Problem 17 - Beginning and Intermediate Algebra

Question

Find each product. 3(-11)

Step-by-Step Solution

Answer

-33

Step 1: Understand the Problem

You are asked to find the product of 3 and -11. This means you need to multiply these two numbers together.

Step 2: Identify the Numbers

The numbers in the problem are 3 and -11. The multiplication involves one positive number and one negative number.

Step 3: Multiply the Numbers

Multiply 3 by -11. When you multiply a positive number by a negative number, the product is negative. Therefore, 3 multiplied by -11 equals -33.

Key Concepts

integer multiplication

Multiplication is one of the four basic arithmetic operations. When dealing with 'integer multiplication', it's essential to remember that integers include all whole numbers and their negative counterparts (e.g., -3, 0, 2).
The process of multiplying integers works like multiplying any other numbers. However, the result's sign will depend on the signs of the integers involved. You follow the usual multiplication rules to find the product.

positive and negative numbers

Understanding 'positive and negative numbers' is crucial. Positive numbers are greater than zero (1, 2, 3...), while negative numbers are less than zero (-1, -2, -3...).
When multiplying integers, follow these rules for the signs:

• If both numbers are positive, the product is positive (e.g., 2 * 3 = 6).
• If both numbers are negative, the product is positive (e.g., -2 * -3 = 6).
• If one number is positive and the other is negative, the product is negative (e.g., 2 * -3 = -6).

This exercise, involving multiplying 3 (positive) by -11 (negative), falls into the third category.

product of numbers

The 'product of numbers' is the result of multiplying two numbers.
To find the product, follow these simple steps:

• Identify the numbers to multiply. In the given exercise, these numbers are 3 and -11.
• Recognize the signs of the numbers. One is positive (3), and the other is negative (-11).
• Multiply the absolute values: 3 * 11 = 33.
• Determine the sign of the result using the rules from the previous section. Since a positive and a negative number are being multiplied, the product will be negative.

Therefore, the product of 3 and -11 is -33.
By understanding these key concepts, you can solve problems involving multiplication of integers more easily.