Problem 14 - Elementary Algebra

Question

Find \(65 \%\) of 130 .

Step-by-Step Solution

Answer

65% of 130 is 84.5.

Step 1 - Understand the Problem

To find 65% of 130 means finding the fraction of 130 that corresponds to 65 percent.

Step 2 - Convert the Percentage to a Decimal

Convert 65% to a decimal by dividing 65 by 100. This gives us:\[ 0.65 \]

Step 3 - Multiply the Decimal by the Number

Now, multiply 0.65 by 130 to find 65% of 130:\[ 0.65 \times 130 \]

Step 4 - Perform the Calculation

Calculate the multiplication from the previous step:\[ 0.65 \times 130 = 84.5 \]

Key Concepts

Converting Percentages to Decimals

To start solving any problem that involves percentages, the first step is to convert the percentage into a decimal. This is essential because math operations like multiplication and division are typically done using decimals, not percentages. To convert a percentage to a decimal, simply divide the percentage by 100. For example, to convert 65%, we divide 65 by 100, resulting in 0.65. So, 65% expressed as a decimal is 0.65. It’s a straightforward step, but it's crucial to getting the right answer.

Multiplying Decimals

Once you have the percentage as a decimal, the next step often involves multiplication. In this case, you're looking to find 65% of 130, which means you need to multiply the decimal by 130. Multiplying decimals might seem a bit tricky at first, but it's just a matter of following some simple steps.

For example, to multiply 0.65 by 130, write down the numbers aligning them by the decimal point and proceed with the multiplication as if they were whole numbers. After you get the answer, count the total number of decimal places in both the numbers you're multiplying. Place the decimal point in your answer, counting from right to left, according to the total decimal places you counted. In this example:

• 0.65 has 2 decimal places.
• 130 has no decimal places.

Thus, the final product should have 2 decimal places. So, after multiplying 0.65 and 130 as if they were whole numbers, the result is 8450. Place the decimal point and you'll get 84.5.

Step-by-Step Problem Solving

Breaking a problem into manageable steps can make it much easier to solve. Here's how we can approach calculating 65% of 130 in a series of simple steps:

• Step 1: Understand what the problem is asking. Finding 65% of 130 means finding which part of 130 corresponds to 65%.
• Step 2: Convert the percentage to a decimal. For 65%, divide 65 by 100 to get 0.65.
• Step 3: Multiply the decimal by the number. Multiply 0.65 by 130 to get the result.
• Step 4: Perform the calculation. Calculate 0.65 times 130, which equals 84.5.

By following these steps, you can solve similar percentage problems with ease. This methodical approach helps ensure you don’t miss any steps and can find the correct answer confidently. Remember, breaking down the problem and solving it step-by-step makes it much simpler to handle.