๐ What are Fractions?
A fraction represents a part of a whole. It's written as one number over another, like $\frac{1}{2}$. The top number is the numerator, and it tells you how many parts you have. The bottom number is the denominator, and it tells you how many total parts there are in the whole.
๐งฎ What Does it Mean to Compare Fractions?
Comparing fractions means figuring out which fraction represents a larger or smaller part of a whole. There are a few ways to do this, and we'll explore the most common methods.
๐ Comparing Fractions: Methods
Here's a breakdown of different ways to compare fractions:
| Method |
Definition |
How It Works |
| Common Denominator |
Finding a common multiple for the denominators of both fractions. |
- Find the Least Common Multiple (LCM) of the denominators.
- Convert each fraction to an equivalent fraction with the LCM as the new denominator.
- Compare the numerators. The fraction with the larger numerator is the larger fraction.
|
| Cross-Multiplication |
Multiplying the numerator of one fraction by the denominator of the other. |
- Multiply the numerator of the first fraction by the denominator of the second fraction.
- Multiply the numerator of the second fraction by the denominator of the first fraction.
- Compare the products. The fraction corresponding to the larger product is the larger fraction.
|
| Visual Representation |
Drawing diagrams to represent the fractions and visually comparing their sizes. |
- Draw two identical shapes (e.g., rectangles or circles).
- Divide each shape according to the denominator of each fraction.
- Shade in the number of parts equal to the numerator of each fraction.
- Visually compare the shaded areas to determine which fraction is larger.
|
โ๏ธ Key Takeaways
- ๐ Common Denominator:
- โ Find the Least Common Multiple (LCM) of the denominators.
- ๐ก Convert fractions so they have the same denominator.
- ๐ Compare the numerators โ the larger the numerator, the larger the fraction.
- ๐ Cross-Multiplication:
- โ๏ธ Multiply diagonally across the fractions.
- โ๏ธ Compare the products to determine which fraction is larger.
- ๐ Visual Representation:
- ๐ผ๏ธ Draw pictures to see which fraction covers a larger area.
- ๐จ A great way to understand fractions, especially for beginners.