Problem 16 - Calculate With Confidence

Question

What percentage of 6.4 is 1.6? _________________

Step-by-Step Solution

Answer

1.6 is 25% of 6.4.

Step 1: Understand the Problem

We are asked to find out what percentage 1.6 is of 6.4. This involves determining what fraction 1.6 is of 6.4 and then converting that fraction into a percentage.

Step 2: Write the Fraction

To find what fraction 1.6 is of 6.4, divide 1.6 by 6.4: \[ \text{Fraction} = \frac{1.6}{6.4} \]

Step 3: Simplify the Fraction

Simplify the fraction \( \frac{1.6}{6.4} \) by dividing both the numerator and the denominator by 1.6:\[ \frac{1.6 \div 1.6}{6.4 \div 1.6} = \frac{1}{4} \]

Step 4: Convert Fraction to Percentage

To convert the fraction \(\frac{1}{4}\) into a percentage, multiply it by 100:\[ \text{Percentage} = \frac{1}{4} \times 100 = 25\% \]

Step 5: Verify the Calculation

Check if 25% of 6.4 equals 1.6 to ensure the calculation is correct:\[ 0.25 \times 6.4 = 1.6 \]The calculation is correct.

Key Concepts

Fraction Simplification

Simplifying a fraction is an essential step in many mathematical calculations. It means reducing the fraction to its lowest terms, where the numerator and the denominator have no common factors other than 1.

In our problem, we initially have the fraction \( \frac{1.6}{6.4} \). To simplify, we divide both the numerator (1.6) and the denominator (6.4) by their greatest common divisor (GCD). In this case, the GCD is 1.6.

• When you divide the numerator 1.6 by 1.6, you get 1.
• Similarly, divide the denominator 6.4 by 1.6 to get 4.

Thus, the fraction simplifies to \( \frac{1}{4} \). Simplifying fractions helps in making future calculations easier and more intuitive.

Convert Fraction to Percentage

After simplifying a fraction, the next step is to convert it into a percentage. Understanding percentages is vital, as they are widely used in everyday life to express proportions and comparisons.

To convert a simplified fraction like \( \frac{1}{4} \) to a percentage, you need to multiply it by 100. This is because "per cent" means "per hundred," and converting to percentage equals expressing the fraction as parts out of 100.

• The calculation is \( \frac{1}{4} \times 100 = 25 \% \).

This tells us that \( \frac{1}{4} \) represents 25% of a quantity, meaning if you have a whole piece divided into four equal parts, one part represents 25% of the whole.

Verification of Calculation

Verification is a vital part of solving mathematical problems—it enables you to confirm the accuracy of your results. After calculating that \( 1.6 \) is 25% of \( 6.4 \), it's wise to double-check your work.

Verification involves re-running the calculation in reverse or testing the original figures. In this case, you want to check if taking 25% of 6.4 gives you back the value of 1.6.

• Calculate \( 0.25 \times 6.4 \), which should equate to \( 1.6 \).

Since the multiplication \( 0.25 \times 6.4 \) indeed equals \( 1.6 \), the initial percentage calculation is confirmed correct. This shows the reliability of your process and helps to build confidence in your math skills.