Problem 70 - Elementary and Intermediate Algebra

Question

Add. $$ -13+(-16)+4 $$

Step-by-Step Solution

Answer

The sum is \(-25\).

Step 1: Identify the Numbers

Recognize the numbers involved in the problem: \(-13\), \(-16\), and \(4\). We are adding these three numbers together.

Step 2: Group Negative Numbers

Combine \(-13\) and \(-16\), which are both negative numbers. Add them as follows:\[-13 + (-16) = -29\]

Step 3: Add the Positive Number

Now add the result from Step 2, which is \(-29\), to \(4\), which is the positive number:\[-29 + 4 = -25\]

Step 4: Verify the Result

Double-check the calculations to ensure the addition is accurate. The sum of \(-13\), \(-16\), and \(4\) is indeed \(-25\).

Key Concepts

Understanding Negative Numbers

Negative numbers are numbers less than zero, and they are represented with a minus sign (−) in front. They are important in the context of arithmetic operations, especially when it comes to addition, subtraction, and other calculations.

• Negative numbers are often dealt with in real-life scenarios such as calculating debts or temperatures below zero.
• In addition operations, when two negative numbers are added together, their magnitudes (absolute values) are added, and the result stays negative.
• Example: For \(-13 + (-16)\), consider the magnitudes: \(|13| + |16| = 29\). Since both are negative, the result is \(-29\).

Remember, think of negative numbers like depths below sea level; the further you go, the larger the negative value!

Exploring Positive Numbers

Positive numbers, on the other hand, are numbers greater than zero and are represented without a sign. They are the straightforward numbers we encounter in everyday counting and calculations.

• Positive numbers are involved in sums for adding quantities like money, objects, or even time.
• To add a positive number to any other number, you move to the right on a number line. This will increase the value unless it's added to a larger negative number.
• Example: Adding \(4\) (a positive number) to \(-29\) results in \(-25\) because you are moving 4 steps closer to zero.

Think of positive numbers as upward steps where each step moves you above ground level!

Arithmetical Operations Simplified

Arithmetic operations are the basic computations of mathematics, involving addition, subtraction, multiplication, and division. Addition is one of the simplest and most fundamental operations.

• Addition: This combines numbers to get a total sum. It can involve any combination of positive and negative numbers.
• When adding numbers, identify their types (positive, negative) as this affects how you combine them.
• Example: In the problem \(-13 + (-16) + 4\), start by grouping like types, adding negatives together first, then adjust by adding the positive number.

Use visual aids like number lines or counters to better understand how numbers interact during these operations.