Problem 72 - Elementary Algebra

Question

$$ \text { Find } 5 \% \text { of } 40 \text {. } $$

Step-by-Step Solution

Answer

5% of 40 is 2.

Step 1: Understand the Problem

The problem requires finding 5% of the number 40.

Step 2: Convert Percentage to Decimal

Percentages are converted to decimals by dividing by 100. So, 5% becomes \( \frac{5}{100} \) or 0.05.

Step 3: Multiply the Decimal by the Number

Next, multiply the decimal (0.05) by the number 40: \( 0.05 \times 40 \).

Step 4: Perform the Multiplication

Calculate \( 0.05 \times 40 \): \( 0.05 \times 40 = 2 \).

Step 5: Write the Solution

The answer is 2. Therefore, 5% of 40 is 2.

Key Concepts

percentages

A 'percentage' represents a fraction of 100. The symbol % is used to denote it. For example, 5% means 5 out of 100. The concept of percentages is widely used in everyday life.
Calculating percentages helps us understand proportions and comparisons. It is a way of expressing ratios in a standard format.
Here are some steps to calculate percentages:

• Identify the percentage you need to find.
• Convert the percentage to its decimal form.
• Multiply the decimal by the number to find your result.

decimal conversion

To convert a percentage to a decimal, you divide by 100. For example, converting 5% to a decimal involves dividing 5 by 100: \[ \frac{5}{100} = 0.05 \]
Decimals make it easier to perform calculations and solve problems. Converting percentages to decimals is a crucial step in many arithmetic operations.
Here’s a quick guide to converting percentages to decimals:

• Take the percentage value.
• Divide by 100.
• Write the decimal equivalent.

multiplication

Multiplication is one of the basic arithmetic operations. It combines groups of the same size to find the total amount. When you use multiplication with decimals, it helps to understand scales, proportions, and more.
In the context of percentage calculations, multiplying a decimal by a number gives you the portion of the number represented by that percentage. For example:
\[ 0.05(5\text{%}) \times 40 = 2 \]
Tips for multiplication:

• Check your decimal places.
• Align the numbers correctly.
• Multiply as if you're dealing with whole numbers, and place the decimal in the correct position at the end.

Understanding how to multiply decimals is essential for solving various types of problems, from simple to complex ones.