The question involves understanding the order of operations and the use of parentheses in mathematical expressions. To solve the given equation for it to equal 25, parentheses must be added to change the order in which operations are performed. According to the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), multiplication is performed before addition and subtraction. However, with the proper placement of parentheses, we can alter this order.
To solve this equation: 7+9×3−1=25, we notice that 9×3 equals 27, and if we subtract 1, and then add 7, we do not arrive at 25. Thus, we need to group the terms in a way that allows for a different operation to be performed first. If we put parentheses around (7+9), we get the following expression: (7+9)×3-1. Now, we calculate inside the parentheses first: 16×3 = 48, then subtract 1 to get 47 which is not equal to 25. This indicates that we need a different placement of parentheses.
Considering the need to arrive at 25, the correct placement of parentheses would be to group 9×3 together like this: 7+(9×3)-1. However, this also does not help as it results in the same calculation as without parentheses. We need to place parentheses such that the result is 25. We can achieve this by putting parentheses like so: 7+9×(3-1). This gives us the expression 7+9×2, which simplifies to 7+18 and finally equals 25.
Placing parentheses around 3 − 1 in the equation 7 + 9 × 3 − 1 leads to a result of 25. This changes the order of operations, allowing for the correct calculations to be performed. Therefore, the modified expression is 7 + 9 × ( 3 − 1 ) = 25 .
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