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Chapter 1: Problem 19

Evaluate each of the following: a. \(15-(-8)=\) b. \(-8+(-22)=\) c. \(4 \times(-2)+6=\)

Short Answer

Expert verified
a. 23, b. -30, c. -2

Step by step solution

01

Solving 15-(-8)

Start by recognizing that subtracting a negative number is the same as adding a positive number. So, 15 - (-8) becomes 15 + 8. Then add the numbers together: 15 + 8 = 23.
02

Solving -8+(-22)

When adding two negative numbers, simply add their absolute values and keep the negative sign. So, add 8 and 22 to get 30. Because both numbers are negative, the result is negative: -8 + (-22) = -30.
03

Solving 4 \times (-2) + 6

First, solve the multiplication part. Multiply 4 by -2 to get -8. So the equation becomes: -8 + 6. Next, add -8 and 6. Since you are adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value, and take the sign of the larger absolute value. 6 - 8 = -2.

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Key Concepts

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

subtraction
Subtraction is one of the four basic arithmetic operations. It represents taking something away from a group or number of things. In our exercise, one specific case involves subtracting a negative number. This can be tricky.
When you subtract a negative number, it's the same as adding its positive counterpart.
For example:
  • 15 - (-8) becomes 15 + 8
  • This is because subtracting a negative is like adding
  • So, 15 + 8 = 23
This step is crucial to understand, as it can often appear in various mathematical problems.
addition
Addition is another fundamental arithmetic operation where quantities are combined. When working with numbers, it's important to consider their signs.
For instance, adding two negative numbers requires adding their absolute values and then applying the negative sign to the result.
Here is an example:
  • -8 + (-22) means you should add 8 and 22 first, which gives you 30
  • Since both numbers are negative, the result is also negative: -30
Practicing these types of problems helps in understanding the interaction between different signed numbers.
multiplication
Multiplication, another key arithmetic operation, involves repeated addition of a number. In the given exercise, we face multiplication with a negative number, which can be confusing at first.
The rule is:
  • Multiplying a positive number by a negative number gives a negative product
  • For instance, 4 times -2 equals -8
Understanding this helps solve complex expressions that involve multiple operations.
negative numbers
Negative numbers are numbers less than zero. They often represent values below a defined level, such as temperatures below freezing.
Handling negative numbers in arithmetic requires understanding how they interact under different operations. For instance:
  • Subtracting a negative number turns the operation into an addition
  • Adding two negative numbers results in a more negative value
  • Multiplying a negative with a positive gives a negative result
Grasping these basic interactions allows you to handle more complex mathematical expressions with confidence.

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Most popular questions from this chapter

On the first chemistry test, 12 students got As, 18 students got Bs, and 20 students got Cs. (1.4) a. What is the percentage of students who received Bs? Express your answer to the ones place. b. What is the percentage of students who received Cs? Express your answer to the ones place.

Write each of the following in scientific notation: \((1.5)\) a. 1050000 b. \(0.000038\) c. \(0.09006\) d. 2700000

Identify each of the following as an observation (O), a hypothesis (H), an experiment (E), or a conclusion (C): a. One hour after drinking a glass of regular milk, Jim experienced stomach cramps. b. Jim thinks he may be lactose intolerant. c. Jim drinks a glass of lactose-free milk and does not have any stomach cramps. d. Jim drinks a glass of regular milk to which he has added lactase, an enzyme that breaks down lactose, and has no stomach cramps.

Which of the following will help you develop a successful study plan? (1.3) a. studying all night before the exam b. forming a study group and discussing the problems together c. working problems in a notebook for easy reference d. copying the homework answers from a friend

Identify each of the following activities in the scientific method as an observation (O), a hypothesis (H), an experiment (E), or a conclusion (C): a. Formulate a possible explanation for your experimental results. b. Make notes about nature. c. Design an experimental plan that will give new information about a problem. d. State a generalized summary of your experimental results.
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