Problem 20 - Calculate With Confidence

Question

Change each of the following percentages to a ratio, and reduce to lowest terms. A client is on a 1,000 mL fluid restriction per 24 hours. At breakfast and lunch the client consumed 40% of the fluid allowance. How many milliliters did the client consume? __________________________

Step-by-Step Solution

Answer

The client consumed 400 mL.

Step 1: Understand the Given Information

The client has a total fluid allowance of 1,000 mL per 24 hours. They have consumed 40% of this allowance during breakfast and lunch.

Step 2: Convert Percentage to Decimal

40% can be converted to a decimal by dividing 40 by 100. Thus, 40% becomes 0.40.

Step 3: Calculate the Consumed Fluid Amount

Multiply the total fluid allowance by the decimal equivalent of the percentage consumed: \\[ \text{Consumed amount} = 1000 \, \text{mL} \times 0.40 = 400 \, \text{mL} \]

Step 4: Conclude the Solution

The client consumed 400 mL of their fluid allowance at breakfast and lunch by consuming 40% of it.

Key Concepts

Percentage to Ratio Conversion

Converting percentages to ratios is an important skill that helps in various mathematical problems. A percentage represents a number out of 100. In other words, if you have a percentage like 40%, it is equivalent to saying 40 out of 100 units. To convert this percentage into a ratio, follow these simple steps:

• Write down the percentage as a fraction by placing the percentage number over 100. For example, 40% becomes \( \frac{40}{100} \).
• Next, simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. In the case of \( \frac{40}{100} \), the GCD is 20.
• Finally, divide both the numerator and the denominator by this GCD to reduce the fraction to its simplest form: \( \frac{40 \div 20}{100 \div 20} = \frac{2}{5} \).

So, 40% is expressed as the ratio 2:5 in its lowest terms. This conversion can be particularly useful in real-life scenarios like budgeting, fluid restrictions, and in understanding various statistical results.

Decimal Conversion

Converting percentages to decimals is a straightforward yet powerful tool in mathematics and everyday calculations. Understanding this process makes it easier to handle calculations involving percentages and helps in visualizing data effectively.To convert 40% into a decimal, you need to:

• Recognize that "percent" means per hundred. Therefore, 40% is essentially 40 out of 100.
• Divide the percentage by 100 to find its decimal form. For 40%, perform the division \( 40 \div 100 \).
• The result of the division is 0.40, which is the decimal equivalent of 40%.

This conversion is crucial because using decimals is often easier when performing mathematical operations like multiplication and division. In this exercise, for example, using the decimal form helped to calculate the consumed fluid amount quickly and accurately.

Consumed Fluid Amount Calculation

Calculating consumed fluid amounts is a practical application of mathematical skills in scenarios like diet management and medical care. In this exercise, we knew that the total fluid restriction was 1,000 mL and 40% of this amount was consumed during breakfast and lunch.To calculate the actual fluid consumed, use the following steps:

• First, convert the percentage of fluid consumed (40%) into a decimal, which we've determined to be 0.40.
• Next, multiply this decimal by the total fluid allowance to find the amount consumed. Thus, calculated as: \[ ext{Consumed amount} = 1000 imes 0.40 \].
• This multiplication gives us 400 mL, the quantity of fluid consumed during the specified meals.

Understanding and applying this method allows precise management of fluid intake, which is particularly important in medical settings for patients with specific dietary needs.