91Ó°ÊÓ

When multiplying two negative numbers, the result is always positive. This might seem confusing at first, but it is a fundamental rule in arithmetic and algebra. Consider the expression \(-20(-7)\). Each of these numbers is negative. When we multiply them together, we flip the negative signs, resulting in a positive product. The calculation goes like this: \(-20 \times -7 = 140\).

• Negative \- multiplied by negative \+ gives positive
• Example: \(-4 \times -5 = 20\)

This rule helps in evaluating expressions accurately. Always remember: negative times negative equals positive!

On the other hand, multiplying a negative number by a positive one keeps the result negative. For instance, \(-7 \times 3 = -21\).

Subtracting negative numbers can be tricky but is easy once you understand the rule. Think of \(-\text{(-number)}\) as adding the absolute value of that number. In simpler terms, \(-(-5)\) is the same as \(+5\). Look at the part of the expression 140 - (-78). Here, you subtract a negative \(-78\). This subtraction actually turns into addition: \(140 - (-78) = 140 + 78\). This gets us to \(218\).

• Subtracting a negative is like adding a positive
• Example: \(-3 - (-2) = -3 + 2 = -1\)

Using this logic makes solving algebraic problems more straightforward since you can convert complex subtractions into simple additions.

For simple positive subtractions, where you subtract a number directly, continue following the basic rules without needing to convert anything.

Evaluating algebraic expressions means simplifying them to find a single numeric value. It often involves multiple steps like multiplication, addition, and subtraction. The sequence in evaluating our expression involves performing operations in the correct order: \(-20(-7)-13(6)\). First, resolve the multiplications:

• \(-20 \times -7 = 140\)
• \(-13 \times 6 = -78\)

Next, proceed with the subtraction, keeping in mind the rules for negative numbers:

• \(140 - (-78) = 140 + 78 = 218\)

Following this sequence ensures accuracy in arriving at the final result. It's crucial to follow the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). This is often remembered by the acronym PEMDAS.