Answer :
Sure! Let's go through the problem step-by-step to determine the correct answer.
Mary's problem was:
[tex]\[ 57 - 6^2 + (10 + 2) \][/tex]
To solve this, we'll follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
1. Parentheses: First, evaluate the expression inside the parentheses.
[tex]\[ 10 + 2 = 12 \][/tex]
So, the expression becomes:
[tex]\[ 57 - 6^2 + 12 \][/tex]
2. Exponents: Next, evaluate the exponent.
[tex]\[ 6^2 = 36 \][/tex]
Now the expression is:
[tex]\[ 57 - 36 + 12 \][/tex]
3. Addition and Subtraction: Finally, perform the addition and subtraction from left to right.
- First do the subtraction:
[tex]\[ 57 - 36 = 21 \][/tex]
- Then add the remaining number:
[tex]\[ 21 + 12 = 33 \][/tex]
So, the correct value should be [tex]\( 33 \)[/tex].
Now let's match this with the provided statements:
1. It is wrong because [tex]\(57 - 48\)[/tex] is 11:
- This statement refers to a subtraction step that is not present in the correct approach. The subtraction in the correct steps is [tex]\( 57 - 36 = 21 \)[/tex], not [tex]\( 57 - 48 \)[/tex].
2. It is wrong because the subtraction should have been done before the addition:
- This statement misunderstands the order of operations. The subtraction and addition were done correctly from left to right in the last step.
3. It is wrong because [tex]\(6^2\)[/tex] is 12:
- This statement is incorrect because [tex]\( 6^2 \)[/tex] is actually 36, not 12.
4. It is correct:
- This statement is incorrect because Mary’s final answer was 9, which doesn't match the correct value of 33.
Therefore, the most accurate statement is:
It is wrong because [tex]\(57 - 48\)[/tex] is 11.
Mary's problem was:
[tex]\[ 57 - 6^2 + (10 + 2) \][/tex]
To solve this, we'll follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
1. Parentheses: First, evaluate the expression inside the parentheses.
[tex]\[ 10 + 2 = 12 \][/tex]
So, the expression becomes:
[tex]\[ 57 - 6^2 + 12 \][/tex]
2. Exponents: Next, evaluate the exponent.
[tex]\[ 6^2 = 36 \][/tex]
Now the expression is:
[tex]\[ 57 - 36 + 12 \][/tex]
3. Addition and Subtraction: Finally, perform the addition and subtraction from left to right.
- First do the subtraction:
[tex]\[ 57 - 36 = 21 \][/tex]
- Then add the remaining number:
[tex]\[ 21 + 12 = 33 \][/tex]
So, the correct value should be [tex]\( 33 \)[/tex].
Now let's match this with the provided statements:
1. It is wrong because [tex]\(57 - 48\)[/tex] is 11:
- This statement refers to a subtraction step that is not present in the correct approach. The subtraction in the correct steps is [tex]\( 57 - 36 = 21 \)[/tex], not [tex]\( 57 - 48 \)[/tex].
2. It is wrong because the subtraction should have been done before the addition:
- This statement misunderstands the order of operations. The subtraction and addition were done correctly from left to right in the last step.
3. It is wrong because [tex]\(6^2\)[/tex] is 12:
- This statement is incorrect because [tex]\( 6^2 \)[/tex] is actually 36, not 12.
4. It is correct:
- This statement is incorrect because Mary’s final answer was 9, which doesn't match the correct value of 33.
Therefore, the most accurate statement is:
It is wrong because [tex]\(57 - 48\)[/tex] is 11.
