Problem 32 - Algebra 1: Concepts and Skills

Question

Solve the percent problem. 9 people is what percent of 60 people?

Step-by-Step Solution

Answer

9 is 15% of 60.

Step 1: Write down the percentage formula

The basic formula for calculating percent is \(\frac{part}{whole}\) * 100. So we need to substitute 9 in 'part' and 60 in 'whole'.

Step 2: Substitute the values into the formula

Substitute 9 in place of 'part' and 60 in place of 'whole' in the formula. It should look like this: \(\frac{9}{60}\) * 100.

Step 3: Solve the fraction and multiply by 100

First simplify the fraction \(\frac{9}{60}\). Then, multiply the result by 100 to get the percentage.

Step 4: Calculation

First, simplify the fraction 9/60 = 0.15. Second, multiply the result 0.15 * 100 = 15.

Key Concepts

Basic Percentage Formula

Understanding the basic percentage formula is key to solving any percentage problem. This formula helps you determine what percentage a "part" is of a "whole". The standard percentage formula is:\[\left( \frac{\text{Part}}{\text{Whole}} \right) \times 100\]In this formula:

• "Part" refers to the portion in question. For example, in the exercise, it is 9 people.
• "Whole" represents the total number. In our case, this is 60 people.
• The fraction is then multiplied by 100 to convert it into a percentage.

Applying this formula correctly is crucial. Once you do this, it allows you to see the magnitude of the part compared to the whole in percentage terms. This forms the basis of calculating percentages in both simple and complex scenarios.

Fraction Simplification

Simplifying fractions makes calculations easier, especially when they involve percentages. A fraction is in simplest form when no number other than one divides evenly into both the numerator and the denominator.Using the exercise example, we have the fraction \( \frac{9}{60} \). To simplify this fraction:

• Look for the greatest common divisor of both numbers. In this case, it is 3.
• Divide both the numerator (9) and the denominator (60) by this number.

This gives:\[\frac{9 \div 3}{60 \div 3} = \frac{3}{20}\]Simplified fractions lead to easier calculations in the next steps, like multiplying by a percentage later. For percentage calculations, having the fraction in its simplest form makes it more manageable and minimizes errors in subsequent operations.

Multiplying Decimals

Multiplying decimals is another fundamental skill required in percentage calculations. Once you have simplified the fraction into a decimal, it's straightforward:For instance, from the exercise, the simplified fraction \(\frac{3}{20}\) converts into a decimal like this:\[3 \div 20 = 0.15\]Next, multiply this decimal by 100 to find the percentage:\[0.15 \times 100 = 15\]Why multiply by 100? Because the percentage system is based on "per hundred". Essentially, this conversion is straightforward:

• Move the decimal point two places to the right for multiplying by 100.
• Make sure to line up decimals carefully to maintain accuracy.

Understanding how to handle decimals correctly when multiplying ensures your final percentage calculation is exact and precise.