Question

A client's intake decreased from 2,500 milliliters (mL) per day to 2,000 milliliters per day. What was the percent of decrease?

Short answer

The percent decrease in intake is 20%.

Step-by-step solution

Understanding the problem

Identify the initial intake amount and the new intake amount. In this problem, the initial intake was 2,500 milliliters per day, and it decreased to 2,000 milliliters per day.

Calculate the decrease in intake

To find the decrease in intake, subtract the new intake from the initial intake: $$2,500\text{mL}-2,000\text{mL}=500\text{mL}$$

Find the percent decrease

To find the percent decrease, divide the decrease in intake by the initial intake and multiply by 100:$$\left(\frac{500}{2500}\right)\times 100\mathrm{\%}$$

Simplify the fraction and calculate

First, simplify the fraction $\frac{500}{2500}$ to get $\frac{1}{5}$. Then multiply by 100:$$\left(\frac{1}{5}\right)\times 100\mathrm{\%}=20\mathrm{\%}$$

Key concepts

Understanding Mathematics Education

When diving into concepts like percent decrease, it's essential to understand the role of mathematics in education. Mathematics education helps us develop important skills such as critical thinking, problem solving, and analytical skills. These skills are crucial not only in academic settings but also in everyday life. Percent decrease is a practical tool that pops up in various real-world scenarios. For example, assessing discounts when shopping or determining the extent of improvement or worsening in performance metrics. By learning how percent decrease works, students can better appreciate the value of knowing how to calculate percentage changes. This kind of mathematical literacy equips students to make informed decisions and understand trends or patterns around them.

Breaking Down Basic Arithmetic

Basic arithmetic is fundamental when tackling any mathematical problem, including calculating percent decrease. Basic arithmetic involves operations such as addition, subtraction, multiplication, and division.In this exercise, we used subtraction to determine the change in intake - starting from 2,500 milliliters down to 2,000 milliliters. We found the decrease by performing the subtraction:

• Subtract the new intake from the original:
  $$2,500-2,000=500\text{mL}$$

Understanding how to perform these basic operations is key to solving more complex tasks. Once the difference was found, division and multiplication were used to convert this number into a percentage. This highlights how interconnected mathematical concepts are, as mastering one aspect can simplify understanding others.

Approaching Problem Solving

Problem solving is a significant aspect of mathematics education and involves a clear, logical approach. Let's review the steps taken in the exercise within a problem-solving framework.First, we clearly defined the problem by identifying key quantities, such as initial and new intakes. This aids in understanding what is needed to find a solution. Then, we calculated the decrease by finding the difference. Once we had the decrease, to solve the main question of the problem, we found the percent decrease by:

• Dividing the decrease by the initial amount:
  $$\frac{500}{2,500}$$
• Simplifying the fraction to get meaningful and manageable numbers, $$\frac{1}{5}$$,
  then multiplying by 100 to convert the result into a percentage:
  $$\left(\frac{1}{5}\right)\times 100\mathrm{\%}=20\mathrm{\%}$$

Breaking down a problem methodically ensures that each step is addressed carefully and increases the likelihood of arriving at an accurate solution. This method also enhances students' confidence in tackling unfamiliar or challenging mathematical tasks.