AI Tutor
Imagine you have 12\frac{1}{2} of a giant chocolate bar, and a friend gives you 14\frac{1}{4} of the exact same bar.
How much chocolate do you have in total? You cannot just count two pieces, because the two pieces are completely different sizes!
The bottom number of a fraction is the denominator, and it tells you how many equal pieces make up one whole.
So how can we add these two fractions together when their slices don't match?

Making the Slices Match

Since 44 is a multiple of 22 (2×2=42 \times 2 = 4), we can cut each half in half to turn 12\frac{1}{2} into fourths.
Multiplying both the top and bottom by 22 gives an equivalent fraction: 1×22×2=24\frac{1 \times 2}{2 \times 2} = \frac{2}{4}.
Notice that we only had to change one fraction, because 44 was already a multiple of 22!
What happens when we try another problem, like 13+26\frac{1}{3} + \frac{2}{6}?

Worked Example: Sixths and Thirds

Look at the denominators 33 and 66. Because 3×2=63 \times 2 = 6, the number 66 is our common denominator.