Problem 80 - Elementary Algebra

Question

$$ \text { Find } 125 \% \text { of } 65 $$

Step-by-Step Solution

Answer

81.25

Step 1: Understand the Problem

To find 125% of 65, it means converting 125% into a decimal and then multiplying it by 65.

Step 2: Convert Percentage to Decimal

Convert 125% to a decimal by dividing by 100: \[ 125\% = \frac{125}{100} = 1.25 \]

Step 3: Multiply the Decimal by the Number

Now multiply the decimal (1.25) by the number (65): \[ 1.25 \times 65 = 81.25 \]

Step 4: Write the Final Answer

So, 125% of 65 is 81.25.

Key Concepts

converting percentage to decimal

When working with percentages, it's often necessary to convert them to decimals. This makes calculations easier and more straightforward. To convert a percentage to a decimal, simply divide the percentage by 100. For example, to convert 125% to a decimal, we perform the calculation:
$$ \ 125 \ \ = \ \frac{ 125}{100} \ = \ 1.25 $$
Now, you can use this decimal in other calculations such as multiplication. Remember:

• To convert a percentage to a decimal, divide by 100.

This step is crucial and makes further operations much smoother.

multiplying decimals

Multiplying decimals is a fundamental math skill. After converting percentages to decimals, you will often need to multiply them by other numbers. Let's take our previous example where we converted 125% to 1.25. Now, we need to find 125% of 65.
To do this, we multiply 1.25 by 65:
$$ \ \ 1.25 \times 65 \ = \ 81.25 $$
Here is a simple way to multiply decimals:

• Ignore the decimal points initially and just multiply the numbers as if they were whole numbers.
• Afterward, count the total number of decimal places in both of the original numbers.
• Place the decimal point in the answer, so it has the same number of decimal places as the total count from the original numbers.

Practicing this method will make you more comfortable and faster at multiplying decimals.

percentages in math

Percentages appear frequently in math problems and daily life. Understanding how to work with them is essential. Percentages can represent:

• Parts of a whole (e.g., 50% of a pizza).
• Increases and decreases (e.g., a 20% discount).
• Comparisons between different quantities.

To handle percentages, you often use:

• Conversion between percentages, decimals, and fractions.


• Multiplication and division to find portions of quantities.

The key steps involved in our example were:

• Converting 125% to a decimal (1.25).


• Multiplying this decimal by 65 to find the part of the quantity.

Building these skills will help you tackle a wide range of math problems effectively!