Problem 99 - Beginning and Intermediate Algebra

Question

Write a numerical expression for each phrase, and simplify the expression. The sum of -5 and 12 and 6

Step-by-Step Solution

Answer

The simplified expression is 13.

Step 1: Identify the Numbers

The numbers given in the phrase are -5, 12, and 6.

Step 2: Write the Expression

The phrase requests the sum of the numbers. So, write the expression: -5 + 12 + 6

Step 3: Simplify the Expression

Perform the addition step-by-step: First, add -5 and 12: -5 + 12 = 7Then, add the result to 6: 7 + 6 = 13

Step 4: Write the Simplified Expression

After performing the addition, the simplified expression is 13.

Key Concepts

Numerical Expression

A numerical expression is a combination of numbers and operations (like addition, subtraction, multiplication, and division) that represents a specific quantity. In our exercise, the phrase 'the sum of -5, 12, and 6' needs to be turned into a numerical expression.
First, we identify the numbers mentioned in the phrase: -5, 12, and 6.
Next, because the phrase asks for the sum, we know we will be using the addition operation. Putting it all together, the numerical expression for this exercise is: -5 + 12 + 6.
Writing out numerical expressions helps us clearly see the math we need to do.

Simplifying Expressions

Simplifying an expression means performing all the operations to reduce the expression to its simplest form. For our numerical expression, -5 + 12 + 6, this process involves a couple of steps.
First, we add -5 and 12. Adding these two numbers gives us 7 because -5 + 12 = 7.
Next, we add this result to 6. Continuing the simplification, 7 + 6 = 13.
Now, our expression is simplified to just the number 13. Simplifying expressions can make it easier to understand and work with the numbers.

Integer Addition

Integer addition involves adding whole numbers that can be positive, negative, or zero. Let's take a closer look at this process using our exercise. We need to add -5, 12, and 6.
Adding integers follows specific rules:

• If both numbers are positive, simply add their absolute values.
• If both numbers are negative, add their absolute values and place a negative sign before the result.
• If one number is positive and the other is negative, subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value.

Applying these rules:
For -5 + 12, we subtract 5 (the absolute value of -5) from 12, resulting in 7, which is positive because 12 is larger.
We then add this result to 6: 7 + 6 = 13.
This step-by-step adherence to rules simplifies even complex expressions. By practicing integer addition, we become more comfortable manipulating and understanding numbers of different signs.