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Chapter 2: Problem 3

Find the difference. \(10-12\)

Short Answer

Expert verified
The difference is \(-2\).

Step by step solution

01

Identify the Operation

The problem provides us with an expression, \(10 - 12\). This is a subtraction problem, where we are asked to find the difference between the two numbers, 10 and 12.
02

Subtract the Numbers

To find the difference, subtract 12 from 10. This subtraction involves finding how much more 12 is than 10. This operation results in a negative number, as 12 is larger than 10.
03

Calculate the Result

Perform the subtraction: \(10 - 12 = -2\). This calculation shows that the difference is \(-2\), because when you subtract a larger number from a smaller number, the result is negative.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Negative Numbers
Negative numbers are numbers less than zero. Think of them as positions to the left of zero on the number line.
They represent values that are less than nothing, often used to denote losses or deficits.
  • Negative numbers are important in various fields, such as finance and science.
  • They help compare values and show a decrease or deficit.
For instance, if you have \(10 and owe \)12, your balance becomes $-2, representing a debt. Understanding negative numbers is crucial for problems involving operations where results can fall below zero. In the subtraction problem of \(10 - 12\), the result is a negative number because you're removing more than the available amount.
Basic Mathematical Operations
Mathematical operations refer to calculations involving numbers, such as addition, subtraction, multiplication, and division. Subtraction is one of the core operations and is used to find differences between numbers.
  • Subtraction can result in both positive and negative numbers.
  • When subtracting, the order matters: \(a - b \) is not the same as \(b - a\).
Performing mathematical operations properly lets us solve various real-world and mathematical problems effectively. In our example, subtraction helps us determine how much greater 12 is than 10. When we subtract a larger number from a smaller one, the outcome, as seen, is negative due to the difference being in the opposite direction on the number line.
Exploring Integer Arithmetic
Integer arithmetic involves the use of whole numbers, both positive and negative, including zero.
This form of arithmetic is vital in discrete math where whole number operations are needed. Integers are numbers without fractional parts.
  • Within integer arithmetic, rules dictate how numbers interact, especially when negative numbers are involved.
  • Operations with integers follow specific properties: the closure, associative, and commutative properties.
For subtraction, the outcome may yield a negative result as seen in \(10 - 12 = -2\). Here, the integer rule of dealing with negative results shows that the difference goes beyond zero, accounting for negative integers in calculations.

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Most popular questions from this chapter

Simplify the given expression. \(\frac{7^{2}-6^{2}}{6 \cdot 3-5}\)

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