Problem 30 - Beginning and Intermediate Algebra

Question

Use a signed number to express each number in boldface italics. Between 2015 and \(2016,\) the number of movie screens in the United States increased by 218 . (Data from Motion Picture Association of America.)

Step-by-Step Solution

Answer

+218

Step 1: Identify the Type of Change

Determine whether the number of movie screens has increased or decreased between 2015 and 2016.

Step 2: Assign a Positive or Negative Sign Based on Change

Since the number of movie screens in the United States increased, the change is positive.

Step 3: Write the Signed Number

Express the given change using a signed number. Since it is an increase of 218, the signed number is +218.

Key Concepts

positive and negative numbers

Positive and negative numbers are fundamental in algebra. They help us represent both increases and decreases in quantities. A positive number is any number greater than zero. It shows an increase or a gain. For instance, when more movie screens are added, we use a positive number to express this growth, like +218 in our example.
On the other hand, a negative number is any number less than zero. It signifies a decrease or a loss. For example, if the number of movie screens had decreased by 218, we would represent it as -218.
It's essential to understand this concept as it forms the basis for many algebraic operations and real-world applications.

algebraic expressions

An algebraic expression is a combination of numbers, variables, and operators (like + and -) that represents a mathematical relationship. In our example, the signed number +218 is a simple algebraic expression where the + sign indicates an increase.
More complex algebraic expressions might involve variables, which are symbols that represent numbers. For example, if we let x represent the number change, the expression would be +x for an increase of x movie screens and -x for a decrease.
Understanding algebraic expressions is crucial because they allow us to model and solve various mathematical problems efficiently.

number change identification

Identifying number changes involves recognizing whether there is an increase or decrease in the quantity of interest. The first step is to look at the context. For example, between 2015 and 2016, the number of movie screens increased; thus, we need to express this change accordingly.
A helpful tip is to use keywords. Words like 'increased', 'gained', or 'added' suggest a positive change, while 'decreased', 'lost', or 'reduced' indicate a negative change.
Once the type of change is identified, we assign the correct sign. Positive changes get a + sign, and negative changes get a - sign. Then, we write the change as a signed number, which clearly communicates the direction and magnitude of the change.