Correct Answer
Explanation
According to the order of operations, multiplication is done before addition. So, in the expression 5 plus 7 times 8, \( 5 + 7 \times 8, \) you first calculate the product of 7 and 8, which is 56, and then add 5, resulting in 5 plus 56 equals 61. \( 5 + 56 = 61. \) The expression represents "5 more than the product of 7 and 8."
In the expression 5 times 7 plus 8 \( 5 \times 7 + 8, \) you do the multiplication first as well. So, you calculate the product of 5 and 7, which is 35, and then add 8, resulting in 35 plus 8 equals 43. \( 35 + 8 = 43. \) This shows that the expression represents "8 more than the product of 5 and 7."
In the expression 5 times open parenthesis 7 plus 8 close parenthesis \( 5 \times (7 + 8), \) the parentheses tell you to perform the addition first because parentheses take priority in the order of operations. So, you first calculate the sum of 7 and 8, which is 15, and then multiply that by 5, resulting in 5 times 15 equals 75. \( 5 \times 15 = 75. \) The parentheses are used to group 7 and 8 together, ensuring that you calculate the sum before multiplying, which is why the expression represents "5 times the sum of 7 and 8."
In the expression open parenthesis 5 plus 7 close parenthesis times 8, \( (5 + 7) \times 8, \) the parentheses indicate that you should perform the addition first. So, you calculate the sum of 5 and 7, which is 12, and then multiply that by 8, resulting in 12 times 8 equals 96. \( 12 \times 8 = 96. \) The parentheses are needed to ensure that the sum of 5 and 7 is calculated before multiplying by 8, which is why the expression represents "8 times the sum of 5 and 7."