Myrtle Said:

Is there a way to multiply or divide mix numbers without converting them to improper fractions?

We Answered:

Example: 3 5/12 divided by 7 3/8.

3+ 5/12
---------
7 + 3/8

Multiply both top and bottom by the least common multiple of 12 and 8, namely 24:

24 x 3 + 10
-------------- =
24 x 7 + 9

82
---
177

Paul Said:

When converting decimals to fractions with bar notations, is it always divided by 9 or 99?

We Answered:

It depends on how many digits repeat. If you had 4.4 barred, you'd do the .4 barred which will come out 4/9 then make it a mixed number, 4 4/9. 8.7 barred 7 would be 8 7/9. Sometimes you'll end up with a number other than 9 or 99 at the end but you always use 9, 99, 999, etc to start.
Like for 0.1363636 (barred 63)
Two digits repeat so multiply by 100 (two zeros)
100x = 13.636363
   - x =   0.136363
-----------------------------
  99x = 13.500000

so x = 13.5/99 but you can't have a decimal in a fraction so multiply top and bottom by 10
135/990 (then reduce)

Kathleen Said:

How do negative exponents work when converting to fractions?

We Answered:

3 ^ (-2) = 1 / (3^2)


When converting a negative exponent to a fraction, just put the whole power in the denominator, and flip the sign on the exponent to positive.

General form:
a ^ (-b) = 1 / (a^b)

Mathew Said:

Converting fractions with whole numbers to decimals?

We Answered:

Take the numerator divided by the denominator then ADD the whole number.

Herbert Said:

Is there a formula for converting radian decimals to radian fractions?

We Answered:

Hi

Divide the decimal by ?.

If you divide 3.67 by ?, you get 3.67/? ? 1.168 ? 1.666… = 7/6. If you had more digits for the 3.67, you would get a value closer to 1.666… and you would recognize right away that it is equal to 7/6. Once you have that, you can do:

3.67/? ? 7/6
3.67 ? 7?/6

I hope this helps!