Problem 65 - Elementary Algebra

Question

Perform the operations. $$ -44 / 11 * 2 $$

Step-by-Step Solution

Answer

The result of the operation is -8.

Step 1: Perform Division

Start with the given expression \(-44 / 11 * 2\).First, perform the division operation. Divide \(-44\) by \(11\).\[-44 / 11 = -4\]

Step 2: Multiply the Result

Next, take the result from the division which is \(-4\) and multiply it by \(2\).\[-4 * 2 = -8\]

Key Concepts

Division

Division is the process of splitting a number into equal parts. Imagine dividing a chocolate bar among friends. You would break it into pieces so everyone gets an equal share. In our expression, we start with \[-44 / 11\] . The goal is to divide \(-44\) into \(11\) equal parts.

• Divide each part by the divisor: In simpler terms, think about how many times \(11\) can fit into \(-44\)
• Since \(-44\) is negative, the result will be negative. Keep this in mind: dividing a negative by a positive gives a negative result.

Calculating, we find that \(-44 / 11 = -4\). This means \(11\) fits into \(-44\) exactly \(-4\) times. This step is crucial before moving on to multiplication.

Multiplication

Multiplication can be thought of as repeated addition. For example, multiplying \(3 \times 2\) is like adding \(3+3\), which equals \(6\).

After solving the division in our expression, we multiply the result, \(-4\), by \(2\). This is calculated as: \[-4 \times 2\]

• If one number is negative and the other is positive, the result will be negative.
• Consider it as adding \(-4\) twice. So, \(-4 + (-4) = -8\).

Multiplication, when involving a negative number, changes the sign of the result. So \(-4 \times 2 = -8\). This concept is fundamental in mathematics.

Order of Operations

The Order of Operations is a set of rules that determines the order in which calculations should be performed. This is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Multiplication and division are performed from left to right.
• In our expression \(-44 / 11 * 2\), we follow this rule: perform division before multiplication.

So, we first divide: \(-44 / 11 = -4\), and then multiply: \(-4 \times 2 = -8\). Following the correct order ensures that we get an accurate result. Understanding this order prevents mistakes and is essential for solving math problems correctly.