what is three over seven divided by three over five in decimal form?

Question

it is math( dividing rational numbers

Answer 1

It's 5/7, or 0.714285... recurring.

One gets this fraction by using the fact that DIVIDING by a fraction is the same as MULTIPLYING by its inverse.

So, (3/7)/(3/5) = (3/7)*(5/3) = 5/7. ........ ###

You can get the decimal representation by hand or with a calculator. OR, you can just use the following remarkable fact(s).

There's a neat thing about "sevenths" in decimal form:

1/7 = 0.14285714... (yes, it recurs);
2/7 = 0.28571428...;
3/7 = 0.42857142...
4/7 = 0.57142857... , etc.

Clearly we're on a roll! You only have to work out the first decimal figure in n/7, to be able to then fill in the rest automatically --- the very same digits follow on in exactly the order in which they appeared in the original decimal expression for 1/7. Isn't that neat?!

Live long and prosper.

### P.S. I call these repeated fractions like (3/7)/(3/5) ... "Tower of Babel fractions" --- because after enough successive divisions of general fractions like this, written as you'd write them with horizontal lines between them on the page, you're not completely sure which part of any one fraction "talks with" (i.e. should be associated with, or put on the same level as) which part of some other fractional component. For that reason I like to avoid writing them like this, instead turning them upside down and multiplying, instead, at the earliest opportunity.

Answer 2

No calculator:
(3/7) / (3/5)
division is really a dividend being multiplied by the divisor's reciprocal. So 3/7 TIMES 5/3.
The threes cancel out so you are left (after you multiply the top numerators and put the answer in the numerator of the quotient, and multiply the denominators and put the answer in the denominator of the quotient), with 5/7.
Divide 7 into 5.0.
The answer is .71. I only divided as far as the first two places.

Answer 3

.71