how do i rewrite the expression 3x2-1+2 value: 11

Question

How do I rewrite the expression with parentheses to equal the given value of:

3x4-1+2 value: 11

Answer 1

Hi Brenda.  Question such as this are often testing your familiarity with numbers and in particular your understanding of the "order of operations".  Many students learn this as PEMDAS or similar.  For instance, that multiplication in an expression has precedence over addition, and so on, there are many rules.  One rule involved that parenthesis has precedence over multiplication, additional and subtraction.

 

So given you were given:

 

  3*4-1+2

 

you have to multiply, add, and subtract those numbers in such a manner that when you do so, the result is 11.

 

In this case, there are three scenarios:

1) (3 * 4) - 1 + 2

    Do OoO so do parens first -> 12 - 1 + 2 = 9

2) 3 * (4 - 1) + 2

    Do parens first -> 3 * 3 + 2

    Then do multiplication first -> 9 + 2 = 11

3) 3 * 4 - (1 + 2)

    Do parens first -> 3 * 4 - 3

    then do multiplication -> 12 - 3 = 9

 

So (2) is the right answer.  This is taking the simple approach.  It turns out that if that was not the right answer then either you've done the above wrong, OR, there is still another choice.  The above shows (2) to be correct but please note that there IS still another choice:

 

4) (3 * 4) - (1 + 2)

    Do parens first -> 12 - 3 = 9

 

This is worth knowing because there could have been more than one right answer, but not in this case.

 

BTW, please note that (4) is the same expression as (3) because in (3) the multiplication "binds" the 3 and 4 "as if" there was a parenthesis around it.  In other words, it can often be as if there is an implicit parenthesis around certain operators and even certain expressions and even certain values.  But in your problem none of that really needed to come into play however you should still be aware of it.

 

- Greg, from Central Queens, not far from Flushing

Answer 2

3x4-1+2

3x(4-1)+2

3x(3)+2

9+2

11