Question

Tell whether each expression was evaluated correctly using the order of operations. If not, give the correct result. \(54-27 \div 3=45\)

Short answer

The expression was evaluated correctly using the order of operations.

Step-by-step solution

Understand the Order of Operations

The order of operations, also known as PEMDAS/BODMAS, dictates the sequence in which operations should be performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Identify the Operations in the Expression

The given expression is \[54 - 27 \div 3 = 45\] . The operations involved are subtraction and division.

Perform the Division First

According to the order of operations, division comes before subtraction. So, first perform the division: \[ 27 \div 3 = 9\]

Perform the Subtraction

Next, perform the subtraction using the result from the division: \[54 - 9 = 45\]

Compare to the Given Result

The final result is 45, which matches the given result in the expression. Therefore, the expression was evaluated correctly.

Key concepts

Understanding PEMDAS

PEMDAS is a helpful acronym to remember the order of operations in math. It stands for Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction (from left to right). This order is crucial because it dictates how to solve an expression correctly.
If you don’t follow PEMDAS, you might get the wrong answer. For example:

• First, solve any operations inside Parentheses.
• Next, handle Exponents.
• Then, move on to Multiplication and Division in the order they appear from left to right.
• Finally, perform Addition and Subtraction in the order they appear from left to right.

Following these steps ensures you find the correct result for any arithmetic expression.

Mastering Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. These operations are the building blocks of most mathematical calculations.
When dealing with multiple operations, it’s important to know which one to perform first. This is where the order of operations, PEMDAS, comes into play.

• Addition combines two or more numbers to get a sum.
• Subtraction takes one number away from another to find the difference.
• Multiplication involves multiplying numbers to get a product.
• Division splits a number into equal parts to find the quotient.

Understanding and mastering these operations is essential for solving more complex math problems correctly.

Focusing on Division

Division is one of the core operations in arithmetic. It’s about finding out how many times one number is contained within another. The number being divided is called the dividend, and the number by which you divide is the divisor. The result is known as the quotient.
For example, in the expression 27 ÷ 3 = 9, 27 is the dividend, 3 is the divisor, and 9 is the quotient.
According to PEMDAS, division should be done before subtraction when they appear in the same expression. This ensures that the calculations are accurate.
In the given exercise, we first divide 27 by 3 to get 9, and then subtract the result from 54. This ensures we follow the correct order of operations.

Clarifying Subtraction

Subtraction is the process of finding the difference between two numbers. It’s one of the basic arithmetic operations and is symbolized by the minus sign (-).
When you subtract, you remove a certain amount from a total. For example, in the expression 54 - 9 = 45, you are taking 9 away from 54, which leaves you with 45.
In the order of operations, subtraction is performed after division and before addition if they appear together. This means that in an expression like 54 - 27 ÷ 3, you would first perform the division (27 ÷ 3) to get 9, and then subtract 9 from 54 to get the final result.
Mastering subtraction is crucial for solving not only standalone problems but also more complex expressions where multiple operations are involved.