Problem 13 - Prealgebra

Question

Find the percent of each number mentally. $$20 \% \text { of } 105$$

Step-by-Step Solution

Answer

20% of 105 is 21.

Step 1: Understand "Percent of a Number"

To find 20% of a number, we first need to understand that "percent" means "per hundred." So, 20% is equivalent to 20 per 100 or 0.20.

Step 2: Convert Percent to Decimal

Convert 20% to a decimal for easier calculation. This is done by dividing 20 by 100, which gives us 0.20.

Step 3: Calculate the Decimal of the Number

Now, multiply the number 105 by the decimal 0.20. \[ 105 imes 0.20 = 21 \]

Step 4: Interpret the Result

The result, 21, is the 20% of 105. This means that 20% of the number 105 is equal to 21.

Key Concepts

Mental Math

Mental math involves doing calculations quickly and efficiently in your head without relying on tools like calculators or written work. When it comes to calculating percentages, mental math can be handy, especially if the problem involves simple numbers. For instance, when finding 20% of 105 mentally, you can break it into simpler steps using basic arithmetic and approximation.

• First, recognize that 10% of 105 is easy to calculate: just move the decimal one place to the left, so it becomes 10.5.
• Then, double that result to find 20%: 10.5 doubled is 21.

This approach is quick and can be done mentally without complex calculations. Mastering these small tricks can save time and strengthen numerical understanding.

Converting Percentages to Decimals

Converting percentages into decimals is a key math skill that simplifies calculations. Percent means "per hundred," so to convert a percentage into a decimal, you divide by 100. This action shifts the decimal point two places to the left. Let's illustrate this with our exercise:

• Start with the percentage: 20%.
• Divide by 100 to convert it into a decimal: 20 ÷ 100 = 0.20.

Recognizing that converting a percent like 20% to a decimal results in 0.20 makes multiplication with numbers straightforward and accurate. This conversion strips the percentage of its relative complexity and allows for easier manipulation during calculations.

Basic Arithmetic Operations

Basic arithmetic operations are the foundation of solving any math problem. They include addition, subtraction, multiplication, and division. In percentage problems, multiplication is often used to find a portion of a number. Let's recap the steps with the example:

• First, you need a decimal representation of the percentage. With 20% as 0.20, as we previously calculated.
• Then, multiply the decimal by the given number: 105 × 0.20.
• The multiplication results in 21, meaning 20% of 105 is 21.

Understanding and executing these basic operations allows you to tackle more complex math problems confidently. It's essential to ensure arithmetic accuracy by carefully managing decimal positions and ensuring correct operand use.