Problem 9 - Elementary Algebra

Question

Simplify. $$ -(-8) 2 $$

Step-by-Step Solution

Answer

The simplified expression is 16.

Step 1: Simplify the Double Negative

The expression to simplify is \[-(-8)2\]Start by addressing the double negative. The negative of a negative number makes the number positive. Thus, \[-(-8) = 8\] .The expression is now \[8 \times 2\] .

Step 2: Multiply

Now, multiply the simplified result by 2:\[8 \times 2 = 16\]. The expression is now simplified to 16.

Key Concepts

Double Negative

The concept of a 'double negative' can sometimes trip up students, but it's simpler than it first appears. A "double negative" involves two negative signs in sequence, and these negatives actually negate each other. Think of it as the mathematical equivalent to saying "not not going." Just as the two "nots" cancel each other out, yielding "going," two negative signs in math produce a positive value.
For example, consider the expression \[-(-8)\]; here, the negative of a negative number, -8, becomes positive 8. So, \[-(-8) = 8\].
This principle of two negatives making a positive is not only applicable in mathematics but also in everyday language, allowing us to navigate through the language of mathematics with ease!

Multiplication

Multiplication is one of the basic operations in mathematics, and it involves combining equal groups of numbers. When dealing with multiplication, you can think about it visually or conceptually as "adding the same number repeatedly."
For the problem \[8 \times 2\], it can be seen as 8 added to itself twice (8 + 8) which equals 16.
Some key points to understand about multiplication are:

• Multiplication is commutative, meaning that the order of numbers does not change the result: \[8 \times 2 = 2 \times 8\].
• It is the inverse operation of division, which means it can be used to check division results.

Learning to multiply efficiently builds a strong foundation for more advanced math topics such as fractions and algebra.

Integer Operations

Integer operations form the backbone of arithmetic and are crucial for simplifying expressions. Integers include all whole numbers and their negatives, extending to positive and negative numbers without fractions or decimals.
When performing operations with integers, there are some important rules:

• Addition and subtraction: Same signs add and keep the sign, different signs subtract and keep the sign of the larger number.
• Multiplication and division: Multiplying or dividing two integers with the same sign yields a positive result; with different signs, the result is negative.

Understanding these operations helps in solving various mathematical problems, from simple arithmetic to complex algebraic equations, like dealing with the initial step of simplifying the double negative in our original exercise, leading to multiplying positive numbers.