AI Tutor
Imagine sharing an 8-slice pizza with a friend. If you take 2 slices and your friend takes 3 slices, how much of the whole pizza did you two eat?
You ate 5 slices out of 8, or 58\frac{5}{8} of the pizza — definitely not 516\frac{5}{16}! In any fraction, the bottom number is the denominator, which names the size of each slice, while the top number is the numerator, which counts how many slices you have.
Why do we leave the bottom number alone while adding the top?

The Like Denominator Rule

Because both fractions already have the exact same slice size, you only combine the counts: ad+bd=a+bd\frac{a}{d} + \frac{b}{d} = \frac{a+b}{d}.
A common mistake is adding the bottom numbers together to get 28+38=516\frac{2}{8} + \frac{3}{8} = \frac{5}{16}. But cutting a pizza into 16 slices would make each slice twice as small, which did not actually happen to your food!
What should you do when your final fraction can be written using fewer, bigger pieces?

Writing in Simplest Form

A fraction is in simplest form when the numerator and denominator share no common factor other than 1.
Let's add 18+38\frac{1}{8} + \frac{3}{8}. Adding the numerators gives 48\frac{4}{8}, but both 4 and 8 can be divided evenly by 4, leaving 12\frac{1}{2}.
More generally, expressing a result in simplest form (or lowest terms) requires dividing both the numerator and denominator by their Greatest Common Divisor (gcd⁡\gcd): a/gcd⁡(a,d)d/gcd⁡(a,d)\frac{a / \gcd(a, d)}{d / \gcd(a, d)}.