Problem 22 - Prealgebra

Question

Solve each problem using the percent equation. Round to the nearest tenth. 7 is what percent of \(32 ?\)

Step-by-Step Solution

Answer

7 is 21.9% of 32.

Step 1: Understand the Percent Equation

The percent equation is given by the formula \( \text{part} = \frac{\text{percent}}{100} \times \text{whole} \). In this problem, "7" is the "part" and "32" is the "whole". We aim to find the "percent".

Step 2: Set Up the Equation

According to the percent equation, \( 7 = \frac{x}{100} \times 32 \), where \( x \) is the percent we need to find.

Step 3: Solve for the Percent

To solve for \( x \), first multiply both sides by 100 to eliminate the fraction: \( 7 \times 100 = x \times 32 \), which simplifies to \( 700 = 32x \).

Step 4: Isolate the Percent Variable

Divide both sides of the equation by 32 to solve for \( x \): \( x = \frac{700}{32} \).

Step 5: Calculate and Round

Compute \( \frac{700}{32} \), which gives approximately 21.875. Rounding to the nearest tenth results in \( 21.9 \).

Key Concepts

Understanding Percentage Calculations

Percentage calculation is a common and essential skill in math that involves the use of a percent equation.
Percentages describe a number or ratio as a fraction of 100. They are widely used in many areas, from calculating discounts at the store to determining rates of increase or decrease in data.
The basic formula for percentages can be expressed as:

• part = \( \frac{\text{percent}}{100} \times \text{whole} \)

In this equation:

• Part refers to the portion of the whole that the percentage represents.
• Percent is the unknown value we often solve for.
• Whole is the total value or quantity being considered.

Understanding this structure helps in setting up problems correctly and efficiently solving for any unknowns in a percentage calculation scenario.

Problem Solving Steps for Percent Equations

Approaching percent problems systematically simplifies finding the solution, especially when practicing prealgebra.
Here's a breakdown of the step-by-step process:1. **Identify the Components**: Recognize what represents the part, percent, and whole in the problem. For example, in "7 is what percent of 32?", 7 is the part, and 32 is the whole.2. **Set Up the Equation**: Rearrange the percent equation to place your known quantities and the unknown percent into the equation: \( 7 = \frac{x}{100} \times 32 \).3. **Eliminate the Fraction**: To eliminate the fraction, multiply both sides by 100: \( 7 \times 100 = x \times 32 \).4. **Isolate the Percent Variable**: Divide both sides by the whole to solve for the percentage: \( x = \frac{700}{32} \).5. **Calculate and Round**: Compute the fraction, which gives you 21.875, and round it to the nearest tenth to obtain 21.9. Each step is crucial to correctly solving the problem and understanding the roles of the numbers involved.

Building Prealgebra Concepts with Percent Equations

Percent equations provide a foundational concept in prealgebra that supports a broader understanding of algebraic principles.
By learning how percentages work in conjunction with equations, students can build a stronger grasp of algebraic manipulations. Here’s how percent equations reinforce foundational math skills:

• Equation Manipulation: Solving percent problems offers excellent practice with manipulating equations, such as isolating variables and eliminating fractions. These skills are essential in more advanced algebra.
• Understanding Ratios: Percentages are ratios of numbers to 100, giving students experience in working with ratios and proportions, another key prealgebra topic.
• Rounding Skills: The final step of rounding answers to the nearest tenth also enhances number sense and precision, important aspects of prealgebra.

Engaging with these concepts arms students with useful tools for later mathematical learning and problem solving.