Question

Perform the indicated operations. What percentage of 6.4 is \(1.6 ?\)

Short answer

1.6 is 25% of 6.4.

Step-by-step solution

Understand the Problem

We need to find what percentage the number 1.6 is of 6.4. To do this, we will use the formula for percentage calculation: the part (1.6) divided by the whole (6.4) and then multiplied by 100 to get the percentage.

Set Up the Equation

Set up the equation for finding the percentage: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). In this case, the 'part' is 1.6 and the 'whole' is 6.4.

Calculate the Fraction

Calculate the fraction of 1.6 over 6.4. This is done by dividing 1.6 by 6.4: \( \frac{1.6}{6.4} = 0.25 \).

Convert to Percentage

Convert the fraction from Step 3 to a percentage by multiplying by 100: \( 0.25 \times 100 = 25 \% \).

Verify Your Answer

Check the calculation to ensure accuracy. 1.6 divided by 6.4 equals 0.25, and 0.25 times 100 returns 25%. Everything checks out correctly.

Key concepts

Fraction Conversion

Fraction conversion is a fundamental skill in mathematics, crucial for understanding percentages and similar concepts. When we talk about converting a fraction, we generally mean expressing the relation between two numbers in different terms. In our example, we needed to determine the fraction of 1.6 over 6.4.

To find this fraction, we simply divide the 'part' (1.6) by the 'whole' (6.4), which in this case results in a decimal: 0.25. But what does this decimal tell us? It represents the same relationship as the fraction itself, showing the part-to-whole relationship in a way that's easy to interpret, especially when converting to percentages.

While a fraction like 1.6/6.4 might not be readily recognizable, simplifying it down to a decimal form makes subsequent calculations, like converting to a percentage, far more manageable.

Step-by-Step Solution

Solving math problems becomes a lot easier when you break them down into step-by-step processes. This structured approach not only helps in solving the problem but also aids in building a deeper understanding of mathematical concepts. Let's revisit the solution to our percentage problem.

• Step 1: Clearly understand what the problem asks. In our case, it's about finding the percentage of 1.6 in relation to 6.4.
• Step 2: Set up the equation using the formula for percentage: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
• Step 3: Calculate the fraction. Division of 1.6 by 6.4 gives us 0.25.
• Step 4: Convert the decimal to a percentage. Here, multiply by 100 to get 25%.
• Step 5: Verify your calculations to ensure you haven't missed anything and your answer remains consistent.

Each step builds on the previous one to ensure a logical and clear path to the final solution.

Math Problem Solving

Problem-solving in mathematics is like piecing together a puzzle. Each problem has its own structure and contextual clues to guide you towards the solution. Here's how you can effectively tackle math problems involving percentages.

Begin by clarifying the question you need to solve. What exactly are you asked to find out? Once that's clear, decide on the mathematical tools and formulas required. In our example, understanding what percentage 1.6 is of 6.4 involves knowing how to calculate percentages through fractions.

After setting up your equation correctly, perform each mathematical operation carefully. Here, calculating \[ \frac{1.6}{6.4} \] and then multiplying by 100 is key. Finally, always double-check your work. Is each step logical? Does your answer make sense in the context of the problem? Always remember, practice is essential for improving your math problem-solving skills. The more problems you solve, the more intuitive and efficient your approach will become.