# Going insane!

#### Forscythe87

Hi All,
I have recently decided to go back to college and needless to say my math is absolutely horrible. I have a fairly decent understanding of everything up to basic equations but I am stumped at this problem im currently trying to solve for practice. Id appreciate help with an explanation of hows its solved. I already know the answer but I want to work it to become fluent. (Wink)

Problem is:

3 1/6 + (2 1/3 divided by 3.6)^3

I worked everything out and converted fractions to decimals. Id greatly appreciate any help possible! I want to learn math correctly this time around. I am trying to be disciplined and know why and how I come to an answer instead of just coming to it .

#### Sudharaka

Hi All,
I have recently decided to go back to college and needless to say my math is absolutely horrible. I have a fairly decent understanding of everything up to basic equations but I am stumped at this problem im currently trying to solve for practice. Id appreciate help with an explanation of hows its solved. I already know the answer but I want to work it to become fluent. (Wink)

Problem is:

3 1/6 + (2 1/3 divided by 3.6)^3

I worked everything out and converted fractions to decimals. Id greatly appreciate any help possible! I want to learn math correctly this time around. I am trying to be disciplined and know why and how I come to an answer instead of just coming to it .
Dear Forscythe87,

I need a bit of clarification about the expression. Is it, $$\displaystyle 3\frac{1}{6}+\left(2\frac{1}{3}\div{3.6}\right)^3$$ ??

#### Mukilab

I hope this is correct (I am unsure whether you mean $$\displaystyle 3*\frac{1}{6}$$ or $$\displaystyle \frac{19}{6}$$

Here are my workings:
$$\displaystyle \frac{19}{6}+(\frac{7}{3}*\frac{1}{3.6})^3 \longrightarrow \frac{19}{6}+(\frac{7}{3*3.6})^3\longrightarrow \frac{19}{6}+0.27=3.44$$

All decimals are to 2 decimal places.

#### Forscythe87

Dear Forscythe87,

I need a bit of clarification about the expression. Is it, $$\displaystyle 3\frac{1}{6}+\left(2\frac{1}{3}\div{3.6}\right)^3$$ ??
Yes thats correct. The exponent applies to both the 2 1/3 and 3.6 right?

#### Sudharaka

Yes thats correct. The exponent applies to both the 2 1/3 and 3.6 right?
Dear Forscythe87,

First you need to convert the improper fractions into proper fractions.

$$\displaystyle 3\frac{1}{6}+\left(2\frac{1}{3}\div{3.6}\right)^3$$

$$\displaystyle =\frac{19}{6}+\left(\frac{7}{3}\div{\frac{36}{10}}\right)^3$$

$$\displaystyle =\frac{19}{6}+\left(\frac{7}{3}\times{\frac{10}{36}}\right)^3$$

$$\displaystyle =\frac{19}{6}+\left(\frac{35}{54}\right)^3$$

$$\displaystyle =3.167+0.648^3$$

$$\displaystyle =3.167+0.272$$

$$\displaystyle =3.439$$

#### Wilmer

3 1/6 + (2 1/3 divided by 3.6)^3
Are you SURE that's properly posted? Do you have the answer?

#### Forscythe87

Are you SURE that's properly posted? Do you have the answer?
Im starting to think my answer worksheet is wrong. The answer according to the answer key I have is 3 3389/7986.

#### Sudharaka

Im starting to think my answer worksheet is wrong. The answer according to the answer key I have is 3 3389/7986.
Dear Forscythe87,

$$\displaystyle 3\frac{3389}{7986}=3.42436.....$$

$$\displaystyle \frac{19}{6}+\left(\frac{35}{54}\right)^3=3.43895....$$

#### earboth

MHF Hall of Honor
Hi All,
I have recently decided to go back to college and needless to say my math is absolutely horrible. I have a fairly decent understanding of everything up to basic equations but I am stumped at this problem im currently trying to solve for practice. Id appreciate help with an explanation of hows its solved. I already know the answer but I want to work it to become fluent. (Wink)

Problem is:

3 1/6 + (2 1/3 divided by 3.6)^3

I worked everything out and converted fractions to decimals. Id greatly appreciate any help possible! I want to learn math correctly this time around. I am trying to be disciplined and know why and how I come to an answer instead of just coming to it .
If indeed the given answer is

$$\displaystyle 3 + \frac{3389}{7986} = \frac{27347}{7986}$$

then the bracket has the value $$\displaystyle \frac7{11}$$

This is only possible if the number 3.6 in the bracket was originally $$\displaystyle \frac{11}3$$.

I don't know if you transformed the fraction $$\displaystyle \frac{11}3$$ into 3.6 - then you have made the assumption that an approximate value equals the fraction - or if the 3.6 was given in the first place. If so the authors of the book had made a mistake.

#### Sudharaka

If indeed the given answer is

$$\displaystyle {\color{red}3 + \frac{3389}{7986} = \frac{27347}{7986}}$$

then the bracket has the value $$\displaystyle \frac7{11}$$

This is only possible if the number 3.6 in the bracket was originally $$\displaystyle \frac{11}3$$.

I don't know if you transformed the fraction $$\displaystyle \frac{11}3$$ into 3.6 - then you have made the assumption that an approximate value equals the fraction - or if the 3.6 was given in the first place. If so the authors of the book had made a mistake.
Dear earboth,

Not that it really matters, just in case to avoid confusion, the highlighted part should be, $$\displaystyle 3\frac{3389}{7986} = \frac{27347}{7986}$$