How to Balance the Scales: Inequalities in Decimal Addition and Subtraction
Inequalities are mathematical expressions that describe the relationship between two quantities. When working with decimals, inequalities can help us understand which of two quantities is larger or smaller, or if they are equal. Let's explore how to approach inequalities involving decimal addition and subtraction.
Key Symbols:
– \(<\): Less than
– \(>\): Greater than
– \(=\): Equal to
– \(\geq\): Greater than or equal to
– \(\leq\): Less than or equal to
Inequalities in Decimal Addition and Subtraction
Example 1: Evaluating an Addition Inequality
Is \(2.45 + 3.56 > 6\)?
Solution Process:
Add the decimals: \(2.45 + 3.56 = 6.01\).
Since \(6.01 > 6\), the inequality is true.
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Example 2: Evaluating a Subtraction Inequality
Is \(7.89 – 4.44 < 3.5\)?
Solution Process:
Subtract the decimals: \(7.89 – 4.44 = 3.45\).
Since \(3.45 < 3.5\), the inequality is true.
Inequalities involving decimal addition and subtraction provide a deeper understanding of the relationships between quantities. By evaluating these inequalities, you can determine the relative sizes of different quantities, helping you make informed decisions and comparisons. Whether you’re comparing expenses, distances, or any other decimal values, understanding inequalities is a crucial skill. With practice, you’ll become adept at quickly evaluating and interpreting these relationships, making you a master of decimal dynamics!
Practice Questions:
1. Determine if \(3.56 + 4.45 > 8\).
2. Evaluate if \(9.01 – 5.67 < 3.5\).
3. Is \(2.34 + 5.67 \leq 8.01\)?
4. Determine if \(8.90 – 4.45 \geq 4.5\).
5. Evaluate if \(4.56 + 2.34 > 7\).
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Answers:
1. True (\(3.56 + 4.45 = 8.01\))
2. True (\(9.01 – 5.67 = 3.34\))
3. True (\(2.34 + 5.67 = 8.01\))
4. True (\(8.90 – 4.45 = 4.45\))
5. False (\(4.56 + 2.34 = 6.90\))
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