determine where grouping symbols should be placed so that the value of the expression shown below is 4. Justify your answer.
40-28/4+3*9
To determine where grouping symbols should be placed in the expression 40 - 28 / 4 + 3 * 9 to get a value of 4, we can follow the order of operations (also known as PEMDAS) to simplify the expression step by step.
1. Parentheses: Evaluate any expressions inside parentheses first. Since there are no parentheses in the original expression, we move to the next step.
2. Exponents: Evaluate any exponentiation operations. There are no exponents in the original expression.
3. Multiplication and Division: Perform any multiplication and division from left to right.
Let's consider the division first:
40 - 28 / 4 + 3 * 9
= 40 - 7 + 3 * 9
Now, perform the multiplication:
= 40 - 7 + 27
4. Addition and Subtraction: Finally, perform any addition and subtraction from left to right.
= 33 + 27
= 60
Now, since the expression evaluated to 60 and not 4, we need to try placing grouping symbols in different positions to achieve the desired result.
If we place parentheses around the division operation, we get:
40 - (28 / 4) + 3 * 9
Now let's evaluate the expression again:
= 40 - (7) + 3 * 9
= 40 - 7 + 27
= 60
Placing parentheses around the division operation did not give us the desired result of 4.
Next, let's try placing parentheses around the multiplication operation:
40 - 28 / 4 + (3 * 9)
Evaluating the expression:
= 40 - 28 / 4 + (27)
= 40 - 7 + 27
= 60
Again, placing parentheses around the multiplication operation did not give us the desired result.
Since there are no other operations left to consider, and we have tried placing parentheses around both the division and multiplication operations without success, it is not possible to obtain a value of 4 in the expression 40 - 28 / 4 + 3 * 9 by rearranging the grouping symbols.