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To compare mixed numbers, you can follow these steps:
Convert the mixed numbers to improper fractions:
For a mixed number like 3 1/2, you would convert it to the improper fraction 7/2.
The formula to convert a mixed number to an improper fraction is:
Improper Fraction = (Whole Number × Denominator) + Numerator) / Denominator
Once you have both mixed numbers converted to improper fractions, you can compare them using the standard fraction comparison rules:
Compare the numerators if the denominators are the same.
Convert the fractions to a common denominator if the denominators are different, then compare the numerators.
Here’s an example:
Compare 3 1/2 and 4 1/4:
Step 1: Convert the mixed numbers to improper fractions:
3 1/2 = (3 × 2 + 1) / 2 = 7/2
4 1/4 = (4 × 4 + 1) / 4 = 17/4
Step 2: Compare the improper fractions:
7/2 < 17/4 (since the numerators are different and 7 < 17)
Therefore, 3 1/2 is less than 4 1/4.
The key is to always convert mixed numbers to improper fractions before comparing them, as this allows you to use the standard fraction comparison rules.