Which two signs should be interchanged to make the following equation correct? 29 × 145 + 5 − 640 ÷ 15 = 216

Question

Accepted Answer

Let's analyze the original equation: 29 × 145 + 5 − 640 ÷ 15 = 216

Step 1: Calculate the left side as is:
29 × 145 = 4205
4205 + 5 = 4210
640 ÷ 15 ≈ 42.6667
4210 − 42.6667 ≈ 4167.3333 which is not equal to 216.

Step 2: Check each option by interchanging the signs and evaluating:

Option 1: Interchange − and ×
Equation becomes: 29 − 145 + 5 × 640 ÷ 15
Calculate:
5 × 640 = 3200
3200 ÷ 15 ≈ 213.3333
29 − 145 = -116
-116 + 213.3333 = 97.3333 ≠ 216

Option 2: Interchange ÷ and +
Equation becomes: 29 × 145 ÷ 5 − 640 + 15
Calculate:
29 × 145 = 4205
4205 ÷ 5 = 841
841 − 640 = 201
201 + 15 = 216
This matches the right side.

Option 3: Interchange − and +
Equation becomes: 29 × 145 − 5 + 640 ÷ 15
Calculate:
29 × 145 = 4205
640 ÷ 15 ≈ 42.6667
4205 − 5 = 4200
4200 + 42.6667 = 4242.6667 ≠ 216

Option 4: Interchange ÷ and ×
Equation becomes: 29 ÷ 145 + 5 − 640 × 15
Calculate:
29 ÷ 145 ≈ 0.2
640 × 15 = 9600
0.2 + 5 = 5.2
5.2 − 9600 = -9594.8 ≠ 216

Therefore, the correct interchange is ÷ and + (Option 2).

Answer

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