Problem 64 - Algebra 1

Question

Find the number. $$ 5.5 \% \text { of } \$ 74 $$

Step-by-Step Solution

Answer

The result is \$4.07.

Step 1: Convert the Percentage to Decimal

To convert a percentage to decimal, you need to divide it by 100. So: \[ 5.5 \% = \frac {5.5} {100} = 0.055 \]

Step 2: Multiply the Decimal by the Amount

Once the decimal equivalent of the percentage is found, it needs to be multiplied by the given amount. Hence: \[ 0.055 * \$74 = \$4.07 \]

Key Concepts

Convert Percentage to Decimal

Converting a percentage to a decimal is one of the foundational math skills. It is very simple and involves dividing the percentage by 100. This is because the word 'percent' means 'per hundred.' So, if you have 5.5%, you want to find out what 5.5 out of 100 equals as a decimal number. This is done by dividing 5.5 by 100.
This conversion can be thought of as shifting the decimal point two places to the left. So, for 5.5%, the decimal point moves from behind the 5.5 to before it, making it 0.055.

• Example: Convert 75% to a decimal.
  Start with 75, divide by 100:
  \(75\div 100 = 0.75\)

Mastering this step is crucial for calculations involving percentages, like finding discounts or understanding interest rates.

Multiplication of Decimals

After converting a percentage to a decimal, the next step is often to multiply it by another number. This skill is useful in everyday calculations, such as finding a sale price or calculating tips.
To multiply decimals, follow these steps:

• Multiply the numbers ignoring the decimal points.
• Count the total number of decimal places in the two numbers being multiplied.
• Place the decimal in the product so that it has that number of decimal places.

For example, when multiplying 0.055 by 74, you first multiply 55 by 74 normally, and then divide the result by 1000 (since there are three decimal places in total).
Understanding this step ensures accuracy in financial calculations, such as converting percentages into actual costs.

Basic Arithmetic

Basic arithmetic involves simple operations like addition, subtraction, multiplication, and division. These are fundamental and are used in almost all areas of math.
For example, if you are asked to find 5.5% of $74, you first convert the 5.5% into a decimal and then multiply, as explained in the earlier sections.
These basic operations are not only vital in solving academic problems, but they are also used in daily life. From calculating the time it takes to travel a certain distance, to deciding how much of a grocery item you can buy with a specific dollar amount.

• Remember that applying the correct order of operations is key. For instance, multiplying before adding or subtracting in a series of tasks.
• Practice with actual problems enhances comprehension and speed.

Mastery of basic arithmetic sets the groundwork for tackling more complex math concepts in the future.