Problem 100 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. The sum of -3 and 5 and -12

Step-by-Step Solution

Answer

-10

Step 1: Identify the Numbers

Identify the numbers involved in the phrase. In this case, the numbers are -3, 5, and -12.

Step 2: Write the Numerical Expression

Write the numerical expression for the sum of -3, 5, and -12: -3 + 5 + (-12)

Step 3: Simplify the Expression

Simplify the numerical expression step by step. First, add -3 and 5: -3 + 5 = 2 Next, add the result to -12: 2 + (-12) = -10

Key Concepts

sum of numbers

When you encounter phrases like 'the sum of', it simply means you are being asked to add numbers together.
In this particular exercise, you need to find the sum of -3, 5, and -12.

To start:

• Identify the numbers you need to add. Here, the numbers are -3, 5, and -12.

You'll often see this written as -3 + 5 + (-12).

The key is to add each number in sequence:
Adding -3 and 5 first gives you 2, and then you add the result to -12, giving you -10. Remember, the 'sum' means adding every number step by step.

simplifying expressions

Simplifying expressions involves combining all the numbers and operations into a single, simplest form.
Let's walk through the steps to make this clearer:

• Write out the expression: -3 + 5 + (-12).

The first operation is -3 + 5.
When you add these, you get 2. So, the expression now looks like this: 2 + (-12).

Next, you add 2 to -12, which results in -10. By following these steps, you've simplified the original expression to its simplest form, -10.

basic arithmetic

Basic arithmetic is the foundation of all mathematics.
It includes operations like addition, subtraction, multiplication, and division.

In this exercise, we focus on addition involving both positive and negative numbers:

• Add positive and negative numbers step by step.
• Remember the rules for adding positive and negative numbers: Adding a positive number increases the total, while adding a negative number decreases it.

Here, the sequence is important.
Add -3 and 5 first, then take that result and add -12.

Understanding and practicing these basic arithmetic steps will greatly improve your math skills. Plus, you'll find it easier to handle more complex problems in the future.