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Answer :
Let's solve the problem of inserting parentheses into the expression [tex]\(4 \cdot 9 + 9 \cdot 8\)[/tex] so that the result equals 360. We'll evaluate each of the given options to find the correct arrangement of parentheses.
Option A: [tex]\(4 \cdot (9+9 \cdot 8)\)[/tex]
First, inside the parentheses, we calculate [tex]\(9 \cdot 8\)[/tex]:
[tex]\[9 \cdot 8 = 72\][/tex]
Next, add 9:
[tex]\[9 + 72 = 81\][/tex]
Finally, multiply by 4:
[tex]\[4 \cdot 81 = 324\][/tex]
This does not equal 360.
Option B: [tex]\((4 \cdot 9) + (9 \cdot 8)\)[/tex]
Calculate each part separately:
[tex]\[4 \cdot 9 = 36\][/tex]
[tex]\[9 \cdot 8 = 72\][/tex]
Add the results together:
[tex]\[36 + 72 = 108\][/tex]
This does not equal 360.
Option C: [tex]\((4 \cdot 9+9) \cdot 8\)[/tex]
First, inside the parentheses, calculate [tex]\(4 \cdot 9\)[/tex]:
[tex]\[4 \cdot 9 = 36\][/tex]
Add 9:
[tex]\[36 + 9 = 45\][/tex]
Now, multiply by 8:
[tex]\[45 \cdot 8 = 360\][/tex]
This result is equal to 360.
Option D: [tex]\(4 \cdot (9+9) \cdot 8\)[/tex]
First, calculate inside the parentheses:
[tex]\[9 + 9 = 18\][/tex]
Multiply by 4:
[tex]\[4 \cdot 18 = 72\][/tex]
Finally, multiply by 8:
[tex]\[72 \cdot 8 = 576\][/tex]
This does not equal 360.
After evaluating all the options, we find that Option C: [tex]\((4 \cdot 9+9) \cdot 8 = 360\)[/tex] is the correct choice.
Option A: [tex]\(4 \cdot (9+9 \cdot 8)\)[/tex]
First, inside the parentheses, we calculate [tex]\(9 \cdot 8\)[/tex]:
[tex]\[9 \cdot 8 = 72\][/tex]
Next, add 9:
[tex]\[9 + 72 = 81\][/tex]
Finally, multiply by 4:
[tex]\[4 \cdot 81 = 324\][/tex]
This does not equal 360.
Option B: [tex]\((4 \cdot 9) + (9 \cdot 8)\)[/tex]
Calculate each part separately:
[tex]\[4 \cdot 9 = 36\][/tex]
[tex]\[9 \cdot 8 = 72\][/tex]
Add the results together:
[tex]\[36 + 72 = 108\][/tex]
This does not equal 360.
Option C: [tex]\((4 \cdot 9+9) \cdot 8\)[/tex]
First, inside the parentheses, calculate [tex]\(4 \cdot 9\)[/tex]:
[tex]\[4 \cdot 9 = 36\][/tex]
Add 9:
[tex]\[36 + 9 = 45\][/tex]
Now, multiply by 8:
[tex]\[45 \cdot 8 = 360\][/tex]
This result is equal to 360.
Option D: [tex]\(4 \cdot (9+9) \cdot 8\)[/tex]
First, calculate inside the parentheses:
[tex]\[9 + 9 = 18\][/tex]
Multiply by 4:
[tex]\[4 \cdot 18 = 72\][/tex]
Finally, multiply by 8:
[tex]\[72 \cdot 8 = 576\][/tex]
This does not equal 360.
After evaluating all the options, we find that Option C: [tex]\((4 \cdot 9+9) \cdot 8 = 360\)[/tex] is the correct choice.
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