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Brace and brackets confusion

  1. Jun 24, 2016 #1
    Hi. I'm having trouble solving:

    29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }

    My attempt:

    29 - { 8 [ 8 × ( 2 ) ] - 50 } = [ 8 × 2 = 16 ] then { 8 × 16 = 128 - 50 = 78 } - 29 = 49

    but the calculator says the answer is 126 and I don't know how it arrived at that solution. The textbook doesn't have the answer for this particular problem so I don't know where I went wrong. Please help. Thanks
     
  2. jcsd
  3. Jun 24, 2016 #2

    Nidum

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    Look at the 5 and the 3 - have you used them properly ?
     
  4. Jun 24, 2016 #3
    Have I? I think I have lol. I have followed the rule of starting with the inner most bracket which I think is ( 10 - √64 ) then multiplied the result by 8 and jumped to the next bracket over to the left { 5 + 3 }, but something doesn't feel right and I can't see it.
     
  5. Jun 24, 2016 #4

    Nidum

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    5 + 3 * [ ] ?

    It is easier to spot problems if you set calculations out methodically .
     
  6. Jun 24, 2016 #5
    5 + 3 × [2] = 16, no?
     
  7. Jun 24, 2016 #6

    Nidum

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  8. Jun 24, 2016 #7
  9. Jun 24, 2016 #8

    Nidum

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    29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }

    There is an implied multiplication sign between the 3 and the [ 8 × ( 10 - √64 ) ] term .
     
  10. Jun 24, 2016 #9
    OK, so is it 3 × 2 + 5 = 11? I still don't see how that gets me to 126, if that is the right answer. Is 126 the right answer?
     
  11. Jun 24, 2016 #10

    Nidum

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    29 - { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 }

    ( 10 - √64 ) = ?

    [ 8 x ( 10 - √64 ) ] = ?

    3 [ 8 x ( 10 - √64 ) ] = ?

    { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 } = ?

    29 - { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 } = ?

    Put in the numbers and come back .
     
  12. Jun 24, 2016 #11

    ( 10 - √64 ) = 2

    [ 8 × ( 10 - √64 ) ] = 16

    3 [ 8 × ( 10 - √64 ) ] = 48? I don't see how the bracket between the 3 and the 8 means a multiplication.

    { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 } = if it is 48, do I subtract 50 from 48 to get 2?

    29 - { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 } = Do I subtract 2 from 29 to get 27?
     
  13. Jun 24, 2016 #12

    Nidum

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    { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 } = if it is 48, do I subtract 50 from 48 to get 2?

    Actually 5 + 48 - 50 which = 3

    So final answer is 29 - 3 = 26 .
     
    Last edited: Jun 24, 2016
  14. Jun 24, 2016 #13

    Nidum

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    3 [ 8 × ( 10 - √64 ) ] = 48? I don't see how the bracket between the 3 and the 8 means a multiplication.

    How would you work this out :

    a + b(c + d) = ?
     
    Last edited: Jun 24, 2016
  15. Jun 24, 2016 #14
    I still don't understand why the 3 next to the bracket means I have to multiply. Is this always the case? Suppose I'm asked to simplify the following:

    30 - { 4 + 4 [ 7 × ( 10 - √36 ) ] - 50 }

    Would 36 be the correct answer?
     
  16. Jun 24, 2016 #15

    QuantumQuest

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    As Nidum has pointed out, you have to apply the rules. Multiplication has higher priority than addition and subtraction. You can safely start from inner parentheses or brackets but watch out what operations you have to perform and apply the priority rules.
     
  17. Jun 24, 2016 #16

    Nidum

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    How would you work this out :

    a + b(c + d) = ?

    Put some simple numbers in a=1 b=2 c=3 d=4

    1 + 2(3 +4) = ?
     
  18. Jun 24, 2016 #17
    1 + 2(3 +4) = 3 + 4 = 7 × 2 = 14 + 1 = 15

    Is that right?
     
  19. Jun 24, 2016 #18

    Nidum

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    That's it . Good !
     
  20. Jun 24, 2016 #19
    It's just that the bracket highlighted in red threw me off 29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }.
     
  21. Jun 24, 2016 #20
    Awesome, Nidum! Thank you for seeing me through.
     
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