Question

Translate to an equation and solve. \(150 \%\) of 60 is what number?

Short answer

Answer: 90

Step-by-step solution

Convert Percentage to Decimal

To convert 150% to a decimal, we will divide it by 100. This means: \(150 \% = \frac{150}{100} = 1.5\)

Multiply the Decimal by the Given Number

Now, we will multiply the converted decimal (1.5) by the given number (60): \(1.5 \times 60 = 90\)

Interpret the Result

The result of the equation, 90, represents 150% of the given number 60. Therefore, 150% of 60 is equal to 90.

Key concepts

Converting Percentages to Decimals: The Basics

Understanding how to convert percentages to decimals is crucial in solving many mathematical problems. A percentage represents a part out of 100. To convert it to a decimal, you need to divide the percentage by 100. For example, if you have 150%, the process is:

• Take the percentage number (150).
• Divide it by 100 to remove the percentage sign.

The equation becomes: \[150 \% = \frac{150}{100} = 1.5\] In simple terms, 1.5 is the decimal representation of 150%. This conversion helps in performing further mathematical operations with ease.
Always remember: Dividing by 100 shifts the decimal point two places to the left, changing a percentage directly into a decimal value.

Arithmetic Operations: Applying the Conversion

Now that you have converted the percentage into a decimal, the next step involves basic arithmetic operations. Arithmetic is simply the art of numbers, where you perform different operations such as addition, subtraction, multiplication, and division.
In this exercise, once we've converted 150% to 1.5 as a decimal, we use multiplication to find out what 150% of 60 is:

• Multiply the decimal (1.5) by the number in question (60).

This process can be expressed as: \[1.5 \times 60 = 90\]
Here, multiplication is key because it allows you to scale up the number (60) by the factor of 1.5, which represents 150%. The result, 90, indicates that multiplying achieves the desired percentage of the original number.
This simple multiplication effectively demonstrates how arithmetic operations are employed after converting percentages to decimals.

Mathematical Reasoning: Understanding the Process

Mathematical reasoning involves understanding and explaining the problem-solving process. After performing arithmetic operations, it's crucial to interpret the result correctly. Here, mathematical reasoning helps ensure that the conclusion is consistent with the question asked.
Let's recap the problem and solution:

• The initial question asks for 150% of the number 60.
• Through conversion and multiplication, you calculate and obtain the number 90.

Mathematical reasoning confirms that the number 90 indeed represents 150% of 60. How do we know this?

• By realizing that 1.5 times any number increases it by half again, making 90 logical as it is 60 plus half of 60 (which is 30).

Using reasoning helps verify that the calculation correctly reflects the question's intent.
Always follow through on calculations with logical checks to ensure your answer makes sense in context. This is a valuable habit in mathematics.