Problem 102 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. -2 added to the sum of -18 and 11

Step-by-Step Solution

Answer

-9

Step 1: Translate the phrase into a numerical expression

The phrase given is '-2 added to the sum of -18 and 11'. First, find the sum of -18 and 11. This can be represented as o. (-18 + 11). Then add -2 to this sum. The expression becomes (-18 + 11) + (-2).

Step 2: Compute the sum inside the parentheses

Calculate the sum of -18 and 11: (-18 + 11 = -7). So, the expression simplifies to: (-7) + (-2).

Step 3: Add the remaining terms

Add -7 and -2: o. (-7) + (-2) = -9. Therefore, the simplified expression is:-9.

Key Concepts

Sum of Integers

When you see 'sum' in math, it means you're adding numbers together. To find the sum of integers, you combine their values. In our exercise, you need to find the sum of two numbers: -18 and 11. Applying this concept:

- Start by taking the two integers you need to add: -18 and 11.
- Add the numbers together: \(-18 + 11 = -7\).

This means the sum of -18 and 11 is -7. Adding numbers, even with different signs, follows the same rule: combine their values. If the numbers have different signs, subtract the smaller absolute value from the larger one. For example, \(-18 + 11 \) results in -7 because \(|18| - |11| = 7 \). Since 18 is negative and has a greater absolute value, the result is negative.

Addition with Negative Numbers

Adding negative numbers can seem tricky, but it's straightforward once you understand the rules. There are two parts to consider here:

- Adding a negative number to another number
- Adding positive and negative numbers together

Let's break it down:

• Negative + Negative: When you add two negative numbers, their values combine to make a larger negative number. For example: adding \(-7 + -2 = -9\). It's like owing money; if you owe \(7 and borrow \)2 more, you now owe $9.
• Positive + Negative: When the signs are different, subtract the smaller absolute number from the larger. The sign of the result takes the sign of the larger absolute number as seen in \(-18 + 11 = -7\).

Remember, the sum of negatives is always more negative. Meanwhile, combining positives and negatives depends on their absolute values.

Simplifying Expressions

Simplifying expressions means breaking them down into their simplest form. The goal is to make the expression as straightforward as possible. Here’s how it works for our exercise:

- The initial expression was: \((-18 + 11) + (-2)\).
- Simplify inside the parentheses first: \(-18 + 11\). We get \(-7\).
- This changes our expression to \(-7 + (-2)\).
- Finally, add the remaining terms: \(-7 + (-2) = -9\).

This step-by-step method shows how we break down complex parts of an expression. Always perform operations inside parentheses first, then proceed to add or subtract other terms. Simplifying expressions helps avoid errors and makes solving problems easier.