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Chapter 5: Problem 15

Write each number as a decimal. $$ \frac{18}{40} $$

Short Answer

Expert verified
The fraction \( \frac{18}{40} \) as a decimal is 0.45.

Step by step solution

01

Understand the Fraction

The given fraction is \( \frac{18}{40} \). We need to convert this fraction into a decimal format, which essentially means dividing 18 by 40.
02

Simplify the Fraction

First, check if the fraction can be simplified. The GCD (Greatest Common Divisor) of 18 and 40 is 2. So, divide both the numerator and denominator by 2: \( \frac{18 \div 2}{40 \div 2} = \frac{9}{20} \).
03

Perform Division to Convert to Decimal

Now, perform the division of 9 by 20 to convert the simplified fraction into a decimal. Divide 9 by 20, which results in 0.45.

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Key Concepts

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

Simplifying Fractions
Simplifying fractions is the process of reducing a fraction to its simplest form. This is done by dividing the numerator and the denominator by their greatest common divisor (GCD). When fractions are simplified, it makes them easier to work with and compare.
  • First, identify the fraction you are working with. In our example, it is \( \frac{18}{40} \).
  • Next, find the GCD of the numerator and the denominator. This is the largest number that divides both numbers evenly.
  • Once you have the GCD, divide both the numerator and the denominator by it. For \( \frac{18}{40} \), the GCD is 2, so you divide both by 2 to get \( \frac{9}{20} \).
Simplifying makes the fraction easier to handle and is often an important first step before performing other operations.
Greatest Common Divisor
The greatest common divisor (GCD) is a crucial concept in simplifying fractions. It is the largest number that can evenly divide both the numerator and the denominator of a fraction without leaving a remainder.
  • To find the GCD, list the factors of both numbers.
  • Identify the greatest factor that appears in both lists.
  • This number is your GCD, and it is used to simplify the fraction by dividing both the numerator and the denominator.
Finding the GCD is an essential skill that aids in simplifying and comparing fractions effectively. For the numbers 18 and 40, the common divisors are 1 and 2, with 2 being the greatest, hence the GCD.
Division
Division is the mathematical operation used to convert a fraction to its decimal form. By dividing the numerator by the denominator, you can express the fraction as a decimal.
  • First, ensure your fraction is simplified. Using our example, from \( \frac{18}{40} \) to \( \frac{9}{20} \).
  • Perform the division: divide the numerator by the denominator.
  • In this case, divide 9 by 20. Long division or a calculator can be used to find that \( \frac{9}{20} = 0.45 \).
Division is fundamental in mathematics, enabling you to switch between fractions and decimals seamlessly. This conversion is useful in many areas, including finance and science, where decimal notation is often preferred for accuracy and ease of use.

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