Which two signs should be interchanged to make the following equation correct: 247 ÷ 13 + 16 × 3 − 148 = 119?

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Accepted Answer

Let's analyze the equation: 247 ÷ 13 + 16 × 3 − 148 = 119. We are to interchange two signs to make the equation correct.

Let's check each option:

Option 1: Interchange + and ×
Equation becomes: 247 ÷ 13 × 16 + 3 − 148
= (247 ÷ 13) × 16 + 3 − 148
= 19 × 16 + 3 − 148
= 304 + 3 − 148
= 307 − 148 = 159 (Not 119)

Option 2: Interchange − and +
Equation becomes: 247 ÷ 13 − 16 × 3 + 148
= (247 ÷ 13) − (16 × 3) + 148
= 19 − 48 + 148
= (19 + 148) − 48 = 167 − 48 = 119 (This seems correct, but let's check all options for completeness)

Option 3: Interchange − and ×
Equation becomes: 247 ÷ 13 + 16 − 3 × 148
= (247 ÷ 13) + 16 − (3 × 148)
= 19 + 16 − 444
= 35 − 444 = -409 (Not 119)

Option 4: Interchange ÷ and ×
Equation becomes: 247 × 13 + 16 ÷ 3 − 148
= (247 × 13) + (16 ÷ 3) − 148
= 3211 + 5.333... − 148
= 3211 + 5.333... = 3216.333... − 148 = 3068.333... (Not 119)

However, let's double-check Option 2:
247 ÷ 13 − 16 × 3 + 148
= 19 − 48 + 148
= (19 + 148) − 48
= 167 − 48 = 119

So Option 2 is correct. But according to the answer key, Option 4 is marked as correct. Let's check the original equation with Option 4 again:

Interchange ÷ and ×:
So, wherever there is ÷, use × and vice versa.
Equation: 247 × 13 + 16 ÷ 3 − 148
= (247 × 13) + (16 ÷ 3) − 148
= 3211 + 5.333... − 148 = 3216.333... − 148 = 3068.333... (Not 119)

So Option 2 is correct.

Therefore, the correct answer is Option 2: − and +.

Final answer updated accordingly.

Answer

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