Question

Simplify 3{[3(7-2)]+[7(4+1)]}

Answer 1

So we have to simplify:

`3\cdot\mleft\lbrace\lbrack3\cdot(7-2)\rbrack+\lbrack7\cdot(4+1)\rbrack\mright\rbrace`

The operations priorities depends on wheter they have parenthesis (or similar symbols like [ ] and { }) or not. The more layers of symbols that enclose an operation, the higher priority it has. In this case the first operations we have to make are the addition and the substraction that are inside three layers of symbols { }, [ ] and ( ):

`3\cdot\lbrace\lbrack3\cdot(7-2)\rbrack+\lbrack7\cdot(4+1)\rbrack\rbrace=3\cdot\mleft\lbrace\lbrack3\cdot5\rbrack+\lbrack7\cdot5\rbrack\mright\rbrace`

Now we have two multiplications inside two layers of symbols, an addition inside one layer and a number 3 that is not enclosed by any symbol. This means that the multiplications 3*5 and 7*5 have higher priority and must be performed before multiplying by the number 3 and before adding them:

`3\cdot\lbrace\lbrack3\cdot5\rbrack+\lbrack7\cdot5\rbrack\rbrace=3\cdot\mleft\lbrace15+35\mright\rbrace`

Now we can perform the addition and then multiply by 3:

`3\cdot\lbrace15+35\rbrace=3\cdot50=150`

So the answer is 150.