Problem 3 - Fundamentals of Mathematics

Question

Write each expression in words. \(-7+5\)

Step-by-Step Solution

Answer

Negative seven plus five.

Step 1: Identify the Numbers and Symbols

In the expression \(-7 + 5\), identify the components. The numbers are \(-7\) and \(5\). The symbol between them is a plus sign, \(+\).

Step 2: Express the First Number in Words

\(-7\) is a negative number. In words, it is 'negative seven'.

Step 3: Express the Plus Sign in Words

The plus sign \(+\) is expressed as 'plus' in words.

Step 4: Express the Second Number in Words

The number \(5\) is expressed as 'five' in words.

Step 5: Combine All Components in Words

Combine all the parts in words to form the full expression: 'negative seven plus five'.

Key Concepts

Negative Numbers

Negative numbers can initially seem confusing, but they play an essential role in mathematics and our daily lives. They are numbers less than zero and are often used to represent a lack or some form of opposite. For example, temperatures below freezing are considered negative, or when discussing bank balances, a negative amount indicates owing money.
When written, negative numbers are defined by a minus sign in front of them. So, a negative three is written as \(-3\). Here are a few key points:

• Negative numbers are found on the left side of zero on a number line.
• When comparing two numbers, a negative number is always less than a positive number.
• Adding a negative number is the same as subtracting its positive counterpart. For example, adding \(-3\) is like subtracting 3.

Understanding negative numbers is crucial. They help us solve problems involving debts, temperatures, and even scientific calculations.

Addition

Addition is one of the foundational operations in mathematics. It combines two or more numbers to find a total or sum. Adding seems straightforward, but when negative numbers come into play, it requires some finesse.
Let's break down how addition works, especially involving negative numbers:

• If both numbers are positive, you simply add them as usual. For instance, \(3 + 5 = 8\).
• If one number is negative, you actually perform a subtraction. For example, \(3 + (-5)\) translates to \(3 - 5 = -2\).
• If both numbers are negative, you add the absolute values (ignoring the signs) and keep the negative sign. For example, \(-3 + (-5)\) becomes \(-(3 + 5) = -8\).

Understanding these rules helps you confidently work with negative numbers during addition. Always consider the number's sign and use the number line as a visual aid if needed.

Numerical Expression

Numerical expressions are mathematical phrases involving numbers and operational symbols like plus \(+,\) minus \(-\), multiplication \((\times),\) or division \(\div\). These expressions explain operations that need to be performed to reach a solution.
For example, in the expression \(-7 + 5\), the idea is to perform addition operation between \(-7\) and \(5\). This expression instructs that negative seven is added to five.

• It's important to follow order of operations, often remembered by PEMDAS/BODMAS, prioritizing Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication/Division, and Addition/Subtraction.
• When working with numerical expressions that involve both positive and negative numbers, always pay close attention to each number's sign.
• Practicing converting expressions into words, like taking \(-7 + 5\) and saying 'negative seven plus five' can aid comprehension.

By becoming comfortable with creating and interpreting numerical expressions, you set the foundation for more advanced problem-solving skills in math.