Question

a. Explain why the result of \(72 \div 8+4\) is 13 . b. Explain why the result of \(72 \div(8+4)\) is 6 .

Short answer

Question: Explain the difference in the results of the arithmetic expressions 72 ÷ 8 + 4 and 72 ÷ (8 + 4) using the order of operations. Answer: The difference in the results of these two arithmetic expressions is due to the order of operations determined by the presence of parentheses. In the first expression, 72 ÷ 8 + 4, we follow the basic order of operations and first perform the division (72 ÷ 8 = 9) and then addition (9 + 4 = 13), resulting in a final answer of 13. In the second expression, 72 ÷ (8 + 4), parentheses indicate that addition is performed first (8 + 4 = 12), followed by division (72 ÷ 12 = 6), resulting in a final answer of 6.

Step-by-step solution

Expression 1: 72 ÷ 8 + 4

In this expression, we are given the operations to perform, but without any parentheses to determine the order in which to perform them. To handle this situation, we will apply the basic order of operations, which is: 1. Perform any calculations inside parentheses. 2. Calculate exponents. 3. Perform multiplication and division from left to right. 4. Perform addition and subtraction from left to right. Using this, let's perform the mathematical operations step by step: 1. 72 ÷ 8: Since there are no parentheses or exponents in this expression, we perform the division first. \(72 \div 8 = 9\) 2. 9 + 4: Now, the remaining operation is addition. \(9 + 4 = 13\) So, the result of the expression \(72 \div 8+4\) is 13.

Expression 2: 72 ÷ (8 + 4)

In this expression, we have parentheses to guide us to the operations' order. We must also use the basic order of operations described earlier, which says that calculations inside parentheses are performed first. 1. (8 + 4): Perform the addition within the parentheses first. \(8 + 4 = 12\) 2. 72 ÷ 12: Now, we perform division. \(72 \div 12 = 6\) So, the result of the expression \(72 \div (8+4)\) is 6. The difference between these two expressions is mainly due to the parentheses, which affect the operations' order in arithmetic expressions.