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Chapter 1: Problem 127

Perform these computations. $$-\frac{1}{2}-19$$

Short Answer

Expert verified
-19.5

Step by step solution

01

Understand the Problem

The problem requires subtracting 19 from negative one-half.
02

Convert to Decimal Form

Convert \(-\frac{1}{2}\) to its decimal form. \(-\frac{1}{2}\) is equal to \(-0.5\).
03

Perform the Subtraction

Subtract 19 from -0.5. This can be written as: \(-0.5-19\).
04

Calculate the Answer

Solve \(-0.5-19 \: -0.5 - 19 = -19.5\).

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Key Concepts

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

Decimal Conversion
Decimal conversion is the process of changing a fraction or another type of number into a decimal. In our problem, we converted \(-\frac{1}{2}\) into its decimal form. The fraction \(-\frac{1}{2}\) can be easily converted by dividing the numerator by the denominator. Here, \(-1 梅 2 = -0.5\). Simple steps for decimal conversion include:
  • Identify the numerator and the denominator.
  • Perform the division operation.
  • Assign the negative sign if the original fraction is negative.
Understanding this step is crucial because it simplifies further calculations, like subtraction in our example.
Negative Numbers
Negative numbers are numbers less than zero, often found describing loss, decrease, or below-standard values. They are represented with a minus sign (鈭�).
In the computation \(-0.5 - 19\), both \(-0.5\) and \(-19\) were negative. Calculating with negative numbers follows specific rules:
  • When both numbers are negative, subtract normally then add a negative sign to the result.
  • When subtracting a number from a negative number, like in our example, perform the regular subtraction then apply the negative sign.
For example, in \(-0.5 - 19 = -19.5\), we added the magnitudes (0.5 and 19) and retained the negative sign, giving us the final result: \(-19.5\).
Subtraction
Subtraction is one of the basic arithmetic operations where we find the difference between numbers. For negative numbers, subtraction involves understanding the direction on the number line.
In the equation \(-0.5 - 19\), you start from \(-0.5\) and move 19 units further left on the number line. Essential steps include:
  • Ensure numbers are in the same format (both decimals or both fractions).
  • Understand the signs (positive or negative) involved.
  • Perform the subtraction operation properly, taking care of signs.
This operation can create deeper negative values, as displayed in the result \(-19.5\), derived from starting at \(-0.5\) and subtracting 19.

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Most popular questions from this chapter

Simplify. $$ -\frac{1}{2} m\left(-\frac{1}{2} m\right)-\frac{1}{2} m-\frac{1}{2} m $$

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