You compare unlike fractions by first finding a common denominator, then comparing the equivalent fractions that result. Here's a more detailed breakdown:
Steps to Compare Unlike Fractions
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Find a Common Denominator: The most efficient method is to find the Least Common Denominator (LCD). The LCD is the least common multiple (LCM) of the denominators of the fractions you want to compare.
- Example: Comparing 1/3 and 1/4. The multiples of 3 are 3, 6, 9, 12, 15... The multiples of 4 are 4, 8, 12, 16, 20... The Least Common Multiple (LCM) and therefore the LCD is 12.
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Create Equivalent Fractions: Convert each original fraction into an equivalent fraction with the LCD as the new denominator. To do this, determine what number you must multiply the original denominator by to get the LCD. Then, multiply both the numerator and denominator of the original fraction by that number.
- Example (continued):
- For 1/3, we multiply both the numerator and denominator by 4: (1 4) / (3 4) = 4/12
- For 1/4, we multiply both the numerator and denominator by 3: (1 3) / (4 3) = 3/12
- Example (continued):
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Compare the Numerators: Once the fractions have the same denominator, you can directly compare their numerators. The fraction with the larger numerator is the larger fraction.
- Example (continued): Now we compare 4/12 and 3/12. Since 4 is greater than 3, 4/12 is greater than 3/12. Therefore, 1/3 is greater than 1/4.
Examples
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Compare 2/5 and 3/8:
- LCD: The LCD of 5 and 8 is 40.
- Equivalent Fractions:
- 2/5 = (2 8) / (5 8) = 16/40
- 3/8 = (3 5) / (8 5) = 15/40
- Comparison: 16/40 > 15/40, therefore 2/5 > 3/8.
Why This Works
Finding a common denominator essentially divides a "whole" into the same number of parts for both fractions. This allows you to directly compare how many of those equal-sized parts each fraction represents by looking at their numerators. It's like comparing apples to apples instead of apples to oranges.
