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Magazine Chapter 6: Problem 3
Use the percent proportion to solve each problem. What percent of 5 is \(14 ?\)
Short Answer
Expert verified
280% of 5 is 14.
Step by step solution
01
Set up the Percent Proportion
The percent proportion compares part of a quantity to the whole quantity using the formula \( \frac{part}{whole} = \frac{percent}{100} \). Here, the part is \(14\) and the whole is \(5\).
02
Identify the Known and Unknown Values
In the proportion \( \frac{part}{whole} = \frac{percent}{100} \), we know the part is \(14\), the whole is \(5\), and we are solving for the percent. So, the equation becomes \( \frac{14}{5} = \frac{percent}{100} \).
03
Solve for the Percent
Cross-multiply to find the percent. This gives \( 14 \times 100 = percent \times 5 \). Simplify to find \( 1400 = 5 imes percent \).
04
Divide to Solve for the Percent
To isolate the percent, divide both sides of the equation by \(5\): \( percent = \frac{1400}{5} \).
05
Calculate the Percent
Calculate \( \frac{1400}{5} = 280 \). So, the percent is \( 280\% \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Problem Solving Steps
When approaching a problem that involves finding a percent of a number, it's useful to follow a structured set of steps. This makes the process clear and manageable. Here's how you can tackle such a problem using percent proportions:
- Understand the Problem: Start by identifying what the problem is asking you to find. In our example, the question is "What percent of 5 is 14?" This means we need to find out how much 14 is as a percentage of 5.
- Use the Percent Proportion Formula: The formula for percent proportion is \( \frac{\text{part}}{\text{whole}} = \frac{\text{percent}}{100} \). In this scenario, "part" is 14, and "whole" is 5.
- Set Up the Equation: Substitute the known values into the percent proportion, which results in the equation \( \frac{14}{5} = \frac{\text{percent}}{100} \).
- Solve for the Unknown: Use algebraic methods such as cross multiplication to solve for the unknown value, which is the percent in this case.
- Calculate and Conclude: Perform the calculations to find the solution and interpret it in context. Here, the calculation shows that 14 is 280% of 5.
Fractions to Percent Conversion
Converting fractions to percents is an essential skill in understanding various mathematical concepts, especially when working with proportions. Here's a simple way to do it:
- Identify Part and Whole: Recognize the fraction as a division of the part by the whole. In this example, the fraction is \( \frac{14}{5} \).
- Multiply by 100 to Convert: To convert a fraction to a percent, multiply the fraction by 100. This step translates the fraction into a language everyone understands - percentages! For \( \frac{14}{5} \), you compute \( \frac{14}{5} \times 100 = 280\% \).
- Percentage Interpretation: The result of 280% indicates how many times 14 compares to 5 in terms of hundreds. It depicts that 14 is more than 5 by 180% more, considering 100% would be equal.
Cross Multiplication in Proportions
Cross multiplication is a nifty technique that works wonderfully when solving proportions. It allows you to find an unknown by transforming a proportion into an equation. Let's explore this process:
- Set Up the Proportion: In the percent proportion \( \frac{14}{5} = \frac{x}{100} \), each side of the equation is a fraction depicting a relationship.
- Apply Cross Multiplication: This involves multiplying across the equals sign in a proportion, or crossing over the diagonal. Here, you multiply 14 by 100 and 5 by the unknown percent \( x \). This gives the equation \( 14 \times 100 = 5 \times x \).
- Simplify and Solve: By simplifying, you get \( 1400 = 5x \). Solve for \( x \) by dividing both sides by 5, which isolates \( x \) on one side of the equation. Thus, \( x = 280 \).
- Verify Your Solution: Check if the calculated percentage fits the context of the problem to ensure accuracy.
