To determine if 1⁄2 is greater than 1⁄3, we need to compare the two fractions.
Comparing Fractions
Fractions can be compared by converting them to equivalent decimals or by finding a common denominator. Let’s use both methods to compare 1⁄2 and 1⁄3.
Method 1: Converting to Decimals
To convert a fraction to a decimal, we divide the numerator by the denominator. So, 1⁄2 = 1 ÷ 2 = 0.5 and 1⁄3 = 1 ÷ 3 = 0.33 (rounded to two decimal places). Since 0.5 is greater than 0.33, we can conclude that 1⁄2 is greater than 1⁄3.
Method 2: Finding a Common Denominator
To find a common denominator, we need to find the least common multiple (LCM) of 2 and 3, which is 6. Then, we convert both fractions to have a denominator of 6: 1⁄2 = 3⁄6 and 1⁄3 = 2⁄6. Since 3⁄6 is greater than 2⁄6, we can conclude that 1⁄2 is greater than 1⁄3.
- 1/2 = 0.5 (decimal)
- 1/3 = 0.33 (decimal)
- 3/6 (1/2 with common denominator) > 2/6 (1/3 with common denominator)
| Fraction | Decimal Equivalent | Common Denominator |
|---|---|---|
| 1/2 | 0.5 | 3/6 |
| 1/3 | 0.33 | 2/6 |
Key Points
- 1/2 is greater than 1/3 based on decimal conversion.
- 1/2 is greater than 1/3 based on common denominator comparison.
- The decimal equivalent of 1/2 is 0.5.
- The decimal equivalent of 1/3 is 0.33 (rounded to two decimal places).
- Converting fractions to decimals or finding a common denominator are effective methods for comparing fractions.
In conclusion, by comparing the decimal equivalents or using a common denominator, it is clear that 1⁄2 is greater than 1⁄3.
How do I compare fractions with different denominators?
+You can compare fractions with different denominators by converting them to equivalent decimals or by finding a common denominator. This allows for a direct comparison of the fractions.
What is the least common multiple (LCM) used for in comparing fractions?
+The LCM is used to find a common denominator for fractions, enabling a straightforward comparison. It is the smallest number that both denominators can divide into evenly.
Why is converting fractions to decimals a useful method for comparison?
+Converting fractions to decimals is a useful method for comparison because it allows for a direct numerical comparison. Decimals are often easier to understand and compare than fractions, especially for those less familiar with fraction arithmetic.
