Ratios and Fractions I am trying to assist my daughter with holiday work, please help me with these questions:

Q1: Find the ratio $a:b$, when  $\frac{a+b}{a-b}=\frac{11}{5}$

Q2: Find the the ratio $a:b:c$ when   $\frac{1}{c}=\frac{2}{3b}=\frac{3}{4a}$

Q3: Evaluate $\frac{3a-b}{a+2b}$ if $\frac{a}{b}=\frac{4}{5}$
For the first, try to get things in terms of the quantity $x=a/b$. Use the fact that $r+s$ can be written as $s(\frac{r}{s}+1)$, which you can verify by multiplying it out.
$$\frac{11}{5}=\frac{b\left(\frac{a}{b}+1\right)}{b\left(\frac{a}{b}-1\right)}=\frac{x+1}{x-1}.$$
Solve this for $x$.

For the second, take the reciprocal:
$$c=\frac{3}{2}b=\frac{4}{3}a.$$

For the third, again, try to get things in terms of $x=a/b=4/5$.
$$\frac{3a-b}{a+2b}=\frac{b\left(3\frac{a}{b}-1\right)}{b\left(\frac{a}{b}+2\right)}=\frac{3\cdot\frac{4}{5}-1}{\frac{4}{5}+2}.$$

Note that all three of Ragnar's answers are wrong at the time of this post, so don't be alarmed if your answers don't match his.
Q1: You can rewrite this to $5(a-b)=11(a+b)$, and thus $-6a=16 b$. It follows that $\frac ab=-\frac 38$.

Q2: Take the inverse: $c=\frac 32 b=\frac 43 a$, thus $a:b:c=\frac 34:\frac 23:1$.

Q3: $\frac{3a-b}{a+2b}=\frac{2\frac ab-1}{\frac ab+2}=\frac{2\frac 45-1}{\frac 45+2}=\frac{\frac 35}{\frac {14}5}=\frac 3{14}$