Question

Change each of the following percentages to a ratio, and reduce to lowest terms. \(16 \%\)

Short answer

The ratio is 4:25.

Step-by-step solution

Understand the Percentage

A percentage is a way of expressing a number as a fraction of 100. The percentage given here is 16%.

Convert Percentage to Fraction

Since 16% means 16 out of every 100, we convert this to a fraction as \( \frac{16}{100} \).

Simplify the Fraction

Find the greatest common divisor (GCD) of 16 and 100, which is 4. Then divide both the numerator and the denominator by 4. \[ \frac{16 \div 4}{100 \div 4} = \frac{4}{25} \]

Write the Fraction as a Ratio

A ratio compares two quantities. Write the simplified fraction as a ratio: 4:25.

Key concepts

Simplifying Fractions

Simplifying fractions is a key mathematical skill that allows us to reduce fractions to their simplest form, making them easier to work with. When you simplify a fraction, you find a smaller equivalent fraction that retains the same value.
Start by determining the greatest common divisor (GCD) of both the numerator and the denominator. The GCD is the largest number that can evenly divide both numbers. For the fraction \( \frac{16}{100} \), the GCD is 4.
Next, divide both the numerator and the denominator by the GCD.

• Numerator: \( 16 \div 4 = 4 \)
• Denominator: \( 100 \div 4 = 25 \)

So, \( \frac{16}{100} \) simplifies to \( \frac{4}{25} \). Simplifying fractions makes calculations easier and keeps numbers manageable.

Understanding Percentages

Percentages are a way of expressing numbers as parts per hundred. This means any percentage expresses a proportion relative to a total of 100.
For example, when you see 16%, it represents 16 parts out of 100. Understanding percentages helps in making sense of proportions and scaling.

• Convert percentages to fractions by placing the percentage number over 100. So, 16% becomes \( \frac{16}{100} \).
• Recognize that converting percentages to fractions makes it easier to perform many mathematical operations, such as simplifying fractions or comparing ratios.

Learning to convert and interpret percentages is useful in everyday contexts, like calculating discounts or understanding statistics.

Mathematical Ratios

Ratios are a fundamental concept used to compare quantities. A ratio tells you how much of one thing there is compared to another.
To form a ratio from a fraction, consider each part of the fraction as a separate quantity. For the fraction \( \frac{4}{25} \), the ratio becomes 4:25. This means for every 4 units of one quantity, there are 25 units of another.

• Ratios provide a simple way to communicate relationships between numbers.
• They are useful for solving problems in fields ranging from culinary recipes to engineering and business analytics.

Understanding how to express a fractional quantity as a ratio simplifies interpreting part-to-whole and part-to-part comparisons, making ratios a versatile tool in both academia and real-world applications.