Understanding the Problem: Calculating AB

The question asks us to find the product of two quantities, A and B, where A and B are defined by simple arithmetic expressions involving addition and subtraction of integers. We need to calculate the value of A first, then the value of B, and finally multiply these two values together to find AB.

Step-by-Step Calculation of A and B

Let's calculate the value of A.

• A is given by the expression $(-14 + 4)$.
• When adding a negative number and a positive number, we can think of it as finding the difference between their absolute values and using the sign of the number with the larger absolute value.
• The absolute value of -14 is 14. The absolute value of 4 is 4.
• The difference between 14 and 4 is $14 - 4 = 10$.
• The number with the larger absolute value is -14, which is negative.
• Therefore, $A = -14 + 4 = -10$.

Now, let's calculate the value of B.

• B is given by the expression $(4 - 14)$.
• Subtracting a larger number from a smaller number results in a negative number.
• We can rewrite $4 - 14$ as $4 + (-14)$.
• This is the same calculation as we did for A.
• Therefore, $B = 4 - 14 = -10$.

So, we have found that $A = -10$ and $B = -10$.

Calculating the Product AB

The question asks for the value of AB, which means A multiplied by B.

• We need to calculate $AB = A \times B$.
• Substitute the values we found: $AB = (-10) \times (-10)$.
• When multiplying two negative numbers, the result is a positive number.
• $10 \times 10 = 100$.
• Since both numbers are negative, the product is positive.
• Therefore, $AB = (-10) \times (-10) = 100$.

Summary of Calculations

The final value of AB is 100.

Revision Table: Integer Operations

Additional Information: Properties of Integers

Integers are whole numbers (positive, negative, or zero). Understanding how to perform operations with integers is fundamental in algebra.

• Additive Inverse: For every integer 'a', there exists an integer '-a' such that $a + (-a) = 0$. For example, the additive inverse of 14 is -14, and $-14 + 14 = 0$.
• Commutative Property of Addition: The order in which integers are added does not change the sum. $a + b = b + a$. For example, $-14 + 4 = 4 + (-14) = -10$.
• Commutative Property of Multiplication: The order in which integers are multiplied does not change the product. $a \times b = b \times a$. For example, $(-10) \times (-10)$ is the same as $(-10) \times (-10)$.
• Multiplying Negatives: A key rule used in this problem is that the product of two negative numbers is always positive. This is a fundamental concept in integer multiplication.

These properties help simplify calculations and are essential for solving more complex algebraic problems.