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Chapter 3: Problem 78

Find each quotient. $$ \frac{5-(-7)}{-4-(-1)} $$

Short Answer

Expert verified
The quotient is -4.

Step by step solution

01

Simplify the Numerator

The numerator of the expression is \(5 - (-7)\). Simplify this by changing the double negative to a positive: \(5 + 7 = 12\).
02

Simplify the Denominator

The denominator of the expression is \(-4 - (-1)\). Simplify this by changing the double negative to a positive: \(-4 + 1 = -3\).
03

Divide the Numerator by the Denominator

Now, divide the simplified numerator by the simplified denominator: \(\frac{12}{-3} = -4\).

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Key Concepts

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

Simplifying Expressions
Simplifying expressions is an essential skill in mathematics that makes equations easier to handle and understand. In the given exercise, the expression is \(\frac{5-(-7)}{-4-(-1)}\). This expression looks complex at first, but following a methodical approach helps simplify it step-by-step. Start by simplifying the numerator and the denominator independently. This step-by-step simplification clarifies the problem and leads to the final answer more systematically. Remember, simplifying expressions can save time and reduce the chance of making errors. A simplified expression is simpler to interpret and easier to work with in further calculations.
Numerator and Denominator
When dealing with fractions, it is crucial to understand the roles of the numerator and the denominator. The numerator is the top part of the fraction, representing the number of parts we have. In contrast, the denominator is the bottom part of the fraction, representing the total number of equal parts. In the expression \(\frac{5-(-7)}{-4-(-1)}\), the numerator is \(5-(-7)\), and the denominator is \(-4-(-1)\). Simplifying these individually makes the whole process easier. For the numerator, \(5-(-7)\) turns into \(5 + 7 = 12\). For the denominator, \(-4-(-1)\) turns into \(-4 + 1 = -3\). So, the fraction now becomes \(\frac{12}{-3}\).
Double Negative
A double negative occurs when two negative signs appear close together in an expression. In mathematics, a double negative turns into a positive. This rule simplifies expressions and prevents confusion. For example, in the given exercise, the expressions \(5-(-7)\) and \(-4-(-1)\) contain double negatives. The double negative in \(5-(-7)\) turns into \(5+7\), and the double negative in \(-4-(-1)\) turns into \(-4+1\). Understanding the double negative rule is essential and makes simplifying expressions straightforward.

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Most popular questions from this chapter

Solve each problem. As a fundraiser, a club is selling posters. The printer charges a \(\$ 25\) set- up fee, plus \(\$ 0.75\) for each poster. The cost \(y\) in dollars to print \(x\) posters is given by $$ y=0.75 x+25 $$ (a) What is the cost \(y\) in dollars to print 50 posters? To print 100 posters? (b) Find the number of posters \(x\) if the printer billed the club for costs of \(\$ 175 .\) (c) Write the information from parts (a) and (b) as three ordered pairs. (d) Use the data from part (c) to graph the equation.

What is the slope of a line whose graph is parallel to the graph of \(-5 x+y=-3 ?\) Perpendicular to the graph of \(-5 x+y=-3 ?\)

Graph each linear equation. \(x-1=-4\)

Solve each equation. $$ -5+t=3 $$

Do \((3,4)\) and \((4,3)\) correspond to the same point in the plane? Explain.
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