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Chapter 3: Problem 80

Find each quotient. $$ \frac{5-7}{-4-2} $$

Short Answer

Expert verified
The quotient is \( \frac{1}{3} \).

Step by step solution

01

- Simplify the Numerator

First, subtract the numbers in the numerator: \(5 - 7\). This gives \(-2\).
02

- Simplify the Denominator

Next, subtract the numbers in the denominator: \(-4 - 2\). This gives \(-6\).
03

- Divide the Simplified Numerator by the Simplified Denominator

Finally, divide the simplified numerator \(-2\) by the simplified denominator \(-6\). This gives \( \frac{-2}{-6} = \frac{1}{3} \).

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Key Concepts

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

Numerator Simplification
To start simplifying a fraction, you should focus on the numerator first. The numerator is the top part of the fraction. In this problem, the numerator is expressed as \(5 - 7\).

Begin by performing the subtraction inside the numerator. For \(5 - 7\), you subtract 7 from 5, which equals \(-2\).
This means that the simplified numerator of our fraction becomes \(-2\). Breaking down calculations one step at a time helps you avoid confusion and ensures accuracy.

Always double-check your work to prevent mistakes.
Denominator Simplification
Next, turn your attention to the denominator, which is the bottom part of the fraction. In this case, it is written as \(-4 - 2\).

Just as we did with the numerator, complete the subtraction inside the denominator. Calculating \(-4 - 2\) involves subtracting 2 from \-4\, which yields \(-6\).

Hence, our simplified denominator is \(-6\). Simplifying both the numerator and the denominator separately ensures clarity and helps in dividing them correctly later.
Make sure to handle negative signs carefully to avoid errors.
Fraction Simplification
Once we have simplified both the numerator and the denominator, it's time to divide them to simplify the fraction.

We have the simplified fraction \(\frac{-2}{-6} \). When dividing two negative numbers, the negatives cancel each other out. Thus, \(\frac{-2}{-6} \) simplifies to \(\frac{1}{3} \).

To summarize the steps:
  • Simplify the numerator: \(5 - 7 = -2\)
  • Simplify the denominator: \(-4 - 2 = -6\)
  • Divide the simplified numerator by the simplified denominator: \(\frac{-2}{-6} = \frac{1}{3}\)

Simplifying fractions entails reducing both the numerator and the denominator to their simplest forms. This often makes the fraction easier to understand and work with in further calculations.

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Most popular questions from this chapter

Suppose a factory can have no more than 200 workers on a shift, but must have at least 100 and must mamufacture at least 3000 units at minimum cost. The managers need to know how many workers should be on a shift in onder to produce the required units at minimal cost. Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for such problems. Let \(x\) represent the number of workers and y represent the mumber of units manufactured. Work Exercises \(47-52\) in order. Write three inequalities expressing the conditions given in the problem.

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