Problem 48 - Prealgebra

Question

Use any of the rules developed in this chapter and the rule for order of operations to simplify each of the following expressions as much as possible. [Examples 6–9] $$-500 \div 50 \div 10$$

Step-by-Step Solution

Answer

The simplified expression is \(-1\).

Step 1: Evaluate the First Division

First, simplify the expression by performing the division from left to right as per order of operations. Start by evaluating the division of \(-500\) and \(50\). - Calculation: \(-500 \div 50 = -10\).

Step 2: Evaluate the Second Division

Next, use the result of the first division to perform the next division with \(10\). - Calculation: \(-10 \div 10 = -1\).

Key Concepts

Understanding Division

Division is one of the basic arithmetic operations. It involves splitting a number into equal parts. When we divide, we are essentially asking: how many times does one number fit into another? To solve a division problem, you need to know:

• The dividend (the number you are dividing up) and
• The divisor (the number you are dividing by).

For example, in the expression \(-500 \div 50\), the dividend is \(-500\) and the divisor is \(50\). When you divide, it's crucial to apply the operation from left to right, especially in expressions with multiple division signs, following the order of operations.

Simplifying Expressions

Simplifying expressions means reducing them to their simplest form. This makes the expression easier to understand or solve.

In the context of arithmetic operations, especially involving division, the goal is to perform calculations step by step and reduce complex expressions into a single number.

• Always begin by addressing division and multiplication before moving on to addition and subtraction, according to the order of operations (PEMDAS/BODMAS).
• Handle any negative signs carefully, as these can change the direction of the inequality or the overall sign of the result.

By simplifying \(-500 \div 50 \div 10\), we follow this structured approach to reach a simple result without losing accuracy.

Step-by-Step Solutions

Understanding step-by-step solutions is crucial for learning how to tackle math problems efficiently. Breaking down problems into smaller, more manageable parts helps in understanding each operation's role and ensures that nothing is overlooked.

Let's look at the expression \(-500 \div 50 \div 10\):
1. **Step 1:** Evaluate the first division by dividing \(-500\) by \(50\), which results in \(-10\).
2. **Step 2:** Use the result from Step 1. Divide \(-10\) by \(10\) to obtain the final result, which is \(-1\).

Each step builds on the previous one, ensuring that the solution is accurate and each operation is performed in the correct order.