Problem 16 - Algebra 1: Concepts and Skills

Question

Solve the percent problem. How much money is 35% of $750?

Step-by-Step Solution

Answer

35% of $750 is $262.50.

Step 1: Identify the Total Amount

Recognize that the total amount is $750.

Step 2: Convert Percentage to Decimal

Convert the percentage (35%) into a decimal. To do this, the percentage is divided by 100, resulting in 0.35.

Step 3: Multiply the Decimal with the Total

Multiply the conversion of the percentage (0.35) by the total amount ($750). Perform the calculation \(0.35*750\) to get the amount that 35% represents.

Key Concepts

Percent to Decimal Conversion

When tackling percentage problems, a crucial step is converting the given percentage into decimal form. This conversion simplifies the computation process.
To convert a percentage into a decimal, you divide the percentage value by 100. For example, if you have 35%, you divide 35 by 100, which equals 0.35.

• The percentage value is the number followed by the percent sign (%).
• Divide the percentage by 100 to shift the decimal point two places to the left.
• Example: 35% = 35/100 = 0.35

Converting percentages to decimals is necessary because most mathematical operations involving percentages require them to be in decimal form.

Total Amount in Percentage Problems

Percentage problems often involve finding a portion of a total amount, typically expressed in terms of a percentage. The total amount is the base figure from which the percentage is calculated.
In our example, the total amount is $750. Recognizing and clearly identifying the total amount is essential, as it forms the basis for further calculations.

• Total amount refers to the entire value before the percentage is applied.
• It's vital to distinguish the total from any percentage or portion values.
• This figure remains constant as it is central to solving percentage problems.

Clearly understanding the role of the total amount ensures accuracy in determining the correct portion or value associated with the percentage.

Multiplying to Find Percentage Amount

After converting the percentage to a decimal and identifying the total amount, the next step is to find what portion of the total amount corresponds to the given percentage.
This is achieved by multiplying the decimal form of the percentage by the total amount.
This step is straightforward: multiply the decimal (0.35) by the total, which in this case is $750.

• The calculation: 0.35 x 750 = 262.5
• Resulting in $262.50 as the amount that represents 35% of $750
• Always ensure multiplication is done accurately to get the correct answer.

Through multiplication, the percentage is effectively applied to the total amount, giving you the amount that corresponds to that percentage.