Problem 81 - Prealgebra

Question

Perform the indicated operations. $$(6 \cdot 3) \div 2$$

Step-by-Step Solution

Answer

The result of the operation is 9.

Step 1: Perform the Multiplication

Begin solving the expression inside the parentheses. You have \(6 \cdot 3\), which means you must multiply 6 by 3.\[6 \cdot 3 = 18\]

Step 2: Divide the Result

Now take the result from Step 1, which is 18, and divide it by 2 as indicated by the expression.\[18 \div 2 = 9\]

Key Concepts

Order of Operations

The order of operations is a fundamental principle in mathematics used to determine the sequence in which operations should be performed in a mathematical expression. It is vital because performing operations out of order can lead to incorrect results.
The commonly used acronym to remember the order is PEMDAS:

• Parentheses - First, do calculations that are inside parentheses.
• Exponents - Next, calculate exponents or powers.
• Multiplication - From left to right. This has the same priority as division.
• Division - Also from left to right. Same level as multiplication.
• Addition - From left to right. Same level as subtraction.
• Subtraction - From left to right.

In our exercise, we see the operation \((6 \cdot 3) \div 2\).
According to the order of operations, solve any tasks inside parentheses first, which lead us to multiply, then move onto division.

Multiplication

Multiplication is one of the four basic arithmetic operations, representing the "times" process. It is a short-hand way of adding the same number multiple times.
For instance, think of multiplication as groups of items.
If you have 6 groups of 3 apples, instead of adding 3 six times, you can multiply:
\(6 \cdot 3\).
To multiply, you calculate how many items there are in total in all the groups, leading to the result of 18.
Multiplication is often shown with the symbol \(\cdot\) or simply as adjacent numbers.In our exercise:
We have \(6 \cdot 3\), which simplifies by multiplying 6 by 3, resulting in 18.
After completing this, it's essential to check if more operations need to be conducted, such as division, as seen in our next step.

Division

Division is another fundamental arithmetic operation. It can be seen as distributing a number into equal parts.
Think of it as sharing or grouping. If you have 18 candies and want to share them equally between 2 friends, you would use division.
To divide, you determine how many times the divisor (the number you're dividing by) fits into the dividend (the number being divided). The result is known as the quotient.
In mathematical terms, for the expression \(18 \div 2\), you ask:"How many times does 2 fit into 18?"
The answer is 9, which is the quotient of this division.In our exercise:After finding the result 18 from the multiplication, we divide it by 2 as the expression indicates. This step ensures we follow through the order of operations and conclude precisely, resulting in an exact answer of 9.