Our comparing fractions calculator is designed to help users compute the relative size or value of two or more fractions using formula a/b = (a * (LCM(b, d) / b)) / LCM(b, d).
Let’s say we want to compare 3/4 and 2/3. A comparing fractions calculator would quickly determine that 3/4 is greater than 2/3, saving time and reducing the chance of error in manual calculations.
Comparing Fractions Calculator
| Fraction 1 | Fraction 2 | Comparison Result |
|---|---|---|
| 1/2 | 3/4 | 1/2 < 3/4 |
| 5/6 | 3/8 | 5/6 > 3/8 |
| 2/3 | 4/9 | 2/3 > 4/9 |
| 1/4 | 1/3 | 1/4 < 1/3 |
| 7/10 | 2/5 | 7/10 > 2/5 |
| 3/5 | 2/7 | 3/5 > 2/7 |
| 1/8 | 1/2 | 1/8 < 1/2 |
| 5/12 | 1/3 | 5/12 > 1/3 |
| 3/10 | 7/20 | 3/10 > 7/20 |
| 2/5 | 4/10 | 2/5 = 4/10 |
| 1/6 | 1/2 | 1/6 < 1/2 |
| 9/10 | 3/4 | 9/10 > 3/4 |
| 5/8 | 3/5 | 5/8 > 3/5 |
| 1/3 | 1/4 | 1/3 > 1/4 |
| 7/12 | 2/3 | 7/12 < 2/3 |
Comparing Fractions Formula
- a/b = (a * (LCM(b, d) / b)) / LCM(b, d)
- c/d = (c * (LCM(b, d) / d)) / LCM(b, d)
The formula for comparing fractions involves finding a common denominator for the fractions being compared. Once a common denominator is established, we can directly compare the numerators to determine which fraction is greater.
- Comparing 2/5 and 3/7:
- LCM of 5 and 7 is 35.
- 2/5 = (2 7) / (5 7) = 14/35.
- 3/7 = (3 5) / (7 5) = 15/35.
- 15/35 > 14/35, so 3/7 > 2/5.
- Comparing 4/9 and 5/12:
- LCM of 9 and 12 is 36.
- 4/9 = (4 4) / (9 4) = 16/36.
- 5/12 = (5 3) / (12 3) = 15/36.
- 16/36 > 15/36, so 4/9 > 5/12.
How do you compare two fractions?
- Check for same denominators: If the fractions have the same denominator, simply compare the numerators. The fraction with the larger numerator is greater.
- Find a common denominator: If the denominators are different, find the least common multiple (LCM) of the denominators.
- Convert fractions: Multiply both the numerator and denominator of each fraction by the appropriate factor to reach the common denominator.
- Compare numerators: Once both fractions have the same denominator, compare their numerators. The fraction with the larger numerator is greater.
- Consider negative fractions: Remember that negative fractions are less than positive fractions, and larger negative fractions are actually smaller in value.
- Use cross-multiplication: For a quick comparison, multiply the numerator of each fraction by the denominator of the other fraction. Compare the results to determine which fraction is greater.
Let’s compare 5/8 and 7/12:
- The denominators are different, so we need to find the LCM of 8 and 12, which is 24.
- Convert 5/8 to an equivalent fraction with denominator 24:
- 5/8 = (5 3) / (8 3) = 15/24.
- Convert 7/12 to an equivalent fraction with denominator 24:
- 7/12 = (7 2) / (12 2) = 14/24.
- Now we can directly compare 15/24 and 14/24.
- Since 15 > 14, we conclude that 5/8 > 7/12.
Which fraction is greater?
Fractions with the same denominator: The fraction with the larger numerator is greater.
Example: 5/7 > 3/7.Fractions with the same numerator: The fraction with the smaller denominator is greater.
Example: 4/5 > 4/9.Fractions close to 1: Compare how close each fraction is to 1 by subtracting from 1.
Example: 9/10 > 11/12 because 1 - 9/10 = 1/10, which is less than 1 - 11/12 = 1/12.Benchmark fractions: Compare fractions to common benchmarks like 1/2, 1/4, or 3/4.
Example: 7/12 > 1/2, while 5/12 < 1/2.Cross-multiplication: Multiply the numerator of each fraction by the denominator of the other fraction and compare the results.
Example: For 3/4 and 5/6, cross-multiply: 3 * 6 = 18 and 4 * 5 = 20. Since 20 > 18, 5/6 > 3/4.Which is bigger, 5’8″ or 3/4″?
To compare 5’8″ and 3/4″, we need to convert them to the same unit of measurement. Let’s convert both to inches:
- 5’8″ = (5 * 12) + 8 = 68 inches.
- 3/4″ = 0.75 inches.
Clearly, 68 inches is much larger than 0.75 inches. Therefore, 5’8″ is bigger than 3/4″.
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