Switching Numbers and Negating on Subtraction

When a subtraction problem results in a negative answer (e.g., subtracting a larger number from a smaller one), it's often easier to switch the order of the numbers, perform the subtraction, and then negate the result.

This uses the principle $a - b = -(b - a)$.

For example, to calculate $4\frac{5}{6} - 10\frac{11}{12}$, you can instead calculate $-(10\frac{11}{12} - 4\frac{5}{6})$. This simplifies the process by avoiding borrowing across the whole number in a negative context.

$-(10\frac{11}{12} - 4\frac{10}{12}) = -(6\frac{1}{12})$.