Ethereum: How does multiplication and division by density work?

Ethereum: How Multiplication and Division Work in Solidity

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In Solidity, the order of operations is crucial for accurate calculations. Two common arithmetic operations that can lead to confusion are multiplication and division. In this article, we’ll explore how these operations work in Solidity, specifically focusing on how they’re calculated.

Precedence and Order of Operations

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Solidity follows a specific precedence rule when it comes to arithmetic operations:

• Parentheses: Evaluate expressions inside parentheses first.

• Exponents (e.g., **): Evaluate any exponents next.

• Multiplication and Division (e.g., 2 * 3): The order is multiplication before division.

• Addition and Subtraction (e.g., 5 + 3): The order is addition before subtraction.

Let’s examine the example you provided:

Amount = (15-10)  10 / 15  (10000 - 5000) / 10000;

Breaking down this expression, we can follow the precedence rules:

• Evaluate expressions inside parentheses: (15-10) and (10000 - 5000)

* 15-10 = 5 (exponentiation not applicable)

* 10000 - 5000 = 5000 (exponentiation not applicable)

• Multiply 5 by 10: 5 * 10 = 50

• Divide 50 by 15: 50 / 15 = 3.333... (division is not exact due to floating-point arithmetic)

• Finally, multiply the result by (5000 / 10000): (3.333...) * (5) = 16.666...

So, the correct calculation should indeed be:

Amount = 50 / 15 * 5000 / 10000;

Not 5 * 10 / 15.

Common Mistakes

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To avoid common mistakes when working with arithmetic operations in Solidity:

• Always evaluate expressions inside parentheses first.

• Be mindful of exponents (e.g., **) and ensure you’re performing the operation correctly.

• When dividing, use floating-point arithmetic to avoid issues due to integer division.

Best Practices

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To write accurate and efficient Solidity code:

• Use parentheses to group operations for clarity.

• Follow the order of precedence rules carefully.

• Be aware of exponentiation (e.g., **) when performing calculations involving large numbers or exponential growth.

By understanding how multiplication and division work in Solidity, you’ll be able to write more accurate and reliable smart contracts that take advantage of the language’s unique features.

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