Ordering fractions means arranging them from least to greatest or greatest to least. When fractions have the same denominator (the bottom number), it’s easy – just compare the numerators (the top numbers)! For fractions with different denominators, you'll need to find a common denominator before you can compare them. This makes sure you're comparing apples to apples!
Let's say you want to order $\frac{1}{2}$, $\frac{1}{4}$, and $\frac{3}{4}$ from least to greatest. First, notice that $\frac{1}{4}$ and $\frac{3}{4}$ already have a common denominator. You can convert $\frac{1}{2}$ to $\frac{2}{4}$. Now, comparing $\frac{1}{4}$, $\frac{2}{4}$, and $\frac{3}{4}$ is simple! The order is $\frac{1}{4}$, $\frac{1}{2}$, $\frac{3}{4}$.
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Numerator | A. The number below the fraction bar |
| 2. Denominator | B. Fractions that represent the same value |
| 3. Common Denominator | C. The number above the fraction bar |
| 4. Equivalent Fractions | D. A shared multiple of the denominators |
| 5. Ordering Fractions | E. Arranging fractions from least to greatest or greatest to least |
Complete the following sentences with the correct words:
To order fractions with different ____________, you need to find a ____________ denominator. Once the fractions have the same ____________, you can compare the ____________ to determine their order. Ordering fractions helps us understand the ____________ size of each fraction.
Explain why finding a common denominator is important when ordering fractions with different denominators. Use an example to illustrate your explanation.
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