To find the half of 1 1⁄2, we first need to convert the mixed number into an improper fraction or a decimal to make the calculation easier.
1 1⁄2 can be converted into an improper fraction as follows: 1 1⁄2 = (1*2 + 1)/2 = 3⁄2.
To find the half of 3⁄2, we multiply 3⁄2 by 1⁄2: (3⁄2) * (1⁄2) = 3⁄4.
So, the half of 1 1⁄2 is 3⁄4.
Let’s break down the steps and explore the concepts behind fractions and mixed numbers to understand this calculation better.
Understanding Mixed Numbers and Improper Fractions
Mixed numbers are a combination of a whole number and a fraction. For example, 1 1⁄2 indicates one whole and one half. To convert a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and then add the numerator. This sum becomes the new numerator, while the denominator remains the same.
For 1 1⁄2, the conversion is: - Multiply the whole number (1) by the denominator (2): 1*2 = 2 - Add the numerator (1) to this result: 2 + 1 = 3 - The denominator remains 2, so the improper fraction is 3⁄2.
Calculating with Fractions
When multiplying fractions, we simply multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator.
In our case, to find half of 3⁄2, we multiply 3⁄2 by 1⁄2: - Numerators multiplied: 3 * 1 = 3 - Denominators multiplied: 2 * 2 = 4 - Result: 3⁄4
Practical Applications
Understanding how to work with fractions is crucial in many real-world applications, from cooking and measuring ingredients to construction and science. Being able to convert between mixed numbers and improper fractions, and performing operations like multiplication, can help in solving a variety of problems.
For example, if a recipe calls for 1 1⁄2 cups of flour but you want to make half the recipe, you would need 3⁄4 cup of flour, as calculated above.
Conclusion
Finding the half of 1 1⁄2 involves converting the mixed number to an improper fraction (3⁄2) and then multiplying by 1⁄2, which results in 3⁄4. This calculation demonstrates basic operations with fractions and mixed numbers, highlighting the importance of understanding these concepts for practical problem-solving.
What is the importance of understanding fractions in real-life scenarios?
+Understanding fractions is crucial for various real-life applications such as cooking, measuring ingredients, construction, and science. It helps in solving problems that involve quantities that are not whole numbers.
How do you convert a mixed number into an improper fraction?
+To convert a mixed number into an improper fraction, you multiply the whole number by the denominator and then add the numerator. The result becomes the new numerator, and the denominator remains the same.
In summary, calculating the half of 1 1⁄2 involves a simple conversion and multiplication process, resulting in 3⁄4. This demonstrates the basic principles of working with fractions and mixed numbers, which are essential skills for both academic and practical purposes.
