1. ## Simple expression problem

Hi there,

I'm currently brushing the rust off my algebra. Please can someone show the workings and explain how they would get an answer for the following question...

Question:

2/3(4 + 3 4/5) = ?

The answer according to the book I'm studying is 4 4/15, but I can't arrive at this answer.

2. Hello, mezhopking!

If you typed the problem correctly, the book is wrong.

Evaluate: .$\displaystyle \frac{2}{3}\left(4 + 3\,\frac{4}{5}\right)$

$\displaystyle \frac{2}{3}\left(4 + 3\,\frac{4}{5}\right) \;= \;\frac{2}{3}\left(\frac{20}{5} + \frac{19}{5}\right) \;= \;\frac{2}{{\color{red}\rlap{/}}3}\cdot\frac{{\color{red}\rlap{//}}{39}^{13}}{5} \;=\;\frac{26}{5} \;=\;\boxed{5\,\frac{1}{5}}$

3. I do wish they'd work with improper fractions instead of mixed numbers...

anyway

2/3[4+(19/5)]=?
[(2/3)(4)]+[(2/3)(19/5)]=?
(8/3)+(38/15)=?
26/5=?

2/3[4+(19/5)]=?
2/3(39/5)=?
26/5=?

Am I reading the problem you wrote down wrong?

I see: two-thirds multiplied by the quantity four plus three and four-fifths.

(3 and 4/5 is the same as 19/5 - to get an improper fraction from a mixed number you need to find the numerator of the mixed number by multiplying the whole number (3) by the denominator (5), (which is 15 in our example), plus the numerator (4), (so 19/5 because denominator stays the same))

if you're confused on order of operations, it's PEMDAS

Parenthesis
Exponents
Multiplication
Division
Subtraction

EDIT: damn I need to learn how to use the math script because I can't demonstrate crap!

4. Originally Posted by Soroban
Hello, mezhopking!

If you typed the problem correctly, the book is wrong.

$\displaystyle \frac{2}{3}\left(4 + 3\,\frac{4}{5}\right) \;= \;\frac{2}{3}\left(\frac{20}{5} + \frac{19}{5}\right) \;= \;\frac{2}{{\color{red}\rlap{/}}3}\cdot\frac{{\color{red}\rlap{//}}{39}^{13}}{5} \;=\;\frac{26}{5} \;=\;\boxed{5\,\frac{1}{5}}$

Thanks Soroban, that's a brilliant reply with excellent workings too. It's the same answer I got too. But mine is little less elegant:

2/3 (20/5 + 19/5)
= 2/3 (39/5)
= 78/15
= 5 3/15
= 5 1/5

Ta, Mez