Why Does My Calculation Differ from the Calculator's Result?

[tionis]

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

 

[Nidum]

Look at the 5 and the 3 - have you used them properly ?

 

[tionis]

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.

 

[Nidum]

5 + 3 * [ ] ?

It is easier to spot problems if you set calculations out methodically .

 

[tionis]

5 + 3 * [ ] ?

5 + 3 × [2] = 16, no?

 

[Nidum]

5 + ( 3 * [ ] ) ?

BODMAS rules for calculations .

 

[tionis]

5 + ( 3 * [ ] ) ?

BODMAS rules for calculations .

Sorry, Nidum, but I still don't get it. Why are you putting the 3 inside another bracket?

 

[Nidum]

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

There is an implied multiplication sign between the 3 and the [ 8 × ( 10 - √64 ) ] term .

 

[tionis]

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?

 

[Nidum]

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 .

 

[tionis]

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?

 

[Nidum]

{ 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 .

 

[Nidum]

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) = ?

 

[tionis]

{ 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?

 

[QuantumQuest]

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.

 

[Nidum]

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) = ?

 

[tionis]

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?

 

[Nidum]

That's it . Good !

 

[tionis]

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 }.

 

[tionis]

That's it . Good !

Awesome, Nidum! Thank you for seeing me through.

 

[QuantumQuest]

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.

 

[tionis]

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.

 

[QuantumQuest]

I'll keep that in mind. Thanks for your help.

You're welcome. Also take a look at my edit in my last post.

 

[tionis]

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.

 

[QuantumQuest]

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.

 

[Mark44]

In math, we use three kind of brackets: parentheses (), angle brackets [ ] and curly brackets { }

These -- [ ] -- are brackets.
Angle brackets -- < >
These -- { } -- are braces, but are sometimes called curly brackets.

 

[QuantumQuest]

These -- [ ] -- are brackets.
Angle brackets -- < >
These -- { } -- are braces, but are sometimes called curly brackets.

Sorry, I don't really know where the "angle" came from - maybe overloaded from HTML;). So, it is three kinds of brackets: parentheses (), brackets [ ] and curly brackets { }.