Solve 10:(2:(15:7)) - Sequential Division with Nested Operations

The order of operations requires you to evaluate expressions inside parentheses before anything else. In nested parentheses like $(2:(15:7))$, start with the innermost: $15:7 = \frac{15}{7}$.

Division by a fraction means multiply by its reciprocal. So $a:b = a \times \frac{1}{b}$. When $b = \frac{15}{7}$, then $2:(\frac{15}{7}) = 2 \times \frac{7}{15}$.

An improper fraction has a numerator larger than the denominator, like $\frac{75}{7}$. A mixed number combines a whole number and proper fraction: $10\frac{5}{7}$. Both represent the same value!

Look for common factors in numerator and denominator. In $\frac{10 \times 15}{2 \times 7}$, factor 10 as 5×2, then cancel the 2s: $\frac{5 \times 2 \times 15}{2 \times 7} = \frac{5 \times 15}{7}$.

While possible, fractions give exact answers. Converting $\frac{15}{7}$ to decimal (≈2.14) introduces rounding errors that compound through multiple operations, making your final answer less precise.

Write each step clearly! Start with $15:7 = \frac{15}{7}$, then $2:(\frac{15}{7}) = \frac{14}{15}$, finally $10:(\frac{14}{15}) = \frac{75}{7} = 10\frac{5}{7}$. One step at a time!