AI Tutor
Imagine a research submarine starts at 150 ft150\text{ ft} below sea level, or −14 mile-\frac{1}{4}\text{ mile}. If it drops another 23 mile\frac{2}{3}\text{ mile}, how deep is it now?
To find the final depth, we need to subtract a positive fraction from a negative one: −14−23-\frac{1}{4} - \frac{2}{3}.

The "Add the Opposite" Rule

Subtracting any value is mathematically identical to adding its additive inverse (its opposite sign).
How does this rule help us when the numbers are fractions with the same denominator?

Like Denominators

When fractions share a common denominator, keep the bottom number the same and apply the subtraction rule directly to the numerators.
What happens when the pieces are different sizes and the denominators don't match?

Unlike Denominators

Before you can combine the numerators, you must find the least common denominator (LCD) to make the fractional parts equal in size.
Let's solve −23−14-\frac{2}{3} - \frac{1}{4}. The common denominator for 33 and 44 is 1212.