solving process in mathematics.

Role of Mathematics Education

Mathematics education plays a crucial role in developing cognitive skills by engaging students in exercises involving numbers, symbols, and abstract thinking.
The exercise we are discussing exemplifies how students apply their understanding of basic arithmetic operations such as subtraction and division. Through such exercises:

• Students enhance their computational skills and understanding of number relationships.
• They nurture their ability to transform real-world situations into mathematical expressions.
• They practice simplifying fractions, an essential concept in many advanced mathematical topics.

By engaging in these activities, students cultivate a habit of precision and accuracy which is invaluable in various fields.

Understanding Common Divisor in Simplifying Fractions

The concept of a common divisor is key when simplifying fractions, as it helps reduce fractions to their simplest form.
To simplify the fraction \(\frac{8}{20}\), we first identify the greatest common divisor (GCD) of 8 and 20. The GCD is the largest number that can perfectly divide both numbers without leaving a remainder.
Here's a quick breakdown:

• List the factors of each number. Factors of 8 are {1, 2, 4, 8} and factors of 20 are {1, 2, 4, 5, 10, 20}.
• The common factors are {1, 2, 4}.
• The greatest common factor here is 4.

Using the GCD, both the numerator and the denominator of the fraction are divided by 4, resulting in \(\frac{2}{5}\). Simplifying fractions helps in making calculations easier and results in more understandable expressions.