AI Tutor
Imagine a research submarine diving to 34\frac{3}{4} of a mile below sea level (−34-\frac{3}{4} miles), and then floating up by 12\frac{1}{2} of a mile. Where does it end up?
Adding signed fractions works just like walking on a number line: positive numbers move you right, and negative numbers move you left.
How do we solve this when the slices aren't the same size? Let's look at the basic rule for matching denominators.

Common Denominators First

Before you can add any fractions, the pieces must be the exact same size. That means finding a common denominator, which is a shared multiple of both bottom numbers.
Let's solve −56+23-\frac{5}{6} + \frac{2}{3}. Multiply the top and bottom of 23\frac{2}{3} by 22 to make it 46\frac{4}{6}.
Once the denominators match, keep the denominator and add the numerators: −5+46=−16\frac{-5 + 4}{6} = -\frac{1}{6}
What happens when you have whole numbers mixed into the problem? Let's take a look at mixed numbers.

Adding Signed Mixed Numbers

The cleanest way to add signed mixed numbers is to convert them into improper fractions, where the numerator is greater than or equal to the denominator.
Let's solve 112+(−234)1\frac{1}{2} + \left(-2\frac{3}{4}\right). First, rewrite 1121\frac{1}{2} as 32\frac{3}{2} and −234-2\frac{3}{4} as −114-\frac{11}{4}.