Parts of a Whole
Adding fractions is like putting puzzle pieces together. If you have $\frac{1}{4}$ of a pizza and your friend gives you $\frac{2}{4}$ more, you just count how many fourths you have in total!
The Golden Rule
When the denominators (the bottom numbers) are the same, the "size" of the pieces doesn't change. You only change the top!
| Operation | Rule | Example (LaTeX) |
|---|---|---|
| Addition | Add the numerators. Keep the denominator the same. | $\frac{2}{8} + \frac{3}{8} = \frac{5}{8}$ |
| Subtraction | Subtract the numerators. Keep the denominator the same. | $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$ |
| Wait! | Never add the denominators! $\frac{1}{2} + \frac{1}{2}$ is not $\frac{2}{4}$. | $\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1$ |
Combine the parts:
1
4
2
4
Simplifying Fractions Video
Watch one more quick explanation to reinforce how the GCF makes simplification fast.
Simplifying Fractions
Shortcut: divide numerator and denominator by the greatest common factor (GCF) to write fractions in simplest form.
- Example: $ \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$
- Try to reduce each fraction until no common factors remain.
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Fraction Scientist!
You’ve mastered the art of combining, separating, and simplifying parts of a whole. Excellent lab work!