Problem 33 - Prealgebra

Question

Use the rule for order of operations along with the rules for addition, subtraction, and multiplication to simplify each of the following expressions. $$-10(-2-3)$$

Step-by-Step Solution

Answer

The simplified expression is 50.

Step 1: Simplify Inside Parentheses

First, we simplify the expression inside the parentheses. The expression is \(-2 - 3\). Calculating this, we get:\[-2 - 3 = -5.\] So, the expression now becomes \(-10(-5)\).

Step 2: Apply Multiplication

Next, we multiply the numbers outside and inside the parentheses. Multiply \(-10\) by \(-5\):\[(-10) \times (-5) = 50.\] The product of two negative numbers is positive, so the simplified result is \(50\).

Key Concepts

Understanding Addition

Addition is a fundamental arithmetic operation that involves combining two or more numbers to find their total. It's essential to understand addition as it often appears within larger mathematical expressions. For example, adding numbers helps to simplify expressions within parentheses before performing other operations.

When using addition, the numbers being added are called addends, and the result is the sum. Here's a simple breakdown of how addition works:

• Identify the addends in your expression.
• Combine them by counting all the units together.
• The total is known as the sum.

In the context of complex expressions involving parentheses, addition helps in finding intermediate results, which will later be simplified further using other operations like multiplication and subtraction.

Mastering Subtraction

Subtraction is another key operation that involves taking away one number from another. It's crucial to learn subtraction since it often appears in expressions that need simplification using the order of operations.

In subtraction, you start with a number, known as the minuend, and subtract another number, called the subtrahend, to get the difference. Here’s how to understand subtraction:

• Identify which number needs to be reduced (the minuend).
• Find out how much needs to be taken away (the subtrahend).
• The result after subtraction is the difference.

In mathematical expressions enclosed in parentheses, subtraction is usually simplified first. In our example, the expression \(-2 - 3\) results in \(-5\), demonstrating how subtraction is used to combine values by reducing the overall quantity.

Exploring Multiplication

Multiplication is a powerful arithmetic operation that involves combining groups of equal amounts. It's essential when working with expressions that include multiplication outside or inside parentheses.

To understand multiplication, remember this process:

• Identify the numbers you need to multiply, known as factors.
• Combine multiples of one factor by the other.
• The result is called the product.

In expressions involving the order of operations, multiplication comes after simplifying within parentheses and before addition or subtraction. For example, in the expression \(-10(-2 - 3)\), we first simplified within parentheses to get \(-5\). Then, multiplying by \(-10\) utilizes multiplication rules, resulting in a positive product of \50\, since multiplying two negative numbers yields a positive number.