Embark on a mathematical journey to decipher which expression is equivalent to 486 9 6 33 2. This exploration delves into the intricacies of mathematical operations, equivalent expressions, and the art of simplification, unraveling the mysteries behind this enigmatic expression.
Our quest begins by dissecting the mathematical operations embedded within 486 9 6 33 2, establishing the order of precedence that governs their evaluation. We will then embark on a step-by-step solution, unraveling the expression’s true value and revealing its hidden equivalence.
Understanding the Expression: Which Expression Is Equivalent To 486 9 6 33 2
The expression “486 9 6 33 2” represents a mathematical calculation involving the following operations:
- 486 divided by 9 (486 ÷ 9)
- The result of the previous operation (486 ÷ 9) multiplied by 6 (6 × (486 ÷ 9))
- The result of the previous operation (6 × (486 ÷ 9)) subtracted by 33 (6 × (486 ÷ 9) – 33)
- The result of the previous operation (6 × (486 ÷ 9) – 33) multiplied by 2 (2 × (6 × (486 ÷ 9) – 33))
The order of operations should be followed as per the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Equivalent Expressions
To evaluate the expression “486 9 6 33 2”, we follow the order of operations:
- 486 ÷ 9 = 54
- 6 × 54 = 324
- 324
33 = 291
- 2 × 291 = 582
Therefore, the value of the expression “486 9 6 33 2” is 582.
Other equivalent mathematical expressions that yield the same result as “486 9 6 33 2” include:
- 54 × 6 – 33 × 2
- 324 – (33 × 2)
- 2 × (324 – 33)
Simplifying the Expression
The expression “486 9 6 33 2” can be simplified using mathematical properties:
- Associative property of multiplication:(a × b) × c = a × (b × c)
- Distributive property of multiplication over subtraction:a × (b
- c) = a × b
- a × c
Applying these properties, we can simplify the expression as follows:
- 486 9 6 33 2
- = 486 × (9 × 6) – 33 × 2
- = 486 × 54 – 33 × 2
- = 26244 – 66
- = 26178
Therefore, the simplified expression is 26178.
Applications and Examples
Understanding the equivalence of mathematical expressions is important in various fields:
- Finance:Simplifying complex financial formulas to make them easier to understand and calculate.
- Science:Converting units of measurement and deriving equations for scientific models.
- Engineering:Solving complex engineering problems involving multiple variables and equations.
For example, in finance, the expression “PV = FV / (1 + r)^n” can be simplified to “PV = FV × (1 – (1 + r)^-n) / r” using the formula for the present value of an annuity.
Expert Answers
What is the first step in evaluating the expression 486 9 6 33 2?
The first step is to identify the mathematical operations and their order of precedence. In this case, the order is exponentiation, multiplication, and subtraction.
How can we simplify the expression 486 9 6 33 2?
Using the order of operations, we can simplify the expression as follows: 486^9 = 4.951044e+15, 4.951044e+15 – 6 = 2.9706264e+16, 2.9706264e+16 – 33 = 2.9706261e+16,
2.9706261e+16 / 2 = 1.4853131e+16.
