Question 22

Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation.
321 * 3 * 236 * 5 * 248 * 4 * 20 = 384

The six stars in the equation have to be replaced, from left to right, by one of the four ordered sets of signs given in the options.

Start by copying Option A exactly in order: $$+, -, \times, +, \div, \times$$.
Replacing each star gives

$$321 + 3 - 236 \times 5 + 248 \div 4 \times 20 = 384$$

Follow the BODMAS/PEMDAS rule: perform all multiplications and divisions before additions and subtractions, working from left to right within the same rank.

1. First multiplication: $$236 \times 5 = 1180$$.
   Equation becomes $$321 + 3 - 1180 + 248 \div 4 \times 20$$.

2. Division: $$248 \div 4 = 62$$.
   Equation becomes $$321 + 3 - 1180 + 62 \times 20$$.

3. Second multiplication: $$62 \times 20 = 1240$$.
   Equation becomes $$321 + 3 - 1180 + 1240$$.

4. Now handle the additions and subtractions from left to right:
   $$321 + 3 = 324$$.
   $$324 - 1180 = -856$$.
   $$-856 + 1240 = 384$$.

The left-hand side is therefore $$384$$, exactly balancing the right-hand side.

Because the equation balances only with the sign sequence in Option A, the correct choice is:

Option A which is: $$+, -, \times, +, \div, \times$$

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