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Chapter 5: Problem 411

In the following exercises, write each ratio as a fraction. $$0.56 \text { to } 2.8$$

Short Answer

Expert verified
The ratio 0.56 to 2.8 as a fraction is \(\frac{1}{5}\).

Step by step solution

01

Understand the Ratio

A ratio represents a relationship between two quantities. In this problem, the ratio is given as 0.56 to 2.8.
02

Write the Ratio as a Fraction

To write the ratio as a fraction, place the first number (0.56) as the numerator and the second number (2.8) as the denominator: \(\frac{0.56}{2.8}\)
03

Simplify the Fraction

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, divide both by 0.56:\[\frac{0.56 \div 0.56}{2.8 \div 0.56} = \frac{1}{5}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

writing ratios
A ratio is a way to compare two quantities. It tells us how much of one thing there is compared to another. When you are asked to write a ratio as a fraction, you simply place one quantity over the other in the format of a fraction. For example, the ratio 0.56 to 2.8 can be written as \( \frac{0.56}{2.8} \). This format makes it easier to manipulate and simplify ratios.
simplifying fractions
After writing the ratio as a fraction, the next important step is simplifying it. Simplifying fractions makes them easier to understand and use. To simplify a fraction, you need to divide both the numerator (the top number) and the denominator (the bottom number) by their common factors. For the fraction \( \frac{0.56}{2.8} \), you notice that both 0.56 and 2.8 can be divided by the same number within a range (e.g., 0.56 itself). In this case, dividing both by 0.56 results in the simplified fraction: \[ \frac{0.56 \div 0.56}{2.8 \div 0.56} = \frac{1}{5} \]. Simplifying fractions makes the ratio more understandable and practical.
greatest common divisor
The Greatest Common Divisor (GCD) is the largest number that divides both the numerator and the denominator without leaving a remainder. Finding the GCD is essential for simplifying fractions. For the problem given, the GCD of 0.56 and 2.8 is 0.56. This is because 0.56 is the largest number that can divide both 0.56 and 2.8 evenly. By dividing both the numerator and the denominator by the GCD, you achieve the simplest form of the fraction. For instance, dividing \( \frac{0.56}{2.8} \) by 0.56 gives \[ \frac{0.56 \div 0.56}{2.8 \div 0.56} = \frac{1}{5} \]. Understanding the GCD helps to simplify and work with ratios more effectively.

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