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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

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

For each of the following, indicate if the answer has a positive or negative sign: \((1.4)\) a. A negative number is divided by a positive number. b. Two negative numbers are added.

a. At a local hospital, 35 babies were born. If 22 were boys, what percentage of the newborns were boys? Express your answer to the ones place. b. An alloy contains \(67 \mathrm{~g}\) of pure gold and \(35 \mathrm{~g}\) of pure zinc. What is the percentage of zinc in the alloy? Express your answer to the ones place. c. A collection of coins contains 15 pennies, 14 dimes, and 6 quarters. What is the percentage of pennies in the collection? Express your answer to the ones place.

According to Sherlock Holmes, "One must follow the rules of scientific inquiry, gathering, observing, and testing data, then formulating, modifying, and rejecting hypotheses, until only one remains." Did Holmes use the scientific method? Why or why not? (1.2)

Classify each of the following statements as an observation (O) or a hypothesis \((\mathrm{H}):(1.2)\) a. You are likely to get food poisoning from expired food products. b. Adding \(5 \mathrm{~g}\) of salt to ice decreases the melting temperate to \(-1{ }^{\circ} \mathrm{C}\). c. Adding salt to ice can decrease the melting temperature.
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