Problem 45 - Algebra 1: Concepts and Skills

Question

Evaluate. $$ 45 \% \text { of } 10 $$

Step-by-Step Solution

Answer

45% of 10 equals 4.5

Step 1: Understanding Percentage

Percentage is a way of expressing a number as a fraction of 100. In this case, 45% is the same as 0.45 when expressed as a decimal.

Step 2: Multiply by the Number

To find 45% of 10, you need to multiply 0.45 by 10.

Step 3: Compute the Result

Perform the multiplication: 0.45 * 10 which equals 4.5

Key Concepts

Fraction to decimal conversion

When working with percentages, one of the essential skills is the conversion of fractions to decimals. A percentage is essentially a fraction expressed with a denominator of 100. For example, 45% is equivalent to \( \frac{45}{100} \). To convert this fraction to a decimal, you simply divide the numerator by the denominator.
Performing this division, \( \frac{45}{100} = 0.45 \).
This conversion is crucial because working with decimals is often easier than working directly with percentages or fractions in calculations.

• Step 1: Take the percentage number, such as 45.
• Step 2: Rewrite it as a fraction over 100, \( \frac{45}{100} \).
• Step 3: Divide the numerator (45) by the denominator (100) to get 0.45.

This process applies to any percentage, making it a valuable tool in various mathematical scenarios.

Multiplication of decimals

Multiplying decimals, like multiplying whole numbers, requires careful attention to the placement of the decimal point. When you multiply a decimal by a whole number, align the numbers by their rightmost digits and perform multiplication as if they were whole numbers.
After completing the multiplication, you'll need to position the decimal point in the product. For the example in the exercise, \( 0.45 \times 10 \):

• Step 1: Ignore the decimal point and multiply 45 by 10, giving 450.
• Step 2: Since there are two decimal places in 0.45, count two places from the right in the product (450) to place the decimal, resulting in 4.5.

This ensures your answer maintains the proper precision determined by the original decimal factors. It is essential for accuracy in calculations involving monetary values, measurements, or statistical data.

Basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. These operations form the foundation of most mathematical problems. In the exercise, multiplication is used to find a percentage of a number.
To solve a problem like 45% of 10, conversion into an arithmetic format like 0.45 multiplied by 10 simplifies the process. Basic principles to remember:

• Order of Operations: Follow the BIDMAS/BODMAS rule - Brackets, Indices (or Order), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
• When performing multiplication, consider all digits, including those after the decimal point to ensure precision.
• Use mental math shortcuts, like multiplying the number by 1 (10% as 0.10) and subtracting or adding the results for efficiency.

Being adept at basic arithmetic helps in tackling more complex problems as it expands into algebra, geometry, and beyond. It is fundamental to everyday tasks, like budgeting, cooking, or even shopping discounts.