Problem 48 - Algebra 1: Concepts and Skills

Question

Evaluate. $$ 150 \% \text { of } 300 $$

Step-by-Step Solution

Answer

The answer is 450.

Step 1: Understand the problem

The problem is asking to find 150% of 300. Percent means 'out of 100', so 150% can be written as \( \frac {150}{100} \) or 1.5.

Step 2: Multiply by 150%

To find 150 percent of 300, multiply 300 by 1.5. This is because, in general, to find \(x\%\) of \(y\), you multiply \(y\) by \(x/100\). So, we have \(300 \times 1.5 = 450\).

Key Concepts

Calculating Percentages

Understanding how to calculate percentages is a fundamental skill in both math and real life, as it involves determining a portion or share of a whole. To calculate a percentage of a number, we use the concept of 'per hundred'. For instance, finding 150% of 300 begins with the realization that 'percent' means 'per hundred'. Thus, 150% is equivalent to 150 per 100, which can be written as a decimal or fraction, specifically, 1.5 or \( \frac {150}{100} \).

Once you've converted the percentage into a fraction or decimal, the next step involves basic multiplication. To find the percentage of a given number, you multiply that number by the obtained fraction or decimal. So, 150% of 300 is calculated by multiplying 300 by 1.5, resulting in 450. Remember, the process is the same for any other percentage; convert the percentage to a decimal or fraction, then multiply by the number you wish to find the percentage of.

Percent Arithmetic

Percent arithmetic incorporates basic arithmetic operations such as addition, subtraction, multiplication, and division, but with numbers expressed as percentages. Understanding percent arithmetic is crucial when dealing with various percentages, especially when combining them or comparing them against each other.

For instance, if we want to increase a quantity by a certain percentage, we add that percentage to 100% of the original quantity. Conversely, to decrease a quantity by a percentage, we subtract that percentage from the original 100%. When multiplying percentages, you first convert them to decimals. If solving problems that involve more complex operations, such as finding the percentage difference between two numbers, the same conversion technique is applied before the arithmetic steps.

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and arithmetic operations that represent a specific value or range of values. In percentage problems, algebraic expressions can be used to create general formulas that apply to a variety of situations. For example, to find a given percentage of a number, the algebraic expression would be \( x\% \times y \), where \( x \) represents the percentage we want to find and \( y \) is the number we're finding the percentage of. This simplifies to \( \frac{x}{100} \times y \).

By mastering algebraic expressions in the context of percentages, students can tackle a wide range of problems by plugging in the given values into their expressions. This not only makes it easier to solve problems but also helps in understanding the underlying relationships between the variables.