Problem 73 - Prealgebra

Question

Write each fraction or mixed number as a decimal. \(\frac{3}{5}\)

Step-by-Step Solution

Answer

The fraction \( \frac{3}{5} \) as a decimal is 0.6.

Step 1: Understand the Fraction

The given fraction is \( \frac{3}{5} \). This fraction represents the division of 3 by 5. We need to convert this fraction into a decimal by performing this division.

Step 2: Perform the Division

To convert \( \frac{3}{5} \) to a decimal, divide 3 by 5. Set up the division: 3 divided by 5 can be written as 3.0 divided by 5. Since 5 does not go into 3, you consider 30. 5 goes into 30 six times. Thus, \( 3 \div 5 = 0.6 \).

Step 3: Verify the Decimal

Multiplying the decimal result 0.6 by the denominator 5 should yield the numerator 3: \( 0.6 \times 5 = 3 \). This confirms the conversion is correct.

Key Concepts

Fraction to Decimal Conversion

Converting a fraction into a decimal number is a common task in mathematics that involves division. The essence of this process is understanding that fractions like \( \frac{3}{5} \) represent a division. Here, \( 3 \div 5 \) translates directly into our division setup. In this context, the numerator (3) is divided by the denominator (5). If you're ever uncertain, remember that fractions are simply another way of expressing division, and converting them to decimals is about executing that division.
Consider fractions like \( \frac{1}{2} \). When you perform the division \( 1 \div 2 \), the result is 0.5. This basic operation extends to all kinds of fractions. Hence, for \( \frac{3}{5} \), dividing gives 0.6, indicating that fraction as a decimal.

Division

Division is the operation central to converting fractions into decimals. When dividing numbers like 3 by 5, you transform a fraction into a decimal. To do this, you set up a division problem: think of visualizing how many times the denominator can "fit" into the numerator.
For instance, with \( 3 \div 5 \), we begin by considering 3.0 to allow for decimal placement. Since 5 can't go into 3 without exceeding it, you visualize 30 (as in the expanded form 3.0). 5 goes into 30 six times. Thus, we arrive at the decimal 0.6. Remember: repeating this process for other fractions reinforces this understanding by building familiarity.

Fractions

Fractions are numerical expressions representing a part of a whole. Made up of two parts: the numerator and the denominator, they illustrate division. Fractions such as \( \frac{3}{5} \) can initially feel abstract, but they're everywhere—a slice of pizza represents a fraction of the whole pizza!
Key tips for working with fractions include:

• Identifying the numerator (the top number), which signifies parts of the whole specified by the denominator (the bottom number).
• Understanding that any fraction where the numerator is smaller than the denominator is a proper fraction—its decimal form will be less than 1.
• Fractions like \( \frac{5}{5} \) equal exactly 1, representing a complete whole.

Learning to visualize and perform operations with fractions is essential for an accurate understanding of their decimal equivalents.

Mixed Numbers

Mixed numbers combine whole numbers with fractions, such as 1\( \frac{2}{3} \). When converting mixed numbers to decimals:

• First, convert the fractional part into a decimal—in our \( \frac{2}{3} \) example, 2 divided by 3 leads to an approximate decimal of 0.666.. .
• Add this decimal to the whole number part, resulting in 1 + 0.666.. = 1.666... .

Practicing with mixed numbers helps reinforce the concept that decimals and fractions are closely related. Understand that becoming comfortable with fractions will boost comprehension and proficiency with mixed numbers!
They can appear troublesome, but breaking them into parts where each is simplified separately, then combined like a puzzle, can make the process seamless.