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Which two signs should be interchanged to make the equation correct?
6 + (9 - 3) ÷ (8 + 1) × (7 - 4) = 24
- a)× and ÷
- b)+ and ÷
- c)- and ÷
- d)+ and -
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Which two signs should be interchanged to make the equation correct?6 ...
Understanding the Original Equation
The original equation is:
6 + (9 - 3) ÷ (8 + 1) × (7 - 4) = 24
Let's break this down step by step.
Calculating Each Component
- (9 - 3) = 6
- (8 + 1) = 9
- (7 - 4) = 3
Now, substituting these values back into the equation:
6 + 6 ÷ 9 × 3
Order of Operations (BODMAS)
According to the order of operations (BODMAS/BIDMAS), we perform division and multiplication before addition:
1. 6 ÷ 9 = 2/3
2. (2/3) × 3 = 2
Now we rewrite the equation:
6 + 2 = 8
This is not equal to 24, indicating that we need to interchange some signs.
Identifying the Interchange
The goal is to find two signs to swap that will make the equation true.
If we swap the + and ÷, the equation will become:
6 ÷ (9 - 3) + (8 + 1) × (7 - 4)
Now calculating this:
1. (9 - 3) = 6
2. (8 + 1) = 9
3. (7 - 4) = 3
Substituting gives us:
6 ÷ 6 + 9 × 3
Now, applying order of operations:
1. 6 ÷ 6 = 1
2. 9 × 3 = 27
Now the equation reads:
1 + 27 = 28
This is still not correct.
Correct Swap for the Solution
By interchanging the signs × and ÷, the equation turns into:
6 + (9 - 3) × (8 + 1) ÷ (7 - 4)
Calculating this gives:
1. (9 - 3) = 6
2. (8 + 1) = 9
3. (7 - 4) = 3
The equation now reads:
6 + 6 × 9 ÷ 3
Following the order of operations:
1. 6 × 9 = 54
2. 54 ÷ 3 = 18
Finally:
6 + 18 = 24
Conclusion
Thus, the correct answer is to interchange × and ÷ (Option A) to make the equation true.
The original equation is:
6 + (9 - 3) ÷ (8 + 1) × (7 - 4) = 24
Let's break this down step by step.
Calculating Each Component
- (9 - 3) = 6
- (8 + 1) = 9
- (7 - 4) = 3
Now, substituting these values back into the equation:
6 + 6 ÷ 9 × 3
Order of Operations (BODMAS)
According to the order of operations (BODMAS/BIDMAS), we perform division and multiplication before addition:
1. 6 ÷ 9 = 2/3
2. (2/3) × 3 = 2
Now we rewrite the equation:
6 + 2 = 8
This is not equal to 24, indicating that we need to interchange some signs.
Identifying the Interchange
The goal is to find two signs to swap that will make the equation true.
If we swap the + and ÷, the equation will become:
6 ÷ (9 - 3) + (8 + 1) × (7 - 4)
Now calculating this:
1. (9 - 3) = 6
2. (8 + 1) = 9
3. (7 - 4) = 3
Substituting gives us:
6 ÷ 6 + 9 × 3
Now, applying order of operations:
1. 6 ÷ 6 = 1
2. 9 × 3 = 27
Now the equation reads:
1 + 27 = 28
This is still not correct.
Correct Swap for the Solution
By interchanging the signs × and ÷, the equation turns into:
6 + (9 - 3) × (8 + 1) ÷ (7 - 4)
Calculating this gives:
1. (9 - 3) = 6
2. (8 + 1) = 9
3. (7 - 4) = 3
The equation now reads:
6 + 6 × 9 ÷ 3
Following the order of operations:
1. 6 × 9 = 54
2. 54 ÷ 3 = 18
Finally:
6 + 18 = 24
Conclusion
Thus, the correct answer is to interchange × and ÷ (Option A) to make the equation true.
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Community Answer
Which two signs should be interchanged to make the equation correct?6 ...
After interchanging × and ÷,
We get
6 + (9 - 3) × (8 + 1) ÷ (7 - 4) = 6 + 6 x 9 ÷ 3 = 24
We get
6 + (9 - 3) × (8 + 1) ÷ (7 - 4) = 6 + 6 x 9 ÷ 3 = 24
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