Problem 15 - Prealgebra

Question

WEATHER Jackson, Mississippi, receives an average of 6.0 inches of precipitation in April. In September, the average precipitation is 3.2 inches. What is the percent of change in precipitation from April to September?

Step-by-Step Solution

Answer

The precipitation decreased by approximately 46.7% from April to September.

Step 1: Understand the Problem

We need to find the percentage change in precipitation from April to September. This involves calculating how much the precipitation has decreased as a percentage of the initial amount.

Step 2: Identify the Initial and New Values

The initial value for precipitation in April is 6.0 inches, and the new value in September is 3.2 inches.

Step 3: Calculate the Change in Precipitation

Subtract the precipitation in September from that in April to find the change. Change = Initial Value - New Value = 6.0 - 3.2 = 2.8 inches.

Step 4: Compute the Percentage Change

The formula to calculate percentage change is Percentage Change = \( \frac{\text{Change}}{\text{Initial Value}} \times 100 \). Substituting in the values, we get Percentage Change = \( \frac{2.8}{6.0} \times 100 \approx 46.7\% \).

Step 5: Interpret the Result

The precipitation in Jackson, Mississippi, decreased by approximately 46.7% from April to September.

Key Concepts

Precipitation Calculation

When discussing precipitation, we're talking about any form of water - rain, snow, sleet, or hail - that falls from clouds and reaches the ground. It’s important to understand precipitation calculations because they help us determine weather patterns and prepare accordingly. In our example, we focus on rainfall over specific months.
To calculate the precipitation change, you start by identifying the amount recorded over the set periods you're interested in. For instance, in April, the average precipitation in Jackson, Mississippi is 6.0 inches, compared to 3.2 inches in September.
This measurement gives us two key data points that allow us to see how much the precipitation has changed. This forms the basis for further calculations, such as determining the percentage of change, which gives us a clearer picture of how significant the change is.

Percentage Decrease

A percentage decrease helps quantify how much something has reduced in terms of its initial amount. This becomes particularly useful when you want to compare changes over time, such as changes in precipitation.
To find the percent decrease:

• Calculate the change, which is the difference between the initial and final values.
• Use the formula for percentage change:
  \[ \text{Percentage Change} = \frac{\text{Change}}{\text{Initial Value}} \times 100 \]

For our example with Jackson's precipitation:

• The change from April (6.0 inches) to September (3.2 inches) is 2.8 inches less.
• Using the formula, the percentage change becomes \[ \frac{2.8}{6.0} \times 100 \approx 46.7\% \].
• This indicates a 46.7% decrease in rainfall from April to September.

Such calculations are invaluable in interpreting weather patterns and assessing shifts in the climate.

Prealgebra Problem-Solving

Prealgebra focuses on laying the groundwork for more complex math through basic equations and logical reasoning. Understanding prealgebra is essential because these skills are widely applicable, from solving everyday problems to handling academic challenges.
In our precipitation problem, we applied these prealgebra techniques in a few steps:

• Identifying Known and Unknown Variables: We knew the initial and new precipitation levels. What was unknown was the percentage change.
• Performing Calculations: We used subtraction to determine the difference in precipitation and applied a percentage change formula to find the decrease.
• Interpreting Results: Finally, we interpreted the mathematics in terms of real-world significance, recognizing a substantial decrease in precipitation.

By mastering these skills, you enhance your ability to solve a range of mathematical problems confidently and systematically.