Brace and brackets confusion

  • Thread starter tionis
  • Start date
  • #1
tionis
Gold Member
458
67
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
 

Answers and Replies

  • #2
Nidum
Science Advisor
Gold Member
2,990
848
Look at the 5 and the 3 - have you used them properly ?
 
  • Like
Likes tionis
  • #3
tionis
Gold Member
458
67
Look at the 5 and the 3 - have you used them properly ?
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.
 
  • #4
Nidum
Science Advisor
Gold Member
2,990
848
5 + 3 * [ ] ?

It is easier to spot problems if you set calculations out methodically .
 
  • Like
Likes tionis
  • #5
tionis
Gold Member
458
67
  • #8
Nidum
Science Advisor
Gold Member
2,990
848
29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }

There is an implied multiplication sign between the 3 and the [ 8 × ( 10 - √64 ) ] term .
 
  • Like
Likes tionis
  • #9
tionis
Gold Member
458
67
29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }

There is an implied multiplication sign between the 3 and the [ 8 × ( 10 - √64 ) ] term .
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?
 
  • #10
Nidum
Science Advisor
Gold Member
2,990
848
29 - { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 }

Is 126 the right answer?
( 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 .
 
  • Like
Likes tionis
  • #11
tionis
Gold Member
458
67
29 - { 5 + 3 [ 8 x ( 10 - √64 ) ] - 50 } Put in the numbers and come back .

( 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?
 
  • #12
Nidum
Science Advisor
Gold Member
2,990
848
{ 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:
  • Like
Likes tionis
  • #13
Nidum
Science Advisor
Gold Member
2,990
848
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:
  • Like
Likes tionis
  • #14
tionis
Gold Member
458
67
{ 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 .
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?
 
  • #15
QuantumQuest
Science Advisor
Insights Author
Gold Member
926
485
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.
 
  • Like
Likes tionis
  • #16
Nidum
Science Advisor
Gold Member
2,990
848
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) = ?
 
  • Like
Likes tionis
  • #17
tionis
Gold Member
458
67
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) = 3 + 4 = 7 × 2 = 14 + 1 = 15

Is that right?
 
  • #18
Nidum
Science Advisor
Gold Member
2,990
848
That's it . Good !
 
  • Like
Likes tionis
  • #19
tionis
Gold Member
458
67
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.
It's just that the bracket highlighted in red threw me off 29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }.
 
  • #20
tionis
Gold Member
458
67
That's it . Good !
Awesome, Nidum! Thank you for seeing me through.
 
  • #21
QuantumQuest
Science Advisor
Insights Author
Gold Member
926
485
It's just that the bracket highlighted in red threw me off 29 - { 5 + 3 [ 8 × ( 10 - √64 ) ] - 50 }.
If you start with the innermost parentheses, calculate it and work your way out, giving priority to multiplication over addition / subtraction - unless there is any kind of brackets in which case you just perform the calculations inside them, you'll reach the outermost numbers and operations and finally you're done!

EDIT: Although obvious, I'll stress out that you have to watch out for the same kind of brackets - where they start and end, in order to decide the sequence of the operations you'll perform.
 
  • Like
Likes tionis
  • #22
tionis
Gold Member
458
67
If you start with the innermost parentheses, calculate it and work your way out, giving priority to multiplication over addition / subtraction - unless there is any kind of brackets in which case you just perform the calculations inside them, you'll reach the outermost numbers and operations and finally you're done!
I'll keep that in mind. Thanks for your help.
 
  • #23
QuantumQuest
Science Advisor
Insights Author
Gold Member
926
485
I'll keep that in mind. Thanks for your help.
You're welcome. Also take a look at my edit in my last post.
 
  • Like
Likes tionis
  • #24
tionis
Gold Member
458
67
EDIT: Although obvious, I'll stress out that you have to watch out for the same kind of brackets - where they start and end, in order to decide the sequence of the operations you'll perform.
Yeah! What is up with these different types of brackets lol? My phone's calculator doesn't have but one type only.
 
  • #25
QuantumQuest
Science Advisor
Insights Author
Gold Member
926
485
Yeah! What is up with these different types of brackets lol? My phone's calculator doesn't have but one type only.
In math, we use three kind of brackets: parentheses (), angle brackets [ ] and curly brackets { }, in this order from innermost to outermost. In programming we use only parentheses all over the way.
 
  • Like
Likes tionis

Related Threads on Brace and brackets confusion

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
855
  • Last Post
Replies
8
Views
14K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
11
Views
4K
Replies
11
Views
5K
Replies
4
Views
3K
Replies
5
Views
1K
Top