Problem 44 - Algebra A Combined Function

Question

Add. See Examples 1 through 12,18, and 19. $$ -18+(-6)+(-40) $$

Step-by-Step Solution

Answer

-64

Step 1: Understand Negative Addition

When numbers have a negative sign, they represent a decrease or subtraction from zero. Adding negative numbers will cumulatively decrease the total further.

Step 2: Add the First Two Numbers

Start by adding the first two numbers: \(-18 + (-6) = -24\).Adding two negative numbers results in a more negative number, calculated by simply adding their absolute values.

Step 3: Add the Third Number

Next, add the third negative number to the result from Step 2:\(-24 + (-40) = -64\).Again, you add the absolute values and keep the negative sign.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are usually denoted by a minus sign before the number, such as -18 and -6. Negative numbers represent a deficit or something being taken away. For example, if you have a debt of $18, you can express it as -18. Another important point about negative numbers is when you add them, you are essentially increasing the deficit. In other words, adding negative numbers makes the total sum more negative.

Absolute Values

Absolute value is a measurement of a number without considering its sign. It represents the distance of a number from zero on the number line. For instance, the absolute value of both -18 and 18 is 18. We write the absolute value of a number using two vertical bars, like \(|-18| = 18\) and \(|18| = 18\).

• No matter if a number is negative or positive, its absolute value is always non-negative.
• Absolute values are particularly useful when adding negative numbers, as they help to determine the magnitude of the numbers involved.

Integer Operations

Integer operations include basic operations like addition, subtraction, multiplication, and division, applied to whole numbers, including negative numbers. Let’s focus on addition, particularly when dealing with negatives. When adding integers:

• Two positive integers add up to a positive number.
• Two negative integers add up to a negative number, computed by adding their absolute values and keeping the negative sign.
• To add a positive and a negative integer, subtract the smaller absolute value from the larger absolute value and take the sign of the integer with the greater absolute value.

These rules are foundational to solving problems that involve adding negative numbers.

Basic Arithmetic

Basic arithmetic involves fundamental operations including addition, subtraction, multiplication, and division. When working with negative numbers, addition operates a bit differently compared to positive numbers alone.In the provided problem \(-18 + (-6) + (-40)\):

• First, consider the absolute values: 18, 6, and 40.
• Add them together to get 64.
• Since all numbers are negative, the sum is -64.

Understanding these steps helps in efficiently solving more complex number problems, reinforcing the primary arithmetic operation skills.