Question

The value of the expression \(4+5 \cdot 6-3\) is________.

Short answer

The value of the expression is 31.

Step-by-step solution

Apply the Order of Operations

Use the order of operations (PEMDAS/BODMAS) to solve the expression. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Perform Multiplication

According to the order of operations, address the multiplication part of the expression first: \(5 \times 6 = 30\). Now replace the original expression with this result: \(4 + 30 - 3\).

Perform Addition

Next, perform the addition part of the expression: \(4 + 30 = 34\). Replace the expression with this result: \(34 - 3\).

Perform Subtraction

Finally, perform the subtraction: \(34 - 3 = 31\).

Key concepts

PEMDAS

The order of operations in mathematics is crucial to solving arithmetic expressions correctly. In the United States, we use the acronym PEMDAS to remember this order. It stands for Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
This order is important because it dictates the sequence in which you perform calculations to get the correct result. For example:

• Always solve operations inside parentheses first.
• Next, calculate any exponents.
• After that, do multiplication and division from left to right.
• Lastly, perform addition and subtraction from left to right.

Understanding and applying PEMDAS ensures you solve expressions as intended and avoid common mistakes.

BODMAS

BODMAS is another acronym similar to PEMDAS, commonly used in countries like the UK and India. It stands for Brackets, Orders, Division and Multiplication, Addition and Subtraction.
This method also helps in remembering the correct sequence of operations in arithmetic expressions:

• Brackets first, which include parentheses and other grouping symbols.
• Orders, which means dealing with exponents and roots.
• Division and multiplication from left to right.
• Addition and subtraction from left to right.

While PEMDAS and BODMAS use different terms, they guide you through solving expressions step-by-step to get a correct answer. It’s essential to stick to this order to avoid errors in your calculations.

Arithmetic Expressions

An arithmetic expression is a mathematical phrase that includes numbers, operators, and sometimes parentheses. These expressions can include operations like addition, subtraction, multiplication, and division.
For example, in the expression given in the problem, 4 + 5 * 6 - 3, you must perform operations in the right order to get the correct result. Using PEMDAS/BODMAS will help you simplify and solve these expressions easily and correctly.
Here are few key points about arithmetic expressions:

• An arithmetic expression can have one or more operations.
• Parentheses can change the order of operations by grouping certain parts together.
• Correct order of operations ensures accurate results.

Once you understand and apply these rules, handling arithmetic expressions becomes straightforward.

Mathematical Operations

Mathematical operations are basic processes you perform on numbers, such as addition, subtraction, multiplication, and division. Understanding these operations and their sequence is fundamental in solving arithmetic expressions.
Let's look at each operation briefly:

• Addition (+): Combines two numbers into a larger number. For example, 4 + 5 = 9.
• Subtraction (-): Takes one number away from another. For example, 9 - 3 = 6.
• Multiplication (* or x): Combines multiple groups of a number. For example, 5 * 6 = 30.
• Division (/): Splits a number into equal parts. For example, 30 / 5 = 6.

Each of these operations plays a critical role in solving expressions. When combined correctly, they form the foundation of many mathematical concepts.
Applying the right order ensures we solve expressions like 4 + 5 * 6 - 3 correctly, leading to accurate and reliable results.