What Fraction is LESS than 1 2?
Understanding the Problem
The question "What fraction is LESS than 1 2?" may seem simple, but it can be a bit tricky. It’s essential to understand the concept of fractions and comparing them to understand this question. A fraction is a way to represent a part of a whole. For example, 1/2 is equal to 1 whole divided by 2 parts. In this case, the whole is 1, and the parts are 2.
Calculating the Fraction
To find the fraction that is LESS than 1 2, we need to convert the mixed number 1 2 into a fraction. The decimal 1.2 can be converted into a fraction by multiplying it by 10.
10 × 1.2 = 12
This means that 1 2 is equal to 12. Now, we need to find the fraction that is LESS than 12. The only possible fraction that is LESS than 12 is 1/2 or 1/3 or 2/3.
Why is this the case?
The fraction 1/2 is LESS than 12 because it represents a part of a whole that is larger than 1. The fraction 1/3 is also LESS than 12, as it represents a part of a whole that is between 1 and 2. The fraction 2/3 is also LESS than 12, as it represents a part of a whole that is larger than 2.
Comparing Fractions
When comparing fractions, we need to find a common denominator. A common denominator is a number that both fractions can be expressed as a fraction with.
Finding a Common Denominator
To find a common denominator, we need to find the least common multiple (LCM) of the denominators of the fractions. The LCM of 2 and 3 is 6. So, we can express both fractions with a denominator of 6.
Expressing Fractions with a Common Denominator
We can express 1/2 and 1/3 with a denominator of 6 as follows:
1/2 = 3/6
1/3 = 2/6
2/3 = 4/6
Comparing the Fractions
Now that both fractions have a common denominator, we can compare them:
| Fraction | Numerator | Denominator |
|---|---|---|
| 1/2 | 3 | 6 |
| 1/3 | 2 | 6 |
| 2/3 | 4 | 6 |
As you can see, 1/2, 1/3, and 2/3 are all LESS than 12. They are all smaller than 1 2.
Conclusion
In conclusion, the fraction that is LESS than 1 2 is 1/2, 1/3, and 2/3. These fractions represent a part of a whole that is smaller than 12. To find a common denominator, we need to find the least common multiple (LCM) of the denominators of the fractions. Comparing the fractions, we can see that all three fractions are LESS than 1 2.
Discussion Points
- What is the least common multiple (LCM) of 2 and 3?
- How do we express fractions with a common denominator?
- What is the difference between a fraction and a decimal?
Answers
- The LCM of 2 and 3 is 6.
- To express fractions with a common denominator, we need to find the LCM of the denominators of the fractions. This can be done by finding the least common multiple (LCM) of 2 and 3, which is 6.
- The difference between a fraction and a decimal is that a fraction represents a part of a whole, while a decimal represents a part of 1.