Problem 56 - Elementary Algebra

Question

Rewrite the problem in a simpler form. $$ 15-(-6)-(-5) $$

Step-by-Step Solution

Answer

Answer: 26

Step 1: Change the signs

According to arithmetic rules, two negative signs next to each other can be replaced with a positive sign: $$ 15 - (-6) - (-5) = 15 + 6 + 5 $$

Step 2: Add the numbers

Now we just need to add the numbers together: $$ 15 + 6 + 5 = 21 + 5 = 26 $$ The simplified form of the expression is 26.

Key Concepts

Negative Sign Rules

Understanding how negative signs work in algebra is crucial to correctly simplify expressions. When you see a subtraction sign followed by a negative number, like in the expression \(15 - (-6) - (-5)\), it can be quite confusing. The rule of thumb is that two negatives make a positive. So whenever you have a minus followed by a negative number, you can consider them as plus positive.

In the given exercise, \(15 - (-6) - (-5)\) becomes \(15 + 6 + 5\) after applying this rule. This concept is derived from the idea that subtracting a debt (negative amount) actually increases your wealth (positive value). It's like if someone took away something you owed; you'd be better off!

Arithmetic Operations

Arithmetic operations form the foundation of all algebra. The basic operations are addition, subtraction, multiplication, and division. When simplifying algebraic expressions, you usually perform these operations following the order of PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

However, with the given problem, once the negative signs are taken care of, we are only left with addition: \(15 + 6 + 5\). Adding them up is straightforward, and we proceed from left to right, combining numbers to get the result \(26\). Remember, the key to tackling arithmetic operations is to do them one step at a time and in the correct order.

Basic Algebra

Basic algebra involves solving for unknowns and simplifying expressions, which requires manipulating numbers and variables according to the rules of arithmetic operations and negative signs. The problem \(15 - (-6) - (-5)\) is a simple algebraic expression with no unknown variables but perfectly illustrates how these rules are used in practice.

To master basic algebra, practice exercises like these and remember the significance of negative sign rules and arithmetic operations. With time and practice, you'll find that what might seem complex at first glance becomes much simpler once broken down into smaller, manageable parts.