Problem 4 - Fundamentals of Mathematics

Question

Write each expression in words. \(-10-(+3)\)

Step-by-Step Solution

Answer

Negative ten minus positive three.

Step 1: Identify the Components

First, identify each component of the expression \(-10-(+3)\). This consists of a minus sign, the number 10 which is negative, another minus sign indicating subtraction, and the number 3 which is positive.

Step 2: Interpret Negative Numbers and Subtraction

Understand what each negative sign means in the context: the first one indicates that 10 is negative ('negative ten'), and the second controls the subtraction ('minus'). The positive sign with the 3 indicates that it is simply a positive number, which can be stated as just 'three'.

Step 3: Construct the Expression in Words

Now, write down the entire expression in words based on our interpretations: 'Negative ten minus positive three.'

Key Concepts

Negative Numbers

Negative numbers can be a little challenging at first, but they are simply numbers less than zero. Imagine a number line with zero in the middle. Negative numbers are to the left of zero. For example,

• -1 is one step left of zero.
• -10 is ten steps left of zero.

Negative numbers are used to represent values that are opposite in nature to their positive counterparts, like temperature below freezing, or a decrease in a bank account balance. In the expression \(-10-(+3)\), the \(-10\) is a negative number, informing us that we are starting ten units below zero.

Understanding negative numbers is crucial in various mathematical operations, especially when combined with subtraction.

Subtraction

Subtraction is a core mathematical operation that essentially finds the difference between numbers. In simple terms, it tells us how much less one quantity is from another. The minus sign \(-\) is the key indicator of subtraction.

In the expression \(-10-(+3)\), we are subtracting a positive number \(+3\) from a negative number \(-10\). This might seem tricky as subtraction in combination with negative numbers can alter the typical effect we expect.

• When you subtract a positive number, it moves you further left on the number line.
• If you subtract a negative number, it's like adding that positive number instead.

Here, subtracting \(+3\) from \(-10\) moves us 3 more units to the left, making the overall result \(-13\).

Subtraction is important because it is used widely beyond basic math, in sciences, economics, and everyday problem-solving.

Positive Numbers

Positive numbers are the numbers greater than zero, found on the right side of the number line. They represent quantities like gain, increase, or simply the count of objects. In any mathematical expression, they're usually easy to identify because:

• They either don't have a sign or bear a positive \(+\) sign.
• For instance, the number 3 in \(-10-(+3)\) is positive.

Understanding positive numbers allows us to handle expressions like \(-10-(+3)\), where knowing that \(+3\) is positive guides how we interpret the subtraction process.

Breaking down exponents into simpler words or understanding sequences often rely on the foundation of knowing how positive numbers influence a mathematical expression.