Problem 2 - Fundamentals of Mathematics

Question

Write each expression in words. \(2+(-8)\)

Step-by-Step Solution

Answer

Two plus negative eight.

Step 1: Identify the Terms

The expression is \(2 + (-8)\). Here, 2 is a positive integer, and \(-8\) is a negative integer. We start by identifying these terms so we know which numbers and operations we are working with.

Step 2: Write the Addition Operation

The symbol \(+\) represents the addition operation. Therefore, when we write the expression in words, we have to include the phrase "plus" to denote this operation.

Step 3: Write the Numbers in Words

Translate the numbers into words. The number 2 is written as "two," and the number \(-8\) is written as "negative eight." Remember to use the word "negative" to signify the negative sign in front of the number 8.

Step 4: Combine the Words

Now, combine the translated numbers and the operation using the structure of the expression. The expression \(2 + (-8)\) is written in words as "two plus negative eight."

Key Concepts

Positive and Negative Integers

Understanding positive and negative integers is essential in mathematics. Integers are a set of numbers that include all positive numbers, negative numbers, and zero.

• Positive integers: These are numbers greater than zero, such as 1, 2, 3, etc.
• Negative integers: These are numbers less than zero, like -1, -2, -3, etc.

Positive integers are often used to represent gains or increments, while negative integers can indicate losses or decreases. Knowing these concepts help you understand numerical relationships better.
When dealing with expressions involving integers, it's crucial to pay attention to the sign in front of each number. A positive sign may not always be explicitly stated. In contrast, a negative sign needs to be explicitly written before the number. This ensures clarity, especially when translating numbers into other forms, such as words.

Addition Operation

The addition operation is one of the basic arithmetic operations. It involves combining two or more values to arrive at a sum. Understanding how this operation works with both positive and negative integers is crucial in math.

• The addition symbol is represented by a "+" sign.
• Adding two positive integers results in a larger positive integer.
• Adding a positive integer and a negative integer involves finding the numerical difference between the two, considering the signs.
• The result can be zero if the numbers have the same absolute value, or it can be positive or negative, depending on which has a greater absolute value.

In the expression \(2 + (-8)\), for example, the operation's outcome reflects both addition and subtraction principles due to the presence of a negative integer. Hence, understanding addition operations is critical for mathematical expressions and further computations.

Translating Numbers into Words

Translating numbers into words involves expressing numerical values using the corresponding vocabulary terms. This skill helps in describing and simplifying expressions or equations in written form.

• The number "2" is spelled out as "two".
• The negative number "-8" is translated into "negative eight".

Expressing operations in word form includes describing mathematical operations like addition. For example, the addition operation in the expression \(2 + (-8)\) becomes "plus" in words.
Combined, these elements help convey the mathematical expression effectively and clearly as "two plus negative eight."
Writing expressions in words assists in understanding complex mathematical ideas, providing clarity, and improving communicating the math to others who may not be familiar with numeric notation.