Problem 38 - Prealgebra and Introductory Algebra

Question

Find the product of 100 and \(-7\)

Step-by-Step Solution

Answer

The product of 100 and -7 is -700.

Step 1: Identify the Numbers

Identify the numbers to be multiplied, which are 100 and -7.

Step 2: Multiply the Numbers

On multiplying 100 (a positive number) with -7 (a negative number), remember that the product is negative. So, \(100 \times -7 = -700\).

Key Concepts

Negative Numbers

Negative numbers are numbers that represent values less than zero. They are identified with a minus sign (-) in front of the number. For example, -3, -10, and -7 are negative numbers. These numbers often represent deficits or losses in real-life situations, such as owing money or temperatures below freezing point.

When multiplying or dividing, negative numbers follow a specific rule:

• Multiplying or dividing negative by negative results in a positive number.
• Multiplying or dividing negative by positive results in a negative number.

This is why it's important to pay attention to the signs of numbers in math problems, as they can affect the eventual result. The calculation of a product, as shown in the exercise, illustrates this vital rule.

Product

In mathematics, the term 'product' refers to the result of multiplying two or more numbers. The process of multiplication is one of the four basic arithmetic operations, and it is essentially repeated addition. For example, the product of 4 and 3, or repeatedly adding 4 three times (4 + 4 + 4), is 12.

In the original exercise, we were asked to find the product of 100 and -7. This means we multiplied the two numbers, 100 and -7, to determine their product. Notice that because one of the numbers is negative, the product is also negative. Thus, the product of 100 and -7 is -700, showcasing how multiplication with negative numbers yields negative results.

Integer Multiplication

Integer multiplication involves multiplying whole numbers (integers). Integers include positive whole numbers, negative whole numbers, and zero—such as -2, 0, and 5. The process of multiplication with integers follows the same principles as with regular numbers but requires careful attention to the signs.

Here are some important points about integer multiplication:

• Positive × Positive = Positive (e.g., 3 × 4 = 12).
• Positive × Negative = Negative (e.g., 3 × -4 = -12).
• Negative × Negative = Positive (e.g., -3 × -4 = 12).
• Any Integer × Zero = Zero (e.g., 3 × 0 = 0).

Following these rules ensures that the multiplication of any set of integers results in a predictable outcome, consistent with mathematical principles. This transparency is vital, especially when working with various signs in mathematical computations, ensuring accuracy and understanding in everyday math problems.