Help! Can you reduce equation with fractions like this?

[Jennab]

Does this work?

4/3 x 3.14 x abc/2x2x2 = abc/2.4 ????

 

[JeffM]

Does this work?

4/3 x 3.14 x abc/2x2x2 = abc/2.4 ????

Please do NOT use \(\displaystyle \times\) to indicate multiplication in algebra. Too easy to confuse with \(\displaystyle x.\) Use *.

Did you mean \(\displaystyle \dfrac{4}{3} * 3.14 * \dfrac{abc}{2^3}?\) What you wrote means \(\displaystyle \dfrac{4}{3} * 3.14 * \dfrac{abc}{2} * 2^2.\)

\(\displaystyle \dfrac{4}{3} * 3.14 * \dfrac{abc}{2^3} = 3.14 * \dfrac{4 * abc}{3 * 8} = \dfrac{3.14}{1} * \dfrac{abc}{6} = \dfrac{3.14abc}{6} \approx 0.523abc.\)

\(\displaystyle \dfrac{4}{3} * 3.14 * \dfrac{abc}{2} * 2^2 = 3.14 * 4 * \dfrac{4 * abc}{3 * 2} = \dfrac{12.56}{1} * \dfrac{2abc}{3} =\dfrac{25.12abc}{3} \approx 8.37abc.\)

EDIT: The following post is correct. I DID assume that 3.14 was an approximation for \(\displaystyle \pi.\) I should have made that assumption explicit.

 

[Bob Brown MSEE]

Exact vrs Significant

\(\displaystyle \dfrac{12.56}{1} * \dfrac{2abc}{3} =\dfrac{25.12abc}{3} \approx 8.37abc.\)

JeffM made the assumption that 3.14 is not exact, but is a decimal for which only 3 significant digits are given.

He used two principles.
1) Rounding the answer to the appropriate number of significant digits.
2) Remove any numbers from denominator that are not exact.

PS: If 3.14 is supposed to represent π, then use π in the calculations and answer.

 

[Jennab]

Thanks for your help!

I was playing around with the following equation, trying to get something like: abc/2.4 as an answer. Not possible I guess...
(x = * below):

With approximation of π≈3, the equation simplifies to:

Would like to find abc/2.4 as an answer. But wasn't sure if possible mathematically to arrive at. If used 3.14 for π, was wondering if would get as an answer. Thanks.

 

[Deleted member 4993]

Thanks for your help!

I was playing around with the following equation, trying to get something like: abc/2.4 as an answer. Not possible I guess...
(x = * below):

With approximation of π≈3, the equation simplifies to:

Would like to find abc/2.4 as an answer. But wasn't sure if possible mathematically to arrive at. If used 3.14 for π, was wondering if would get as an answer. Thanks.

6/π =1.909859

 

[Quaid]

I was playing around

In future threads, please let us know up front if you're playing around, and post on the Math Odds&Ends board.

Otherwise, kindly include the complete exercise statement. (Here's a link for the site guidelines.)

Would like to find abc/2.4 as an answer.

Use 2.5 as your approximation for Pi.

If used 3.14 for π, was wondering if would get as an answer.

I don't understand this statement, but JeffM's reply uses 3.14 for Pi (if that helps).

Cheers

 

[JeffM]

Thanks for your help!

I was playing around with the following equation, trying to get something like: abc/2.4 as an answer. Not possible I guess...
(x = * below):

With approximation of π≈3, the equation simplifies to:

Would like to find abc/2.4 as an answer. But wasn't sure if possible mathematically to arrive at. It's not. If used 3.14 for π, was wondering if would get as an answer. Thanks.

\(\displaystyle \dfrac{4}{3} * x * \dfrac{a}{2} * \dfrac{b}{2} * \dfrac{c}{2} = \dfrac{4xabc}{3 * 8} = \dfrac{x * abc}{6} \implies\)

\(\displaystyle \dfrac{4}{3} * x * \dfrac{a}{2} * \dfrac{b}{2} * \dfrac{c}{2} \approx \dfrac{abc}{2.4} \implies \dfrac{x}{6} \approx \dfrac{1}{2.4} \implies x \approx 2.5 \not\approx \pi.\)