Problem 33 - Algebra 1

Question

Find the difference. $$ 15-|-6| $$

Step-by-Step Solution

Answer

The difference is 9.

Step 1: Find the Absolute Value

Firstly, find the absolute value of -6. The absolute value of a number is its value without its sign, so the absolute value of -6 is just 6.

Step 2: Perform the Subtraction

Now, subtract this absolute value from 15. So, perform the operation 15 - 6.

Step 3: Find the Answer

The result of the operation 15 - 6 is 9. This is the final answer.

Key Concepts

Subtraction

Subtraction is one of the four basic operations in mathematics. It involves taking one number away from another. In this exercise, the subtraction operation is between 15 and the absolute value of -6.

• The minuend is 15, which is the number you start with.
• The subtrahend is the number being subtracted, which in this case, is the absolute value of -6.

The operation is as simple as counting backward. Starting from 15 and moving 6 steps back gives us 9, which is the difference.Now, the symbolic representation is often used: \[15 - |-6| = 15 - 6 = 9\]Here, understanding subtraction with positive and negative numbers requires knowing their absolute values, which simplifies the operation.

Integer Operations

Integer operations include addition, subtraction, multiplication, and division performed on whole numbers. These operations are crucial for solving algebraic equations and other mathematical problems.

• In our context, we deal with subtraction using integers.
• To subtract integers, convert them to their absolute values.

For instance, dealing with \(-6\) means only needing to manage its value in a non-negative form using its absolute value, making operations simpler.Understanding integer operations, like in this problem, allows managing equations across various mathematical topics and is a cornerstone in learning algebra.

Algebra

Algebra is a significant area of mathematics that uses symbols and letters to represent numbers and quantities in formulas and equations. This particular exercise hints at algebraic skills because it involves manipulating expressions and understanding operations with negative numbers. Here, knowing what absolute value is helps establish a foundation, allowing navigation through expressions even when negative numbers are involved.

• Absolute values help remove the direction sign, dealing directly with magnitude.
• Solving equations requires understanding basic operations, including subtraction, and manipulation of algebraic expressions.

In algebra, mastering these concepts helps build the capacity to solve more complex equations and problems. Recognizing patterns and working through procedures using the principles of subtraction and integer operations are fundamental skills in algebra.