Problem 54 - Algebra 1: Concepts and Skills

Question

Find the product. $$ 6(-6) $$

Step-by-Step Solution

Answer

The product of 6 and -6 is -36.

Step 1: Identify the Numbers

The numbers that need to be multiplied are 6 and -6.

Step 2: Multiply the Numbers

To find the product, we multiply 6 and -6 which gives -36.

Key Concepts

Integer Operations

Integer operations are the basic arithmetic processes involving whole numbers. These operations include addition, subtraction, multiplication, and division. Working with integers can sometimes be tricky, especially when you are multiplying positive and negative numbers together. When performing integer operations like multiplication, it is essential to remember that:

• Combining two positive integers gives a positive product.
• Combining two negative integers also results in a positive product because the negatives cancel out.
• Combining a positive integer with a negative integer results in a negative product.

This means that when you multiply 6 and -6, you are combining a positive with a negative, and the result will be negative. Hence, the product is -36.

Negative Numbers

Negative numbers are numbers less than zero, represented with a minus sign (-). They represent values that are opposite in direction from positive numbers on the number line. When performing arithmetic operations with negative numbers, it is crucial to remember:

• Negative numbers decrease in value as they move farther from zero on the number line.
• Negative numbers added together become more negative.
• Negative numbers subtracted can actually result in a less negative or even positive number, depending on the values.

In multiplication, when you multiply a negative number by a positive number, the negative always takes precedence, flipping the sign of the final product. In our example, 6 multiplied by -6 will give us -36 because the negative sign affects the result.

Arithmetic Operations

Arithmetic operations refer to the basic mathematical functions: addition, subtraction, multiplication, and division. Understanding these operations is fundamental to solving any math problem. In multiplication, particularly involving integers and negative numbers, the key points to remember are:

• Multiplying any number by zero results in zero.
• Multiplying positive numbers results in a positive number.
• If the signs of two numbers are different, the product will be negative.
• If the signs of two numbers are the same, the product will be positive.

For the exercise given, we multiplied 6 (a positive integer) by -6 (a negative integer). This highlights the rule that differing signs yield a negative product, which explains why the answer is -36.