- The commutative property is represented by A. \(5+3=3+5\).
- The value \(0.393701\) rounded to the nearest thousandth is \(0.394\) and to the nearest hundredth is \(0.39\).
- The solution to \(3x = 84\) is \(x = 28\).
- Rounding \(\$0.368333\) to the nearest cent results in \(\$0.37\).
- Final answers: \(\boxed{A}\), \(\boxed{0.394, 0.39}\), \(\boxed{28}\), \(\boxed{\$0.37}\).
Explanation
- Identify the Commutative Property
- The first problem asks us to identify the commutative property of real numbers. The commutative property states that the order in which we add or multiply two numbers does not change the result: \(a + b = b + a\) and \(a \cdot b = b \cdot a\).
- Option A: \(5 + 3 = 3 + 5\). This fits the definition \(a + b = b + a\).
- Option B: \(5(6 + 7) = 5(6) + 5(7)\). This is the distributive property.
- Option C: \(\left(\frac{1}{2} + \frac{1}{3}\right) + \frac{1}{4} = \frac{1}{2} + \left(\frac{1}{3} + \frac{1}{4}\right)\). This is the associative property.
- Option D: \(-5 + 0 = -5\). This is the identity property of addition.
Thus, the correct statement is A.
- Rounding Decimals
- The second problem asks to round \(0.393701\) to the nearest thousandth and hundredth.
- To round to the nearest thousandth (three decimal places), we look at the fourth decimal digit, which is 7. Since 7 is 5 or greater, we round the third digit (3) up to 4. Result: \(0.394\).
- To round to the nearest hundredth (two decimal places), we look at the third decimal digit, which is 3. Since 3 is less than 5, we keep the second digit (9) as is. Result: \(0.39\).
- Solving a Linear Equation
- The third problem asks to solve \(3x = 84\) for \(x\).
- We divide both sides of the equation by 3 to isolate \(x\):
\[x = \frac{84}{3} = 28\]
The value of \(x\) is 28.
- Rounding Money to the Nearest Cent
- The fourth problem asks to round the cost of an ice cream bar (\(\$0.368333\)) to the nearest cent (the hundredths place).
- We look at the third decimal digit (the thousandths place), which is 8.
- Since 8 is 5 or greater, we round the hundredths digit (6) up to 7.
- Therefore, the cost per bar is \(\$0.37\).
Examples
Understanding these basic arithmetic properties and rounding techniques is essential for everyday tasks. For example, identifying the commutative property helps in simplifying complex mental math expressions, while rounding is vital when handling financial transactions, managing budgets, or converting units like centimeters to inches during home improvement projects or craft work. Mastery of these fundamentals ensures accuracy in both academic and practical environments.