Problem 89 - Elementary Algebra Within Reach

Question

In Exercises 89-96, evaluate the expression. $$ 10-(-7) $$

Step-by-Step Solution

Answer

The evaluation of the expression \(10-(-7)\) is 17.

Step 1: Understanding the problem

The expression \(10-(-7)\) involves subtracting negative 7 from 10. Subtraction of a negative number is the same as addition so this will simplify to the addition of 10 and 7.

Step 2: Execute the addition

10 + 7 equals 17

Key Concepts

Subtracting Negative Numbers

When it comes to subtracting numbers, dealing with negative numbers introduces an interesting twist. Fortunately, it is a simple concept once you understand the rule.
In mathematics, subtracting a negative number is equivalent to adding its positive counterpart. This pivot from subtraction to addition happens because the negative sign in front of the number changes its direction on the number line.

• For example, subtracting negative five (-5) results in the same outcome as adding five (5).
• This concept can be visualized as turning around and stepping forward on the number line instead of stepping backward, which occurs in standard subtraction.

Understanding this rule can help simplify equations and solve problems more efficiently. Always remember: minus a negative equals a plus.

Addition of Integers

Adding integers is a fundamental skill in math that involves combining whole numbers. Whether dealing with positive or negative integers, the rules are consistent and straightforward.
Here's a quick refresher on the mechanics of adding integers:

• If both integers are positive, simply add them like regular whole numbers.
• If one integer is positive and the other is negative, subtract the smaller number from the larger number, then take the sign of the larger number.
• For instance, in our initial problem, when adding 10 and 7, both numbers are positive, making it a standard addition resulting in 17.

Practicing addition with integers can help you develop a deeper understanding of basic and complex algebraic operations.

Algebraic Expressions

Algebraic expressions form the backbone of algebra and involve combining numbers, variables, and arithmetic operations.
An expression such as our example, which contains only numbers and operations, is often referred to as an arithmetic expression. However, once you introduce variables, it becomes an algebraic expression.

• Such expressions can be simplified by following the standard rules of operations, including handling negative numbers and integer operations.
• Knowing how to simplify expressions is crucial in solving more complex algebraic problems.

Algebraic expressions are versatile in mathematics because they can describe patterns, solve equations, and model real-world situations. They are essential tools in your math toolkit.