Problem 19 - Algebra 1: Concepts and Skills

Question

Solve the percent problem. 14% of 220 feet is what length?

Step-by-Step Solution

Answer

The length is 30.8 feet

Step 1: Change Percentage to Decimal

Change the percentage, 14%, into a decimal. This can be done by dividing the percentage by 100 or simply moving the decimal point two places to the left. So, 14% becomes 0.14.

Step 2: Multiply the Decimal by the Whole Quantity

Next, multiply the decimal obtained in step 1 (0.14) by the whole quantity, which is 220. So, the multiplication is \(0.14 \times 220\).

Step 3: Compute the result

After multiplying \(0.14 \times 220\) the result is 30.8.

Key Concepts

Decimal Conversion

Converting percentages to decimals is an essential step in solving many percentage problems. It’s quite straightforward once you grasp the basics. To convert a percentage to a decimal, you simply divide by 100. For example, if you have 14%, you divide 14 by 100, which gives you 0.14. Another quick way is to just move the decimal point two places to the left. So, 14% changes from 14.0% to 0.14, which represents the same value as a decimal. Understanding this conversion is crucial because it allows you to perform operations like multiplication easily.

Multiplication

Once you've converted a percentage to a decimal, the next step is often multiplication, especially in problems where you need to find a portion of a whole. Multiplication involves combining quantities. Here, you use the decimal you calculated to determine the part of the whole you are interested in.
For the problem given, after converting 14% to 0.14, you multiply this decimal by the whole number, which is 220 feet, i.e., \(0.14 \times 220\).
This way, multiplication helps to find what part (in feet, in this case) the percentage equals out of the total number.

Problem Solving Steps

Solving percentage problems involves following a series of logical steps that systematically bring you to the answer. Here's a breakdown of these steps:

• Step 1: Convert Percentage to Decimal - As we discussed, convert the percentage to a decimal fraction by dividing by 100 or shifting the decimal two places to the left.
• Step 2: Multiply - Take the decimal you have and multiply it by the total quantity you're working with.
• Step 3: Calculate Result - Perform the multiplication to find the specific part of the total amount represented by the percentage.

For the example problem, 14% of 220 feet, after performing these steps, you find that 14% of 220 feet is 30.8 feet. By approaching percentage problems with a methodical sequence, you're able to solve them accurately and efficiently.