I need help with this math question plz!?

Question

The number 62/27 can be written in the form v+(1/(w+(1/(x+(1/(y+(1/z))))))) where v,w,x,y,z are positive integers. Evaluate 242v+164w+213x+191y+207z

Anyone know how to do this?

Answer 1

v + 1/(w + 1/(x + 1/(y + 1 / z))) = 62 / 27 = 2 + 8 / 27
v = 2
1/(w + 1/(x + 1/(y + 1 / z))) = 8 / 27

invert:
w + 1/(x + 1/(y + 1 / z)) = 27 / 8 = 3 + 3 / 8
w = 3
1/(x + 1/(y + 1 / z)) = 3 / 8

invert:
x + 1/(y + 1 / z) = 8 / 3 = 2 + 2 / 3
x = 2
1/(y + 1 / z) = 2 / 3

invert:
y + 1 / z = 3 / 2 = 1 + 1 / 2
y = 1
z = 2

so v = 1, w = 3, x = 2, y = 1, z = 2
242v + 164w + 213x + 191y + 207z =
242 + 164 * 3 + 213 * 2 + 191 + 207 * 2 =
242 + 492 + 426 + 191 + 414 =
1765

This works because each subsequent term of the extended fraction must be less than one, so at each step it can be set to the fractional part while the leading term takes the integral part.

Answer 2

62/27 =

2 8/27

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Answer 3

sorry, im studying for my exams so i thought this would be revision , but i don't think my exam will have something close to that. Good Luck!

Answer 4

no