Problem 83 - Elementary Algebra

Question

$$ \text { Find } 6 \% \text { of } 21 $$

Step-by-Step Solution

Answer

1.26

Step 1: Understand the Problem

To find 6% of 21, interpret the problem as finding what is 6 per 100 of the number 21.

Step 2: Convert the Percentage to a Decimal

Convert 6% to a decimal by dividing 6 by 100. This gives you: \[6 \div 100 = 0.06\]

Step 3: Multiply the Decimal by the Number

Multiply the decimal from Step 2 by the number 21. This gives you: \[0.06 \times 21 = 1.26\]

Step 4: Write the Final Answer

The value of 6% of 21 is 1.26.

Key Concepts

percentage to decimal conversion

Understanding how to convert a percentage to a decimal is a fundamental skill in math. A percentage represents a 'part per hundred'. This means 6% is the same as 6 parts out of 100. To convert a percentage to a decimal, you need to divide the percentage by 100. For example, to convert 6% to a decimal, you perform the following division: \[ 6 \div 100 = 0.06 \]
Remember, dividing by 100 simply moves the decimal point two places to the left.
Practicing this with different percentages helps solidify the concept. For instance:

• 50% becomes 0.50
• 25% becomes 0.25
• 1% becomes 0.01

multiplication of decimals

Once you have the percentage converted to a decimal, the next step is to multiply it by the number in question. Here, we multiply our decimal 0.06 by 21. This involves basic decimal multiplication: \[ 0.06 \times 21 = 1.26 \]
To multiply decimals, follow these steps:

• Ignore the decimals initially and just multiply the numbers as whole numbers (6 and 21).
• 6 times 21 is 126.
• Then, count how many digits are after the decimal points in the original numbers. Here, we have two digits after the decimal in 0.06.
• Place the decimal in the result accordingly: 1.26.

With consistent practice, multiplying decimals becomes easier and quicker.

understanding percentages

Grasping the concept of percentages is crucial as it applies to many real-life scenarios, such as discounts, interests, and statistics. A percentage is a way to express a number as a fraction of 100. For instance, 6% means 6 out of every 100.
This is useful when comparing proportions. In our problem, 6% of 21 means we are looking for a small portion of 21. By converting this percent to a decimal (0.06) and multiplying it by 21, we find the exact value of 6% of 21.
Some key points to remember about percentages:

• Percentages can be greater than 100%, meaning more than the whole.
• Percentages less than 1% represent very small fractions.
• Comparative percentages can show growth or reduction, like how much something has increased compared to a previous amount.

Understanding these points can make dealing with percentages much easier and applicable in different scenarios.