Problem 25 - Algebra A Combined Function

Question

Simplify each expression. $$ 18 \div 3 \cdot 2 $$

Step-by-Step Solution

Answer

The simplified expression is 12.

Step 1: Identify the Order of Operations

The expression given is \(18 \div 3 \cdot 2\). According to the order of operations (PEMDAS/BODMAS), division and multiplication are performed from left to right.

Step 2: Perform the Division

Start with the division operation since it appears first when moving from left to right. Divide 18 by 3.\[ 18 \div 3 = 6 \]

Step 3: Perform the Multiplication

Now, take the result of the division (6) and multiply it by 2.\[ 6 \cdot 2 = 12 \]

Key Concepts

Division in Algebra

When you see an expression like \(18 \div 3 \cdot 2\), it’s important to handle operations in a specific order. According to the order of operations, division and multiplication are performed from left to right. The rule is often remembered with the acronym PEMDAS/BODMAS. Here, we focus on the division first.

To divide in algebra, take your dividend (the number being divided) and your divisor (the number you are dividing by). In this case:

• Dividend: 18
• Divisor: 3

Perform the division operation:
18 divided by 3 gives us 6. This part of the expression is now simplified to 6. Scholars must ensure accuracy here because the result of this division influences subsequent operations.

Multiplication in Algebra

After simplifying the division, your next task in the expression \(18 \div 3 \cdot 2\) is to multiply. The multiplication here comes after division based on the order of operations, which involves multiplying left to right as you proceed across the expression.

Now that we have simplified the division part to 6, we multiply 6 by 2. Multiplication in algebra is straightforward:

• Multiplicand: The result from the division, which is 6
• Multiplier: 2

Multiply these values:
6 times 2 equals 12. Thus, the algebra expression is now completely simplified to 12 after performing multiplication.

Simplifying Expressions

Simplifying expressions like \(18 \div 3 \cdot 2\) is essentially about following the correct order of operations and ensuring each step is processed accurately. The goal is to reduce the expression to its simplest form while ensuring all mathematical rules are respected.

Here are some tips for simplifying expressions:

• Perform operations in the order determined by PEMDAS/BODMAS, i.e., Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
• Keep track of your results at every step. Writing things down may help maintain clarity.
• After each step, reassess the expression to ensure that no errors were made before proceeding.

In this scenario, simplifying has turned the original complex expression into just the number 12, which succinctly summarizes the operation performed.