Problem 111 - Algebra 1

Question

EVALUATING EXPRESSIONS Evaluate the expression. $$ -7+9-8 $$

Step-by-Step Solution

Answer

The result of evaluating the expression \(-7 + 9 -8\) is \(-6\).

Step 1: Addition and Subtraction

Start from the left and process each operation in order. Add -7 and 9. The result is 2.

Step 2: Continue with subtraction

Next, subtract 8 from the previous result (2). 2 - 8 gives -6.

Key Concepts

Addition and Subtraction

When evaluating mathematical expressions involving addition and subtraction, it's essential to pay attention to both the numbers and their signs. Addition refers to combining two or more numbers to get a sum, while subtraction involves taking one number away from another. In the given expression, we see `-7 + 9 - 8`.

• Begin from the left with `-7 + 9`. Here, we add 9 to -7. Since 9 is larger than 7, think of it as finding the difference and keeping the sign of the larger number. This gives us 2.
• Next, continue with the result and subtract 8. Since 8 is larger than 2, the result will be negative, reflecting the difference. The outcome is -6.

Keep in mind how numbers 'cancel' out when involving negatives, and always remember, addition may involve subtraction of absolute values depending on the signs. Breaking down operations like this makes them manageable and intuitive.

Step by Step Solution

Tackling expressions methodically can help avoid mistakes. Here we have a step by step approach: - **Step 1: Addition** - Look at `-7 + 9`. Compute this part first. - Picture a number line: start at -7; move 9 spaces right to reach positive 2. - Simplifying the addition of a negative and a positive like this helps reinforce the concept of net movement either side of zero. - **Step 2: Subtraction** - Proceed with `2 - 8`. Again, visualize moving on a number line. Start at 2 and move left 8 spaces. - Understand you end at -6, an intuitive method to grasp negative outcomes. By processing operations in sequence and verifying each step, errors caused by rushing or oversight are minimized. It’s about ensuring clarity at every point.

Order of Operations

Understanding the order of operations is crucial when evaluating expressions. However, for expressions involving only addition and subtraction, as in `-7 + 9 - 8`, the order becomes about left-to-right movement rather than prioritization. - **Key Point**: When only addition and subtraction are present, execute operations sequentially from left to right. - This differs from expressions with multiple operators like multiplication or division, which require following established rules like BODMAS/BIDMAS—Bracket, Order, Division/Multiplication, Addition/Subtraction. - **Why it Matters?**: Consider more complex scenarios. If you mix different operations without clear rules, errors happen easily. - Following left-to-right for add-subtract ensures you manage the sign changes accurately, much like reading a sentence in a specified order. Use this foundational understanding as you progress into more complex equations, ensuring every step is a logical progression from start to finish.