Problem 22 - Elementary Algebra

Question

What percent is \(1.35\) of 90 ?

Step-by-Step Solution

Answer

1.5%

Step 1: Understand the Problem

The problem is asking what percent the number 1.35 is of the number 90.

Step 2: Set Up the Equation

To find the percentage, use the formula: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \] Here, the part is 1.35, and the whole is 90.

Step 3: Plug in the Values

Substitute the given values into the equation: \[ \text{Percentage} = \frac{1.35}{90} \times 100 \]

Step 4: Perform the Division

Divide 1.35 by 90: \[ \frac{1.35}{90} \times 100 \] \[ = 0.015 \times 100 \]

Step 5: Multiply by 100

Now multiply the result by 100 to get the percentage: \[ 0.015 \times 100 = 1.5 \]

Step 6: Conclusion

Therefore, 1.35 is 1.5% of 90.

Key Concepts

Percentage Formula

Calculating percentages is a fundamental skill in mathematics that is widely used in everyday life. To find what percent one number is of another, you can use a basic formula.
The percentage formula is: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]
This formula helps you express one number as a fraction of another number and then multiply by 100 to convert this fraction into a percentage.
Let's break down the formula:

• Part: This is the portion or number you want to convert to a percentage.
• Whole: This is the total or entire number you are comparing against.

For example, in the exercise provided, we want to find what percent 1.35 (the part) is of 90 (the whole). Plugging these numbers into our formula gives us the percentage.

Basic Arithmetic

Understanding basic arithmetic operations is crucial for solving percentage problems. Arithmetic involves simple operations like addition, subtraction, multiplication, and division.
In this context, you'll primarily need to focus on arithmetic operations such as:

• Division: This helps us find the ratio or fraction of the part compared to the whole.
• Multiplication: This allows us to convert a fraction into a percentage by multiplying by 100.

Remember, when you divide a smaller number by a larger number, you get a decimal. Multiplying this decimal by 100 will give you the percentage.
For example, in our exercise:
First, divide 1.35 by 90, which gives you 0.015. Then multiply 0.015 by 100 to get 1.5%. Simple arithmetic makes it effortless!

Division and Multiplication

These two operations, division and multiplication, are often used together in percentage calculations.
Here’s a step-by-step approach:

• First, divide the part by the whole. This division step converts the two numbers into a ratio or a fraction. For instance, 1.35 divided by 90 equals 0.015.
• Second, multiply the result by 100. This multiplication converts the decimal into a percentage. So, 0.015 times 100 equals 1.5%.

Both operations are straightforward but essential:

• Division helps you understand how large the part is in relation to the whole.
• Multiplication converts that relational value into a percentage, making it easier to understand and communicate.

Practice these operations to master them and make percentage calculations second nature.