Problem 34 - Algebra 1: Concepts and Skills

Question

Evaluate the expression. $$ -15-16-81 $$

Step-by-Step Solution

Answer

-112

Step 1: Evaluate -15 - 16

Start by evaluating the first two numbers, subtracting 16 from -15 which equals -31.

Step 2: Evaluate -31 - 81

Continue by subtracting 81 from the result in step 1 (-31), which equals -112.

Step 3: Final Answer

The value of the expression -15 -16 -81 is -112.

Key Concepts

Understanding Integers

Integers are a fundamental part of mathematics and include all positive whole numbers, negative whole numbers, and zero. In other words, they are numbers without fractions or decimals.
Imagine you are moving forward and backward on a number line:

• Positive integers (1, 2, 3, ...) move to the right from zero.
• Negative integers (-1, -2, -3, ...) move to the left from zero.
• The number zero (0) serves as the neutral point.

When working with integers, we often perform operations like addition and subtraction. These operations are all about combining and removing these discrete values on the number line.

Mastering Adding and Subtracting Integers

When adding and subtracting integers, it's all about managing directions on a number line. Think of it as moving:

• To the right for positive numbers
• To the left for negative numbers

Subtracting an Integer

Subtracting a number is like adding its opposite. For example, subtracting 16 is the same as adding -16. Pay attention to:

• When subtracting a positive integer: move left on the number line.
• When subtracting a negative integer: move right, as it's akin to adding.

In the exercise, first, we subtracted 16 from -15:

• This involves moving 16 steps left from -15, landing at -31.

Then, from -31, subtracting 81 means:

• Heading another 81 steps left, ending at -112.

Understanding this directional movement is key to mastering integer operations.

Step by Step Solving Techniques

Breaking down problems into smaller steps is essential for solving mathematical expressions involving integers. This method allows you to spot errors early and clarify each stage.

Step-by-Step Approach

1. **Evaluate Sequentially:** Work with one operation at a time. For -15 - 16 - 81, start with -15 - 16 first.
2. **Document the Process:** Keep a note of each calculation step. For instance, note that -15 - 16 equals -31.
3. **Continue Solving:** Then handle -31 - 81. This incremental solving avoids confusion and builds confidence.

Why is it Useful?

• Keeps calculations organized and avoids mistakes.
• Helps in understanding the flow of operations.
• Enhances problem-solving skills over time.

For our problem: starting with -15 - 16 gives us -31. Next, solving -31 - 81 leads us to the answer, -112. This technique ensures accuracy and clarity in evaluation.