Algebra- order of operations question: (4+52) - (Square root: 81) x (7/3)

[ripple]

Hey Guys,
new to the forum here, studying maths at university as a bridging unit to get into chemistry for which the maths unit is a pre-requisite!
So I am really not a maths guy but do want to learn! For our first assignment we had a question that kinda threw me in terms of order of operations. I am aware of the concept and always follow my PEMDAS or BODMAS but the question that threw me was:

(4+5²) - (Square root: 81) x (7/3)

The answer turns out to be 8 because 29 - (9 x 7)/3

My question is however why do we not do the (7/3) in the brackets first instead of doing 9 x 7 then divided by 3?

Because I thought following PEMDAS, we did all parenthesis first so yeah....

Thanks

 

[Deleted member 4993]

Hey Guys,
new to the forum here, studying maths at university as a bridging unit to get into chemistry for which the maths unit is a pre-requisite!
So I am really not a maths guy but do want to learn! For our first assignment we had a question that kinda threw me in terms of order of operations. I am aware of the concept and always follow my PEMDAS or BODMAS but the question that threw me was:

(4+5²) - (Square root: 81) x (7/3)

The answer turns out to be 8 because 29 - (9 x 7)/3

My question is however why do we not do the (7/3) in the brackets first instead of doing 9 x 7 then divided by 3?

Because I thought following PEMDAS, we did all parenthesis first so yeah....

Thanks

The answer should be same.The only difference would be that in the first case you should not need a calculator - in the second case you do need a calculator to calculate 7/3.

 

[stapel]

(4+5²) - (Square root: 81) x (7/3)

The answer turns out to be 8 because 29 - (9 x 7)/3

My question is however why do we not do the (7/3) in the brackets first instead of doing 9 x 7 then divided by 3?

Because I thought following PEMDAS, we did all parenthesis first...

At this point, you've got a nice big ball of multiplication and division, which is all at the same "level", so to speak. Thus, at this point, the order doesn't matter terribly much. You're welcome to cancel off the 3's first, to give yourself smaller numbers to work with.

 

[HallsofIvy]

Hey Guys,
new to the forum here, studying maths at university as a bridging unit to get into chemistry for which the maths unit is a pre-requisite!
So I am really not a maths guy but do want to learn! For our first assignment we had a question that kinda threw me in terms of order of operations. I am aware of the concept and always follow my PEMDAS or BODMAS but the question that threw me was:

(4+5²) - (Square root: 81) x (7/3)

The answer turns out to be 8 because 29 - (9 x 7)/3

My question is however why do we not do the (7/3) in the brackets first instead of doing 9 x 7 then divided by 3?

Because I thought following PEMDAS, we did all parenthesis first so yeah....

Thanks

Did you try both ways? 7/3= 2.333... or "2 and 1/3". Multiplying that by 9, 2.333.... times 9 is 21. But since 9 is evenly divisible by 3, it is easier to do that division first: (9/3)(7)= 3(7)= 21.

While, yes you must do exponentiation before "multiplication or division" and that before "addition or subtraction", there is no necessary order to "multiplication or division"- they can be done in either order. And there is no necessary order to "addition or subtraction"- they can be done in either order. We have the orders "MD" and "AS" in "PEMDAS" only because one has to come before the other in the mnemonic. It a easily have been "PEDMAS", or "PEMDSA", or even "PEMSDA" although that last is rather hard to pronounce!

 

[JeffM]

Hey Guys,
new to the forum here, studying maths at university as a bridging unit to get into chemistry for which the maths unit is a pre-requisite!
So I am really not a maths guy but do want to learn! For our first assignment we had a question that kinda threw me in terms of order of operations. I am aware of the concept and always follow my PEMDAS or BODMAS but the question that threw me was:

(4+5²) - (Square root: 81) x (7/3)

The answer turns out to be 8 because 29 - (9 x 7)/3

My question is however why do we not do the (7/3) in the brackets first instead of doing 9 x 7 then divided by 3?

Because I thought following PEMDAS, we did all parenthesis first so yeah....

Thanks

You have already received a number of very good answers, but I think you may have a number of sources of confusion.

(1) Addition / subtraction is not sensitive to order

10 - 3 + 5 = (10 - 3) + 5 = (- 3 + 5) + 10 = (5 + 10) - 3 etc.

(2) Multiplication / division is not sensitive to order

10 * 6 / 2 = (10 / 2) * 6 = (6 / 2) * 10 = (10 * 6) / 2.

(3) Unless a fraction has denominator that is a product of powers of 2 and 5, it will not have an exact decimal representation. To get exact answers, avoid decimal representations of fractions if possible.

(4) Remember that roots are fractional exponents, and exponents come before multiplication and division.

(5) Parentheses or brackets are code for any type of grouping symbol including surds.

\(\displaystyle (4 + 5^2 ) + \sqrt{81} * (7 / 3) \implies\)

\(\displaystyle (4 + 25) + 9 * (7 / 3) \implies\)

\(\displaystyle 29 + \dfrac{9 * 7}{3} = 29 + 21 = 50.\)

Notice what happens if you calculate (7 / 3) to two decimal places.

\(\displaystyle (4 + 5^2 ) + \sqrt{81} * (7 / 3) \implies\)

\(\displaystyle (4 + 25) + 9 * 2.33 \implies\)

\(\displaystyle 29 + 20.97 = 49.97.\)

 

[ripple]

You guys are awesome! Confusion completely cleared up!! I feel silly now, as everyone has mentioned the answer turns out to be the same anyway! I think the thing that threw me was getting an imprecise decimal point and my inexperienced brain not making the connection that it equates to the same fraction despite its imprecision... from now on I will try and avoid decimals and stick with fractions!!
Thanks so much for all your help!