Sure! Let's break down the problem and apply parentheses strategically to make the expression equal to 43.
Given the expression:
[tex]\[ 32.6 \div 10 - 5 \times 8 - 9.16 \][/tex]
We need to introduce parentheses such that the value of the entire expression becomes 43.
Here’s how we can achieve that:
First, consider the expression step-by-step and think about how parentheses affect the order of operations. Recall that the order of operations is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
1. Focus on a smaller part of the expression:
- Instead of directly diving into the whole expression, start by isolating parts with parentheses.
2. Experiment with different placements:
- Start by considering how changing the division or multiplication order might affect the result.
Let's try enclosing the division and then the subtraction that follows it:
[tex]\[ 32.6 \div (10 - 5) \][/tex]
- Do the math inside the parentheses first:
[tex]\[ 10 - 5 = 5 \][/tex]
- Now, divide:
[tex]\[ 32.6 \div 5 = 6.52 \][/tex]
3. Consider the remaining part:
Next, we look at the multiplication:
[tex]\[ 6.52 \times 8 \][/tex]
- Perform the multiplication:
[tex]\[ 6.52 \times 8 = 52.16 \][/tex]
4. Subtract the last number:
Finally, subtract 9.16 from the result:
[tex]\[ 52.16 - 9.16 \][/tex]
- Perform the subtraction:
[tex]\[ 52.16 - 9.16 = 43 \][/tex]
So, by applying the parentheses like this:
[tex]\[ 32.6 \div (10 - 5) \times 8 - 9.16 \][/tex]
We achieve the desired result of 43.
Thus, the correct expression with parentheses added is:
[tex]\[ 32.6 \div (10 - 5) \times 8 - 9.16 \][/tex]
