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Chapter 1: Problem 45

Evaluate each of the following a. \(6 \times(-9)\) b. \(+7+(-81)\) c. \(\frac{-120}{-40}\)

Short Answer

Expert verified
a. -54 b. -74 c. 3

Step by step solution

01

Step 1a: Multiplication of Positive and Negative Integers

To evaluate the expression \(6 \times (-9)\), multiply 6 by -9. Remember that a positive number multiplied by a negative number is negative.\[6 \times (-9) = -54\]
02

Step 1b: Addition of a Positive and a Negative Number

To evaluate \(+7 + (-81)\), add 7 and -81. Adding a positive and negative number is the same as subtracting the smaller absolute value from the larger absolute value.\[+7 + (-81) = 7 - 81 = -74\]
03

Step 1c: Division of Two Negative Numbers

To evaluate \(\frac{-120}{-40}\), divide -120 by -40. Dividing two negative numbers results in a positive number.\[\frac{-120}{-40} = 3\]

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Key Concepts

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

Multiplication of Integers
Multiplication of integers involves combining quantities repeatedly. When multiplying integers, it's important to consider their signs:
  • When you multiply two positive integers, the result is positive.
  • When you multiply two negative integers, the result is also positive.
  • When you multiply a positive integer by a negative integer, the result is negative.
  • When you multiply a negative integer by a positive integer, the result is negative.
For example, in the problem given: To evaluate the expression \(6 \times (-9)\), multiply 6 by -9. Recall that a positive number multiplied by a negative number is always negative.
\[6 \times (-9) = -54\]
Thus, the answer is -54.
Addition of Integers
Adding integers involves combining quantities. The critical aspect is managing the signs of the integers. When adding integers:
  • Adding two positive integers gives a positive result.
  • Adding two negative integers gives a negative result.
  • When adding a positive and a negative integer, subtract the smaller absolute value from the larger absolute value. The sign of the result matches that of the integer with the larger absolute value.
For example, in the exercise provided: To evaluate \( +7 + (-81)\), add 7 and -81. Because one number is positive and one is negative, subtract the absolute values. The larger absolute value's sign will be the result.
\[+7 + (-81) = 7 - 81 = -74\]
Hence, the answer is -74.
Division of Integers
Division of integers is the process of determining how many times one number is contained within another. Like with multiplication, the signs of the integers play a crucial role:
  • Dividing two positive integers results in a positive integer.
  • Dividing two negative integers also results in a positive integer.
  • Dividing a positive integer by a negative integer results in a negative integer.
  • Dividing a negative integer by a positive integer results in a negative integer.
For instance, in the problem: To evaluate \(\frac{-120}{-40}\text)\), divide -120 by -40. Since both numbers are negative, the result is positive.
\[\frac{-120}{-40} = 3\]
So, the answer is 3.

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