Problem 6 - Prealgebra

Question

Complete the following tables by converting each fraction to a decimal. Fraction \(\frac{1}{5} \quad \frac{2}{5} \quad \frac{3}{5} \quad \frac{4}{5} \quad \frac{5}{5}\) Decimal

Step-by-Step Solution

Answer

The decimals are 0.2, 0.4, 0.6, 0.8, and 1.

Step 1: Convert Fraction \(\frac{1}{5}\) to Decimal

To convert \(\frac{1}{5}\) to a decimal, divide the numerator 1 by the denominator 5. Performing the division, 1 divided by 5 gives 0.2. Therefore, \(\frac{1}{5} = 0.2\).

Step 2: Convert Fraction \(\frac{2}{5}\) to Decimal

Divide the numerator 2 by the denominator 5. Performing the division, 2 divided by 5 gives 0.4. Thus, \(\frac{2}{5} = 0.4\).

Step 3: Convert Fraction \(\frac{3}{5}\) to Decimal

Divide the numerator 3 by the denominator 5. Performing the division, we get 3 divided by 5 equals 0.6. Therefore, \(\frac{3}{5} = 0.6\).

Step 4: Convert Fraction \(\frac{4}{5}\) to Decimal

Divide the numerator 4 by the denominator 5. Performing the division gives 4 divided by 5 equals 0.8. Thus, \(\frac{4}{5} = 0.8\).

Step 5: Convert Fraction \(\frac{5}{5}\) to Decimal

Since the numerator and the denominator are the same, \(\frac{5}{5} = 1\) because 5 divided by 5 equals 1.

Key Concepts

Understanding Prealgebra Concepts

Prealgebra is an important mathematical foundation that helps in understanding how numbers and operations work. It sets the stage for tackling more advanced math topics like algebra. A crucial aspect of prealgebra is the ability to work with fractions, decimals, and whole numbers, making it easier to switch between these forms when solving problems.

• Fractions: Represent parts of a whole, with a numerator (top number) and a denominator (bottom number).
• Decimals: Another way to express fractions, showing the same part of a whole in a different form.
• Whole Numbers: Numbers without fractions or decimals.

By understanding these basic concepts, students can better explore how different numbers relate to each other and gain confidence in problem-solving.

Numerator and Denominator Explained

In the world of fractions, understanding the roles of the numerator and the denominator is key. A fraction is comprised of these two critical parts that define its value.
The numerator is the top number of a fraction. It tells you how many parts of a whole you have. For instance, in the fraction \( \frac{1}{5} \), the numerator is 1, which means you have 1 part of the whole.
The denominator is the bottom number. It indicates the total number of equal parts the whole is divided into. In \( \frac{1}{5} \), the denominator is 5, meaning the whole is divided into 5 equal parts.

To convert a fraction into a decimal, think of the fraction as a division problem where you divide the numerator by the denominator. This transformation is often straightforward, requiring a simple division that translates a part-whole relationship into a decimal form.

The Division of Fractions to Decimals

Converting fractions to decimals is a fundamental skill in prealgebra. It involves dividing the numerator by the denominator. This process reveals how fractions can be expressed as decimal numbers.
To convert \( \frac{1}{5} \) into a decimal, you divide 1 by 5, which gives you 0.2. Each subsequent fraction, like \( \frac{2}{5} \), follows the same process — dividing 2 by 5 to get 0.4.

• This helps in understanding how fractions translate to decimals in real-world applications, such as in measurements or monetary calculations.
• Sometimes, the division might result in a recurring decimal, which repeats in a pattern. For example, \( \frac{1}{3} \) converts to a decimal as 0.333…, where 3 repeats indefinitely.
• When the numerator equals the denominator as in \( \frac{5}{5} \), it simplifies to a whole number, which is 1 in this case.

Understanding this process enriches your mathematical toolkit, allowing you to handle various numerical forms seamlessly.