# Fractions of a Fraction of 1000

What is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1,000?

### 7 guesses to Fractions of a Fraction of 1000

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• Frank

.05

• Frank

sorry .05*1000=50

• Nah. I think it’s 100. But I’m having trouble concocting a genius explanation of why that is. I just crunched through the math, but there must be an elegant way to show WHY.

• Crabman

Those fractions resolve to 1/10th. 1000/10 = 100

• brent

Taylor, I think the “simplified math” is:

a/b1 x b1/b2 x b2/b3 x … x bn/c
In this case all of the b terms cancel out, because it could be written as a/c x b1/b1 x b2/b2 x b3/b3 … bn/bn
since b1/b1 = 1 and b2/b2 = 1 etc. you are left with a/c (1/10 in our case) x 1000 = 1000.

• Margery

100

• Taylor, you are today’s winner! Thank you Brent for your explanation.
One hundred – work backwards and you will understand.