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Chapter 2: Problem 96

In Exercises 89-96, evaluate the expression. $$ 5(-7) $$

Short Answer

Expert verified
-35

Step by step solution

01

Multiplication of Numbers

To evaluate the expression, simply multiply 5 by -7. According to the rules of multiplication, when a positive number is multiplied by a negative number, the result is a negative number.
02

Calculate the Multiplication

Hence, \(5 \times -7\) would equal to \(-35\).

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are numbers with a value less than zero. They are used to represent values below zero, such as temperatures below freezing or debts. Negative numbers are usually written with a minus sign in front, like -2 or -7.

In terms of their position on the number line, negative numbers are always to the left of zero. This positioning is vital when performing operations involving negatives, as it influences the direction in which you move on the number line. For instance, moving left often implies subtracting or decreasing, while moving right points to adding or increasing.
  • Negative numbers can be added, subtracted, multiplied, and divided like positive numbers, but with specific rules to follow.
  • When operating with negative numbers, keeping track of the signs is crucial to getting the correct result.
Multiplying Integers
Multiplying integers involves straightforward rules. Whether you're handling positive integers or negative ones, the multiplication must respect specific sign rules.

Here's the basic guideline:
  • Multiplying two positive integers results in a positive integer. For example, \(3 \times 4 = 12\).
  • Multiplying two negative integers also results in a positive integer. For instance, \((-3) \times (-4) = 12\). The negative signs "cancel out" each other.
  • Multiplying a positive integer by a negative integer gives a negative result. As an example, \(5 \times (-7) = -35\). The mixed nature of the signs leads to a negative product.
When you multiply, remember to focus on the numbers' values first and then apply the sign rule last to determine the result's sign.
Integer Operations Simplified
Integer operations cover a broad range of arithmetic actions with whole numbers, positive, negative, or zero. They constitute the foundational math skills necessary for more advanced problems. Understanding these operations can help simplify complex equations and solve real-world problems efficiently.

Key Points to Consider:
  • Addition: When adding integers of the same sign, add the absolute values and keep the common sign. For integers of different signs, subtract the smaller absolute value from the larger and apply the sign of the integer with the larger absolute value.
  • Subtraction: To subtract an integer, add its opposite. Thus, \(a - b\) can be rewritten as \(a + (-b)\).
  • Multiplication and Division: These processes involve the rules of combining signs and performing the operations as usual.
Combining these operations accurately allows you to handle any integer-based arithmetic problem with confidence.

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Most popular questions from this chapter

In Exercises \(1-10\), determine whether each value of \(x\) is a solution of the equation. \(3 x-3=0\) (a) \(x=4\) (b) \(x=1\)

In Exercises \(1-10\), determine whether each value of \(x\) is a solution of the equation. \(5 x-1=3(x+5)\) (a) \(x=8\) (b) \(x=-2\)

In Exercises \(63-68\), simplify the expression. $$ \left(-3 y^{3}\right) y^{2} $$

In Exercises \(55-58\), write an algebraic equation. Do not solve the equation. A high school earned \(\$ 986\) in revenue for a play. Tickets for the play cost \(\$ 10\) for adults and \(\$ 6\) for students. The number of students attending the play was \(\frac{3}{4}\) the number of adults attending the play. How many adults and student attended the play?

In Exercises 63-68, translate the verbal phrase into an algebraic expression. Simplify the expression. $$ \text { The sum of } 4 \text { and } x \text { added to the sum of } x \text { and }-8 $$
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