Problem 35 - Algebra 1

Question

Find the percent of a number. $$200 \% \text { of } 130$$

Step-by-Step Solution

Answer

The 200% of 130 is 260.

Step 1: Convert the Percentage to Decimal

To convert a percentage to decimal, divide it by 100. Thus, \( 200 \% = 200 \div 100 = 2\).

Step 2: Apply the Percentage Formula

Substitute the values into the percentage formula, which is \( \text {Percentage} = \text {Rate} \times \text {Base} \) . This gives us \( \text {Percentage} = 2 \times 130\).

Step 3: Calculate the Product

Multiply 2 and 130 to obtain the required percentage. Getting \( 2 \times 130 = 260 \).

Key Concepts

Converting Percentage to Decimal

Converting a percentage to a decimal is a simple, yet fundamental mathematical operation. In a percentage, "percent" actually means "per hundred." Thus, whenever you encounter a percentage, you are dealing with parts out of 100. For example, 200% represents 200 parts out of 100. To convert this into a decimal, simply divide the percentage by 100. This method works for any percentage.
Here is a handy step-by-step guide:

• Take the percentage number.
• Divide it by 100.

So, to convert 200% to a decimal, you perform the operation: \[200 \div 100 = 2\] This means 200% is equal to the decimal 2.
This conversion is crucial to solve percentage problems where multiplication is needed.

Percentage Formula

The percentage formula is your best friend when it comes to calculating percentages from given numbers. It's a straightforward formula that relates three components: the percentage, the rate, and the base. The formula can be represented as: \[\text{Percentage} = \text{Rate} \times \text{Base}\]

• Rate: the percentage you want to find or use.
• Base: the number on which the percentage operates.
• Percentage: the part of the base that the percentage captures.

Let's apply it!
For the problem "200% of 130," where 200% is the rate and 130 is the base, substitute these values into the formula: \[\text{Percentage} = 2 \times 130\] This setup makes complex percentage problems manageable by breaking them into simple calculations.

Multiplication in Percentage Problems

Multiplication plays a key role in percentage problems, especially once the percentage is converted to a decimal. After converting the percentage to a more manageable decimal form, it is time to multiply.
In the exercise under scrutiny, 200% was converted to decimal form \(2\). By multiplying this by the base number, you effectively take 200% of the base. Let's see it in action using the numbers from our example:

• Decimal from percentage: 2 (from 200%).
• Base number: 130.

Perform the multiplication: \[2 \times 130 = 260\]
This product tells us that 200% of 130 is indeed 260. Every time you handle percentage questions involving multiplication, this is the systematic approach that allows you to solve them accurately and efficiently.