Problem 84 - Algebra A Combined Function

Question

Translate each phrase; then simplify. See Example 22. Find the sum of \(-49,-2,\) and 40 .

Step-by-Step Solution

Answer

The sum is -11.

Step 1: Translate the Phrase into a Mathematical Expression

To find the sum of the numbers we need to write the expression based on the problem statement.The expression is:\(-49 + (-2) + 40\).

Step 2: Simplify the Expression

Now, we will add the numbers step by step to simplify the expression. First, add -49 and -2.\(-49 + (-2) = -51\).Next, add -51 and 40.\(-51 + 40 = -11\).

Key Concepts

Addition

Addition is one of the most basic operations in arithmetic. It involves combining two or more numbers to get a total or sum. When you perform addition, you're essentially counting the total amount. Here’s how you can better understand addition:

• When numbers are positive, you can think of adding them as gathering more of something.
• When a number is negative, it means you are reducing or taking away from what's there.

In the exercise, we’re asked to find the sum of three numbers:

• -49,
• -2,
• 40.

To add these, we start with two negative numbers. Adding negatives might feel a bit like subtracting, but it’s really just piling on more negatives. Once you add your negative numbers, you simply add the positive value to see how the total changes. This process simplifies the overall arithmetic.

Negative Numbers

Understanding negative numbers is key to dealing with a wide range of mathematical problems. A negative number is any number that is less than zero. On a number line, these numbers are located to the left of zero. Here's what you need to know:

• Negative numbers show that something is missing or owed.
• They are often used to represent temperatures below freezing, debts, or levels below sea level.
• Adding negative numbers means moving further to the left on a number line. Conversely, subtracting a negative number is like moving to the right.

In terms of arithmetic operations, adding two negative numbers results in a larger negative number. In our exercise, adding -49 and -2 to get -51 shows this. Each negative value increases the 'depth' of the negative sum. This is an essential step before introducing the positive number, like the 40 we add next.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form. This makes it easier to understand and work with the expression. Here's how you can simplify expressions with numbers, including addition and negative numbers:

• Start by grouping similar types of numbers (e.g., all negative or all positive).
• Perform operations step by step. In arithmetic, the order in which operations are performed is important.
• Always be mindful of signs (positive or negative) when performing arithmetic operations.

In the given task, after translating the phrase into the expression \(-49 + (-2) + 40\), we simplify by first dealing with the negative numbers. Combining \(-49\) and \(-2\) gives \(-51\). Next, adding 40 to the result \(-51 + 40 = -11\) shows how we simplify to reach the final value. This final result provides a clearer understanding of the problem's outcome.