Problem 49 - Prealgebra and Introductory Algebra

Question

Find the opposite of the number. $$-88$$

Step-by-Step Solution

Answer

The opposite of -88 is 88.

Step 1: Identify the Number

The number given in the exercise is -88.

Step 2: Find the Opposite

The opposite of -88 is determined by changing the sign. If the original number is negative, the opposite will be positive.

Key Concepts

Negative Numbers

In math, negative numbers are numbers that are less than zero. They are found to the left of zero on the number line. Negative numbers are represented with a minus sign (−) in front of them. For example, in the exercise we have the number -88. When you think of negative numbers, visualize debts or temperatures below freezing. They describe a decrease, such as losing 5 points in a game or an elevator going down 3 floors. Some important points about negative numbers:

• They are used for calculations like credit balances or declines.
• Combining a negative number with another negative leads to addition (i.e. -88 and -12 results in -100).
• Multiply or divide two negative numbers and you end up with a positive result.

Negative numbers play a crucial role in arithmetic and everyday problem-solving scenarios.

Positive Numbers

Positive numbers are numbers greater than zero. These numbers can be found to the right of zero on the number line. Positive numbers are represented without any sign or sometimes with a plus sign (+) in front of them. For example, +88 or simply 88. In daily life, positive numbers appear in situations like gains in finance, counting items, or measuring distances above sea level. They signify growth or increase. Here are some key features of positive numbers:

• They are naturally used in addition and subtraction tasks.
• Adding positive numbers results in a sum that is also positive.
• Multiplying two positives gives another positive result.

Understanding positive numbers allows us to make sense of many mathematical and real-world concepts.

Integer Operations

Integer operations involve calculations using whole numbers, both positive and negative, including zero. These operations include addition, subtraction, multiplication, and division. Integers are represented as whole numbers and form a complete number set without fractions or decimals. To effectively carry out integer operations:

• Adding two positive integers yields a positive sum (e.g., 5 + 8 = 13).
• Adding two negative integers results in a negative sum (e.g., -3 + (-7) = -10).
• When a positive number and a negative number are combined, subtract the smaller from the larger and keep the sign of the larger number (e.g., 9 + (-4) = 5).
• Multiplication or division of two integers with like signs (both positive or both negative) results in a positive product or quotient, while differing signs yield negative outcomes.

Integer operations create a foundation for many mathematical concepts and are essential skills in everyday analytical tasks.