I got -1/9.I am so happy.I used to have problems  with PEMDAS,now I look forward to doing them.Learning  math in my seventies  so I can help my grandchildren.

4/7(7/6)^2 > 4/7 * 49/36 > reduce to 7/9 - 8/9 > -1/9. Why so complex with the fractions ?

-1/9
Instead of doing all that weird converting and cancelling, you could just leave 4/7 × 49/36 alone, since you already solved that part in the previous step, divide 4 and 36 by 4 since one is a numerator and the other a denominator, then divide 7 and 49 by 7 for the same reason, and end up with 1/1 × 7/9, drop the 1s and be left with 7/9 - 8/9 = -1/9. Plus there was an extra step left over with 28/36 - 8/9 that had to be dealt with which would have been eliminated in step 3. I did it my way in four steps.

great factoring, thanks

4/7×49/36  -  8/9
28/36 - 8/9
14/18 - 8/9
7/9 - 8/9
= -1/9

Extremely complicated. No endless writing and explanation needed 😮

Too complicated. Why noit reduce 28/36 by 4 first, which gets us to 7/9 - 8/9 = -1/9?

-1/9.  Thank you

I seldom pause the video and do the problem first on paper.  Today, I did, and I was rewarded by getting this right!  So, no more lazy watching for me!

4/7 • (1/3 + 5/6)^2  -  8/9
4/7 • (2/6 + 5/6)^2  -  8/9
4/7 • (7/6)^2  -  8/9  
4/7 × 49/36  -  8/9
7/9 - 8/9  =  -1/9

Thanks!

(1/3+5/6) =  (2/6+5/6) = (7/6) > 4/7 x 7/6 x 7/6  >  2x2/7 x 7/6 x 7/6  cancel out > 7/3x3 = 7/9 > 7/9 - 8/9 = - 1/9

thanks, nice refresher

Mr. Youtube Mathman certified professional expert, you have taught me PEMDAS so well, I solved this one in my mind.  No skips and no pen or paper, swear to you know who.  I'm not just a fan, I'm a superfan!  You are the leader of the "MAMCA" movement.  Make America Mathematically competent again.  You are the turtle on the rock sunning himself while the others tread water.

I see "order of operations" in the title, but those get punched in the gut right at the start, because PEMDAS has nothing to help with adding fractions of different denominators.

First we need 1/3 and 5/6 to have a like denominator. Easiest way is to multiply 3*6, but the savvy will know that 3 is already a factor of 6, so we only need to factor up the 3 by *2, which is done my scaling up the fraction by a factor of one in the form of 2/2

4/7((1*2)/(3*2) + 5/6)^2 - 8/9
= 4/7(2/6 + 5/6)^2 - 8/9
= 4/7(7/6)^2 - 8/9

To square a number means to multiply that number by itself, which you could do by actually multiplying, but it will be much easier later to just represent it

= 4/7((7/6)(7/6)) - 8/9

Now is the point we tell PEMDAS that's our purse and we don't know him, kick him in the groin, and write the expression for the multiplication of fractions

= (4 * 7 * 7) / (7 * 6 * 6) - 8/9

Now we can do something else PEMDAS can't do: factor our, reduce, and cross cancel. We see our numerator and denominator have a 7 each, so those cancel out (technically they become 1's, but 1 in multiplication is an identity value, so since x * 1 = x we are allowed to simply omit it unless it would leave a numerator empty [which is not the same as the numerator being zero]).

= (4 * 7) / (6 * 6) - 8/9

Now we factor. What is 4? It's 2 * 2. What is 6? It's 2 * 3. Therefore:

= (2 * 2 * 7) / (2 * 3 * 6) - 8/9

We now have a 2 in both the numerator and denominator, so they cancel out.

= (2 * 7) / (3 * 6) - 8 / 9

Are we ready to math yet? No, because we can still factor. What is 6? It's 2 *3. Therefore:

= (2 * 7) / (3 * 2 * 3) - 8 / 9

We once more have a 2 in the numerator and denominator, so they cancel out.

= 7/(3*3) - 8/9

The only factors for our values in numerator and denominator are 1 and themselves, so they are factored as far as they can be and can no longer cancel or reduce, so now we evaluate the denominator of our left fraction, which, yes, is per PEMDAS, as the P step deals with grouping and the denominator of a fraction is understood to be a group (since I have to write it on a straight line parenthesis have been included for clarity).

= 7/9 - 8/9

And finally we subtract.

= -1/9

In full:
4/7(1/3 - 5/6)^2 - 8/9
= 4/7(2/6 + 5/6)^2 - 8/9
= 4/7(7/6)^2 - 8/9
= 4/7((7/6)(7/6)) - 8/9
= (4 * 7 * 7) / (7 * 6 * 6) - 8/9
= (4 * 7) / (6 * 6) - 8/9
= (2 * 7) / (3 * 6) - 85/9
= 7/(3*3) - 8/9
= 7/9 - 8/9
= -1/9

To be fair, if doing this by hand with proper fractions I'd be penciling over the digits to reduce and cross cancel before combining the fractions:
4/7((7/6)(7/6)) - 8/9
= 1/1((1/3)(7/3)) -8/9
= 7/9 - 8/9
"skipping" four steps in the process ("skipping" as in not writing them down since I'd still have some work to show for myself on paper; steps are shown here for clairty of process).

Or you can follow PEMDAS to the letter and end up with 196/252 - 8/9 and, well, good luck with that.

It should also be true to simplify the fraction 28/36 is equal to 7/9.

4/7 (49/36) =7/9 and 7/9 - 8/9 =--1/9......Mental Math

It's often simpler to reduce your fractions as you work.
28/36 reduces to 7/9.
7/9 - 8/9 = -1/9

4/7(1/3+5/6)²-8/9=4/7(7/6)²-8/9=4/7(49/36)-8/9=7/9-8/9=-1/9

It was easier for me to work with 49/36.   Mentally I could easily cross-multiply, for 7/9-8/9, for  -1/9