Problem 49 - Elementary Algebra

Question

Answer the question by setting up and solving an appropriate equation. What is \(7 \%\) of 38 ?

Step-by-Step Solution

Answer

7% of 38 is 2.66.

Step 1: Understand the Problem

We are asked to find 7% of 38. The word "of" in mathematics typically means multiplication.

Step 2: Convert Percentage to Decimal

To convert a percentage to a decimal, divide by 100. So, 7% becomes \( \frac{7}{100} \) or 0.07 as a decimal.

Step 3: Set Up the Equation

To find 7% of 38, we set up the equation: \( 0.07 \times 38 \).

Step 4: Perform the Multiplication

Multiply 0.07 by 38: \( 0.07 \times 38 = 2.66 \).

Step 5: Write the Solution

The result of the multiplication tells us that 7% of 38 is 2.66.

Key Concepts

Convert Percentage to Decimal

Understanding how to convert a percentage to a decimal is a fundamental math skill. In percentage terms, we often encounter values represented by the percent sign, '%'—a symbol indicating a fraction out of 100. To convert a percentage to its decimal form, simply divide it by 100. This transformation allows the percentage to be easily used in calculations. For example:

• To convert 7% to a decimal, you divide 7 by 100. This gives you 0.07 as the decimal equivalent.
• If you want to convert 50%, it becomes 0.50 because 50 divided by 100 is 0.50.
• Another example is converting 125% to a decimal, which results in 1.25.

This conversion is crucial for mathematical operations involving percentages, such as multiplication and solving equations.

Multiplication in Percentages

When dealing with percentages, multiplication plays a key role. Whenever you see the word 'of' in a percentage problem, it generally indicates that multiplication is required. Here is the step-by-step process to follow:

• First, convert the percentage to a decimal (as discussed earlier).
• Next, multiply this decimal by the number in question.

Let's take 7% of 38 as an example:1. Convert 7% to decimal, which is 0.07.2. Multiply 0.07 by 38.The multiplication is straightforward:

• Compute: \(0.07 \times 38 = 2.66\)

Hence, when multiplying percentages, always ensure the percentage is in decimal form before performing the operation. This step ensures accurate results each time you deal with percentage problems in real-life contexts or in a classroom setting.

Solving Equations with Percentages

Solving equations that involve percentages is a useful skill for numerous applications, from finance to day-to-day math problems. To tackle these equations, you often need to set up a formula that incorporates both the percentage (as a decimal) and the number involved. The process is generally as follows:1. Change the percentage to a decimal.2. Construct an equation using multiplication to find the percentage of a number.For instance, here's how you'd solve for 7% of 38:

• Convert 7% to a decimal: 0.07.
• Set up the equation: \(0.07 \times 38 = x\).
• Perform the multiplication to find that \(x = 2.66\).

The result shows that 7% of 38 equals 2.66. In this way, equations with percentages can be solved by carefully converting and computing to find precise answers. Mastering this step enables you to handle varied mathematical scenarios involving percentages with confidence.