Problem 45 - Prealgebra

Question

Add the following numbers left to right. $$-2+(-5)+(-6)+(-7)$$

Step-by-Step Solution

Answer

The total is -20.

Step 1: Add the First Two Numbers

Start by adding the first two numbers, \(-2 + (-5)\).This can be viewed as adding two negative numbers.The sum is \(-2 + (-5) = -7\).

Step 2: Add the Next Number

Now add the result from Step 1 to the next number in the sequence, \(-7 + (-6)\).This can also be viewed as adding another negative number.The sum is \(-7 + (-6) = -13\).

Step 3: Add the Final Number

Finally, take the result from Step 2 and add it to the last number, \(-13 + (-7)\).Once again, we are adding a negative number to another negative number.The sum is \(-13 + (-7) = -20\).

Key Concepts

Integer Addition

When we talk about integer addition in mathematics, we are focusing on adding whole numbers, which can be positive or negative. In the exercise provided, all numbers are negative. Let's understand how to add them efficiently.
To add integers, especially when negative numbers are involved, think of the number line. Every integer can be represented on this line, with zero in the middle, positive numbers on the right, and negative numbers on the left.

• When adding a positive number, move right on the number line.
• When adding a negative number, move left on the number line.

Understanding the movement on the number line simplifies the addition process, whether working through mental math or using a calculator.

Negative Numbers

Negative numbers are numbers less than zero. They are usually represented with a minus sign (-) in front. Consider them as the opposite of positive numbers, and they indicate a reduction, loss, or decrease.
When adding negative numbers, such as the ones in the exercise, the process involves moving further away from zero on the number line toward greater negativity.

• When adding two negative numbers, their absolute values are added, and the result remains negative.
• For example, \(-2 + (-5)\) involves finding the total displacement away from zero, and results in \(-7\).

In practical terms, adding negative numbers can be compared to increasing debt. If you owe more friends money, your total debt increases, hence, your sum becomes more negative.

Basic Arithmetic Operations

Arithmetic operations are the basic calculations we perform with numbers. The primary operations include addition, subtraction, multiplication, and division. In the context of this exercise, we are focusing on addition.
Addition involves combining numbers to find their sum. When we are working strictly with negative numbers, as in this exercise, a few key aspects apply:

• Adding negative numbers involves summing up their absolute values but with negative sign.
• Each integer affects the total based on its own value and sign, leading to a cumulative result for all numbers involved.

This consistent logic helps in quickly processing problems with multiple steps like the one in the exercise. With practice, it becomes easier to understand and calculate these operations intuitively, even with complex integers.