Problem 11 - Beginning and Intermediate Algebra

Question

Find each product. \(-7(4)\)

Step-by-Step Solution

Answer

-28

Step 1: Identify the Numbers

Identify the numbers involved in the multiplication. Here, the numbers are -7 and 4.

Step 2: Multiply the Absolute Values

Multiply the absolute values of these numbers. The absolute value of -7 is 7, and of 4 is 4. So, calculate: 7 * 4 = 28.

Step 3: Determine the Sign of the Product

Determine the sign of the product. Since one number is negative and the other is positive, the product will be negative. Thus, -7 * 4 = -28.

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, without considering its direction.
Absolute values are always non-negative.
For example:

• The absolute value of -7 is 7, because it is 7 units away from zero.
• The absolute value of 4 is 4, because it is 4 units away from zero.

This concept is important in multiplication because it helps us to focus on the magnitude of numbers before worrying about the signs.
In the exercise, we first find the absolute values of -7 and 4, which are 7 and 4, respectively.
Then, we multiply these absolute values together.

Negative Numbers

Negative numbers are numbers that are less than zero.
They are located to the left of zero on the number line.

• For example, -7 is a negative number because it is 7 units to the left of zero.

When dealing with negative numbers in multiplication, it's crucial to remember that they influence the sign of the product.
Multiplying a negative number by a positive number will result in a negative product, as observed in the given exercise where -7 is multiplied by 4.

Sign Rules in Multiplication

Understanding sign rules in multiplication is key when working with integers. It's important to know how the signs of numbers impact the final product:

• If both numbers are positive, the product is positive.
• If both numbers are negative, the product is positive, because the two negatives cancel each other out.
• If one number is positive and the other is negative, the product is negative.

In the exercise where -7 is multiplied by 4, we have one negative number and one positive number, leading to a negative product.
This is why the product of -7 and 4 is -28.