Comparing and ordering mixed numbers involves understanding both the whole number part and the fractional part. First, compare the whole numbers. If they are different, the mixed number with the larger whole number is greater. If the whole numbers are the same, compare the fractions. To compare fractions, they must have the same denominator (the bottom number). If they don't, find a common denominator and convert the fractions. Then, compare the numerators (the top numbers) - the larger the numerator, the larger the fraction. Ordering mixed numbers then becomes a straightforward task of arranging them from least to greatest or greatest to least.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Mixed Number | a. The bottom number of a fraction. |
| 2. Numerator | b. A fraction where the numerator is greater than or equal to the denominator. |
| 3. Denominator | c. A number made up of a whole number and a fraction. |
| 4. Common Denominator | d. The top number of a fraction. |
| 5. Improper Fraction | e. A denominator that is the same in two or more fractions. |
Complete the sentences with the correct words:
To compare mixed numbers, first compare the ________ numbers. If these are the same, compare the ________. To compare fractions, they need a ________ denominator. The mixed number with the larger whole number is ________. If the numerators are the same, the fraction with the _______ denominator is smaller.
Explain in your own words how you would order the following mixed numbers from least to greatest: $2\frac{1}{2}$, $3\frac{1}{4}$, $2\frac{3}{4}$, $3\frac{1}{8}$.
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