Question

How many different answers can you get by grouping differently? Add parentheses to the expression 7+3•4+2 to create new expressions with as many different values as possible.

Answer 1

Answer: The different possible solutions are 42, 21, 31 and 80.

Explanation:

The given expression is,

$7+3\cdot 4+2$

Case 1.

$(7+3)\cdot 4+2=10\cdot 4+2$

$(7+3)\cdot 4+2=40+2$

$(7+3)\cdot 4+2=42$

Case 2.

$7+(3\cdot 4)+2=7+12+2$

$7+(3\cdot 4)+2=21$

Case 3.

$7+3\cdot (4+2)=7+3\cdot 8$

$7+3\cdot (4+2)=7+24$

$7+3\cdot (4+2)=31$

Case 4.

$(7+3)\cdot (4+2)=10\cdot 8$

$(7+3)\cdot (4+2)=80$