Problem 61 - Elementary Algebra

Question

Subtract 23 from the sum of -12 and \(29 .\)

Step-by-Step Solution

Answer

The result is -6.

Step 1: Find the Sum

Calculate the sum of \(-12\) and \(29\) by adding them together: \(-12 + 29 = 17\).

Step 2: Subtract 23

Subtract \(23\) from the sum calculated in Step 1: \(17 - 23 = -6\).

Key Concepts

Addition

Addition is often the first arithmetic operation we learn. In its simplest form, it involves combining two or more numbers to find their total value. This can be thought of as bringing quantities together. When dealing with addition, it's important to understand both positive and negative numbers, as they can significantly change the result.
In the context of the exercise, to add

• -12 + 29, we bring together the value of a negative number (-12) with a positive number (29).
• The operation will find the difference between the magnitudes of these numbers since one is negative and the other is positive.
• Essentially, you're asking "How much more is 29 than 12?" which gives you 17.

Knowing how addition affects numbers is key to mastering basic arithmetic operations. With practice, you'll be able to quickly identify how differing values interact when added.

Subtraction

Subtraction is the process of removing one quantity from another. It's crucial for determining how much is left after taking away a certain amount. While it can seem simple, things can get a little complex when you subtract numbers with different signs or when the subtracted number is larger than the one you're starting with.
In the original problem, once the sum was calculated as 17, the next step was to subtract 23 from it.

• Subtraction here means calculating 17 - 23.
• Because 23 is greater than 17, the result is a negative number, specifically -6.
• This is because subtracting a larger number from a smaller one indicates that more was taken away than what was initially present.

This operation shows how the act of subtraction reduces or eats away at a number, leading to a result that can be positive, zero, or negative depending on the numbers involved.

Negative Numbers

Negative numbers are interesting because they represent values that are less than zero. They play a crucial role in both addition and subtraction, significantly affecting outcomes, just like in the given exercise.
When you encounter negative numbers:

• They indicate a deficiency or a 'below zero' status.
• Adding a negative number is similar to subtracting its positive counterpart.
• Similarly, subtracting a negative number is equivalent to adding its positive counterpart.

In our specific case, seeing -12 shows that we start below zero and work our way up.

• This concept influences both the addition in the first step and the subtraction in the second step.
• The end result was negative, reinforcing the concept that after removing more than you start with, you end in the negative.

Understanding negative numbers is fundamental as they expand the realm of numbers beyond the positive values most people are initially comfortable with.