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Chapter 7: Problem 305

In the following exercises, write as the ratio of two integers. $$ 1.8 $$

Short Answer

Expert verified
\( \frac{9}{5} \)

Step by step solution

01

Understand the problem

You need to express the decimal number 1.8 as the ratio of two integers. This means converting it into a fraction where both the numerator and the denominator are integers.
02

Write the decimal as a fraction

First, represent 1.8 as a fraction. Since 1.8 means 1 point 8 tenths, you can write it as \( \frac{18}{10} \).
03

Simplify the fraction

Next, simplify \( \frac{18}{10} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 18 and 10 is 2. So divide both 18 and 10 by 2: \( \frac{18 梅 2}{10 梅 2} = \frac{9}{5} \).

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Key Concepts

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

Ratios
Ratios are a way to compare two quantities. They show the relative size of one number compared to another. In our exercise, the goal is to write the decimal number 1.8 as the ratio of two integers.
  • A ratio can be expressed using a colon, like this: 4:3
  • It can also be expressed as a fraction, like this: \(\frac{4}{3}\).
With ratios, it鈥檚 essential to ensure that they are in the simplest form, which is often achieved by simplifying the fractions they represent.
Fractions
Fractions represent parts of a whole. A fraction consists of a numerator (the top part) and a denominator (the bottom part). In our exercise, we converted the decimal 1.8 to a fraction to make it easier to understand and work with
  • Start with 1.8. This can be written as 18 over 10, or \(\frac{18}{10}\).
  • The numerator, 18, is the part of the whole we are interested in.
  • The denominator, 10, is the total parts that make up a whole.
Always ensure that your fractions are in the simplest form.
Simplifying Fractions
Simplifying fractions means making both the numerator and the denominator as small as possible while keeping the same value. This helps in making comparisons and calculations easier. In the exercise, we simplified \(\frac{18}{10}\) to make it more manageable.
  • Find the Greatest Common Divisor (GCD) of the numerator and denominator. For 18 and 10, the GCD is 2.
  • Divide both by the GCD: \(\frac{18 \/ 2}{10 \/ 2}\). This results in \(\frac{9}{5}\).
Simplified fractions are cleaner and often easier to work within problems.

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