Question

Order of Operations

Answer 1

Given:

$4 + 9 + 16 \div 4 - 8 -3 \times 5$

To find:

The number of possible solutions, if the Order of Operations did not exist.

Solution:

We have,

$4 + 9 + 16 \div 4 - 8 -3 \times 5$

Now,

Case 1:

$[4 + 9 + 16] \div [4 - 8 -(3 \times 5)]=29\div (4 - 8 -15)$

$4 + 9 + 16 \div 4 - 8 -(3 \times 5)=-\dfrac{29}{19}$

Case 2:

$[4 + 9 + 16] \div (4 - 8 -3) \times 5=29\div (-7\times 5)$

$4 + 9 + 16 \div (4 - 8 -3) \times 5=-\dfrac{29}{35}$

Case 3:

$4 + 9 + (16 \div 4) - 8 -(3 \times 5)=4+9+4-8-15$

$4 + 9 + (16 \div 4) - 8 -(3 \times 5)=-6$

Many more possibilities are there.

Therefore, there are more than 3 possible solutions.