Question

Juan added a set of parentheses and a set of brackets in the expression: 15: 3 x 5 + 4 x 8. Juan's expression has a value of 40. What is one way Juan could have written the grouping symbols?

Answer 1

`[15: (3 * 5) + 4] * 8`

Explanation:

First of all, let us have a look at the rule for solving brackets/parentheses/algebraic operations.

The rule states that the expression must be solved in the following order:

B - Brackets (Innermost parentheses first, then the enclosing brackets are solved)

O - Of (for example 10% of 20)

D - Divide operation

M - Multiplication operation

A - Addition operation

S - Subtraction operation

So, we need to add a set of parentheses i.e. () and a set of brackets i.e. [] in the expression:

`15: 3 * 5 + 4 * 8` such that the result is 40.

Consider the expression:
`[15: (3 * 5) + 4] * 8`

Let us try to solve the expression using the above rule:

`[15: (3 * 5) + 4] * 8`

First of all, the innermost () will be solved:

`(3* 5) = 15`

Now, the expression becomes:

`[15: 15 + 4] * 8`

Now, 15:15 will be solved as 1

`[1+ 4] * 8`

Now, the outer [] will be solved:

`5* 8 = 40`

Hence, the correct answer is:

`[15: (3 * 5) + 4] * 8`