Which of the following interchanges of signs would make the given equation correct?
288×72+36÷12−6=20770

Let's check Option D, interchanging ÷ and +:
The original equation is:
288×72+36÷12−6=20770

After interchanging ÷ and +, the equation becomes:
288×72÷36+12−6=20770

Applying the BODMAS rule:
First, perform the division:
72÷36=2

Now substitute back into the equation:
288×2+12−6=20770

Next, perform multiplication:
288×2=576

Now substitute back:
576+12−6=588−6=582

=20770

Let's re-verify Option C, interchanging + and ×:
The equation becomes:
288+72×36÷12−6=20770

Applying BODMAS:
First, perform division:
36÷12=3

Next, perform multiplication:
72×3=216

Now substitute back:
288+216−6=504−6=498

=20770

Let's look at the options and the value 20770. Since 20770 is a large number, let's look at Option A, interchanging × and −:
288−72+36÷12×6=20770→288−72+3×6=288−72+18=234

=20770.

Let's check Option B, interchanging − and ÷:
288×72+36−12÷6=288×72+36−2=20736+36−2=20772−2=20770.

This perfectly matches the RHS. Thus, interchanging − and ÷ makes the equation correct.