Simplify (w/ no calc.): 3*16 + 32 + 24/3 + 8/9 + 1/27

[lyrem]

I need help with simplifying this without a calculator. I know that the answer is supposed to be

.
But while

is easy, I don't know how to get 7 in the numerator.

 

[Deleted member 4993]

I need help with simplifying this without a calculator. I know that the answer is supposed to be

.
But while

is easy, I don't know how to get 7 in the numerator.

There are many ways - my most direct way

= 48 + 32 + 8 + 8/9 +1/27

= (88 * 27 + 24 + 1)/27

Now:

8 * 27 = 240 - 24 = 216

88 * 27 = 80 * 27 + 8 * 27 = 2160 + 216 = 2376

(88 * 27 + 24 + 1)/27

= (2401)/27

= (343 * 7)/27

= (49 * 7 * 7)/27

= 7⁴/3³

 

[lyrem]

Thank you!