Problem 60 - Prealgebra

Question

Write each fraction or mixed number as a decimal. Use a bar to show a repeating decimal. $$-\frac{13}{20}$$

Step-by-Step Solution

Answer

The fraction \(-\frac{13}{20}\) as a decimal is \(-0.65\).

Step 1: Understanding the Fraction

The first step is to understand the given fraction and recognize that it is a division problem. Here, we have the fraction \(-\frac{13}{20}\), which means we need to divide \(-13\) by \(20\).

Step 2: Performing the Division

We perform the division \(-13 \div 20\). Since \(13\) is less than \(20\), we first convert \(13\) into \(130\) by considering 130 as the dividend. Now, \(130 \div 20 = 6\) with a remainder of \(10\).

Step 3: Finding the Decimal

Continue the division by writing \(10\) as \(100\) (since we are doing long division to form the decimal). Divide \(100 \div 20 = 5\). Now, the entire division gives us \(-0.65\).

Step 4: Writing Final Answer

Ensure there is no remainder (here, there is none) and write the final decimal answer. Since there is no repeating part in this decimal, we finish at this stage.

Key Concepts

Division Strategy

Understanding the division strategy is crucial when converting fractions to decimals. A fraction is essentially a representation of a division problem. In the case of the fraction \(-\frac{13}{20}\), it translates to dividing \(-13\) by \(20\).

To follow this strategy:

• Recognize that the numerator (the top number) is your dividend, which is \(-13\).
• The denominator (the bottom number) is your divisor, which is \(20\).
• You perform the division operation \(-13 \div 20\) to convert the fraction to a decimal.

This division strategy requires aligning the numbers correctly and, if necessary, adjusting values to make division practical as part of an efficient arithmetic process.

Long Division

Long division is a method used to divide larger numbers and to find decimals when converting fractions. It demands careful execution of a sequence of mathematical operations. Let's break it down:

In our example with \(-\frac{13}{20}\):

• You begin by recognizing that \(-13\) is less than \(20\). Therefore, you convert \(13\) to \(130\) by "borrowing" a decimal place, allowing division to take place.
• Next, \(130 \div 20 = 6\) results in a remainder of \(10\).
• To continue, convert \(10\) into \(100\), allowing for continuous division, and then \(100 \div 20 = 5\). This results in the decimal \(0.65\).

Long division challenges you to handle remainders correctly and continue the process until an exact decimal is reached, or you identify a repeating pattern.

Negative Fractions

Negative fractions can seem tricky but are quite similar to positive ones—except they carry a negative sign. Understanding this is vital for correct interpretation of your calculations.

• When dividing a negative fraction, the negative sign remains throughout the division process.
• Starting with \(-\frac{13}{20}\), perform the division as usual: ignore the negative sign initially during calculations.

Once you've completed the division (in this example, obtaining \(0.65\)), reapply the negative sign to your result.

The final result for our problem is \(-0.65\), indicating the decimal representation of the negative fraction. Remember, the placement of the negative sign determines the nature of your solution, signifying a value less than zero.