Problem 19 - Beginning and Intermediate Algebra

Question

Find each sum. $$ -16+7 $$

Step-by-Step Solution

Answer

-9

Step 1 - Identify the Numbers

Identify the numbers involved in the sum. Here, the numbers are -16 and 7.

Step 2 - Understand the Signs

Note that -16 is a negative number and 7 is a positive number. Adding a negative number to a positive number can be understood as moving left on the number line from the positive number.

Step 3 - Perform the Addition

Calculate the sum by adding -16 and 7. Since you are adding a negative number, subtract the absolute value of the negative number from the positive number: 7 - 16 = -9.

Key Concepts

Negative Numbers

Understanding negative numbers is crucial for solving many math problems. A negative number is any number less than zero, represented with a minus sign (-). For example, -1, -16, and -50 are all negative numbers. Negative numbers can be thought of as being 'below' zero. They often represent loss, decrease, or something opposite in direction.
When performing arithmetic operations with negative numbers, it's important to keep track of their signs. Adding a negative number is essentially the same as subtracting its positive counterpart. For instance, adding -3 is like subtracting 3.

Number Line

The number line is a visual representation of numbers placed at equal intervals along a straight line. It helps us understand the order and relative position of numbers, as well as perform basic arithmetic operations.
To use the number line for addition or subtraction:

• Place the first number on the line.
• If you're adding a positive number, move to the right.
• If you're adding a negative number, move to the left.

For example, to calculate -16 + 7:

• Start at 7 on the number line.
• Since -16 is a negative number, move 16 steps to the left from 7.
• You will land on -9, which is the result of the sum.

Absolute Value

The absolute value of a number is a measure of its distance from zero on the number line, regardless of direction. It's always a non-negative value. We denote absolute value with vertical bars, like this: \(|a|\).
Key points to remember about absolute value:

• For positive numbers and zero, the absolute value is the number itself (e.g., \(|7| = 7\)).
• For negative numbers, the absolute value is the positive counterpart (e.g., \(|-16| = 16\)).

Absolute value is useful in various scenarios, including when adding negative numbers. For instance, in the equation -16 + 7, understanding that you're subtracting the absolute value of -16 from 7 (which is the same as 16) helps in determining that the result is -9.