When both amounts are measured against a third, call that third 1 · 12 practice problems

Checking the other way: $\frac{3}{16} \times \frac{8}{3} = \frac{1}{2}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 6 won -- gives 16 and 3 won, whose quotient is the same $\frac{3}{16}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{3}{10} \times \frac{5}{2} = \frac{3}{4}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 8 won -- gives 20 and 6 won, whose quotient is the same $\frac{3}{10}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{3}{10} \times \frac{4}{3} = \frac{2}{5}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 15 won -- gives 20 and 6 won, whose quotient is the same $\frac{3}{10}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{10}{33} \times \frac{11}{4} = \frac{5}{6}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 24 won -- gives 66 and 20 won, whose quotient is the same $\frac{10}{33}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{12}{77} \times \frac{11}{6} = \frac{2}{7}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 42 won -- gives 77 and 12 won, whose quotient is the same $\frac{12}{77}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{15}{136} \times \frac{17}{5} = \frac{3}{8}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 40 won -- gives 136 and 15 won, whose quotient is the same $\frac{15}{136}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{5}{26} \times \frac{13}{4} = \frac{5}{8}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 32 won -- gives 104 and 20 won, whose quotient is the same $\frac{5}{26}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{8}{27} \times \frac{15}{8} = \frac{5}{9}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 72 won -- gives 135 and 40 won, whose quotient is the same $\frac{8}{27}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{5}{18} \times \frac{8}{5} = \frac{4}{9}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 45 won -- gives 72 and 20 won, whose quotient is the same $\frac{5}{18}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{7}{45} \times \frac{9}{2} = \frac{7}{10}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 20 won -- gives 90 and 14 won, whose quotient is the same $\frac{7}{45}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{3}{44} \times \frac{16}{3} = \frac{4}{11}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 33 won -- gives 176 and 12 won, whose quotient is the same $\frac{3}{44}$. Any starting figure gives the same answer, which is why none is needed.

Checking the other way: $\frac{7}{26} \times \frac{13}{6} = \frac{7}{12}$, the sibling's share of mine. And the answer is less than 1, as it must be when the brother gets more than I do and the sibling less.

Another way: Picking a real allowance -- say 72 won -- gives 156 and 42 won, whose quotient is the same $\frac{7}{26}$. Any starting figure gives the same answer, which is why none is needed.