Knight Valdez
02/13/2024 · Junior High School
Select the proper placement for parentheses to speed up the addition for the expression \( 2+9+8+1 \). A) \( (8+2)+(9+1) \) B) \( (1+2)+(9+8) \) C) \( (9+2)+(8+1) \) D) \( (8+9)+(2+1) \)
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Step-by-step Solution
To speed up the addition for the expression \( 2+9+8+1 \), you want to group the numbers that add up to a number close to 10, as this will make the addition easier. Let's evaluate each option:
A) \( (8+2)+(9+1) \)
- \( 8+2 = 10 \)
- \( 9+1 = 10 \)
- \( 10+10 = 20 \)
B) \( (1+2)+(9+8) \)
- \( 1+2 = 3 \)
- \( 9+8 = 17 \)
- \( 3+17 = 20 \)
C) \( (9+2)+(8+1) \)
- \( 9+2 = 11 \)
- \( 8+1 = 9 \)
- \( 11+9 = 20 \)
D) \( (8+9)+(2+1) \)
- \( 8+9 = 17 \)
- \( 2+1 = 3 \)
- \( 17+3 = 20 \)
All the options result in the same sum of 20. However, option A is the most straightforward because it groups the numbers that add up to 10, which is the simplest addition. Therefore, the proper placement for parentheses to speed up the addition is:
A) \( (8+2)+(9+1) \)
Quick Answer
The proper placement for parentheses is A) \( (8+2)+(9+1) \).
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