solve the following: 523 + 523 × 523 ÷ 523
1046
Solving the Mathematical Expression: 523 + 523 × 523 ÷ 523
To solve a mathematical expression like this one, we need to follow a specific set of rules known as the order of operations. This ensures that everyone gets the same answer when evaluating the same expression.
Understanding the Order of Operations (BODMAS/PEMDAS)
The order of operations is commonly remembered using acronyms like BODMAS or PEMDAS.
- BODMAS: Brackets, Orders (powers, square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
- PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
In our expression, $523 + 523 \times 523 \div 523$, we have addition, multiplication, and division. According to the order of operations, multiplication and division should be performed before addition. Multiplication and division are at the same level of precedence, so we perform them from left to right.
Step-by-Step Solution for 523 + 523 × 523 ÷ 523
Let's evaluate the expression step by step:
The expression is: $$523 + 523 \times 523 \div 523$$
Following BODMAS/PEMDAS, we first look at the multiplication and division parts, working from left to right.
First, we encounter the multiplication: $523 \times 523$.
Next, we have the division: $523 \div 523$. This operation comes after the multiplication in the combined multiplication/division sequence $523 \times 523 \div 523$. Within this sequence, we work from left to right.
Let's look at the sequence $523 \times 523 \div 523$. We perform the operations from left to right:
- Calculate $523 \times 523$: $$523 \times 523 = 273529$$
- Now the expression is $523 + 273529 \div 523$.
- Next, perform the division: $273529 \div 523$: $$273529 \div 523 = 523$$
- Now the expression simplifies to $523 + 523$.
Alternatively, consider the sequence $523 \times 523 \div 523$. Since multiplication and division have equal precedence, we work from left to right. However, a simpler way to look at $523 \times 523 \div 523$ is recognising that dividing by 523 after multiplying by 523 effectively cancels out the multiplication, leaving the original number (523). $$523 \times 523 \div 523 = 523 \times \frac{523}{523} = 523 \times 1 = 523$$ So, the entire multiplication and division part evaluates to 523.
The expression now becomes:
$$523 + 523$$Finally, perform the addition:
$$523 + 523 = 1046$$The result of the expression $523 + 523 \times 523 \div 523$ is 1046.
Revision Table: Key Concepts for Solving Expressions
| Concept | Explanation | How it Applies Here |
|---|---|---|
| Order of Operations | Rules (BODMAS/PEMDAS) dictating the sequence of operations in an expression. | Ensures multiplication/division are done before addition. |
| Precedence | The priority of operators (e.g., × and ÷ have higher precedence than +). | × and ÷ are evaluated before +. |
| Left-to-Right Rule | For operators of the same precedence (like × and ÷), evaluate from left to right. | $523 \times 523 \div 523$ is evaluated as $(523 \times 523) \div 523$. |
Additional Information on Operator Precedence
Operator precedence is a fundamental concept in mathematics and programming languages. It defines the order in which operators are applied to their operands. Understanding precedence rules is crucial for correctly interpreting and evaluating complex expressions.
Operators with higher precedence are evaluated before operators with lower precedence. When operators have the same precedence, their associativity (usually left-to-right or right-to-left) determines the order of evaluation. For multiplication and division, and for addition and subtraction, the associativity is typically left-to-right.
In our example, the multiplication and division operators have the same precedence and are evaluated from left to right before the addition operator.
Important Questions from Bodmas Rule
The value of 30 ÷ 6 × 5 of (2 + 3) - 12(3 × 2) is equal to:
The value of 96 - 4 of (18 - 13) + 4 × 7 is:
Find the value of 45 - 3 × (4 of 6 + 12 ÷ 3 × 6 - 4 × 5) + 6.
What is the value of
5 ÷ 10 of 10 × 4 + 4 ÷ 4 of 4 × 10 + (10 - 4) ÷ 16 × 4?
The value of \(\frac{{33}}{{40}} + \frac{1}{5}\left[ {\frac{4}{5} - \frac{1}{5} \times \left( {\frac{7}{8} - \frac{5}{4}} \right)} \right] - \frac{4}{5}\) is:
