To find half of 1 1⁄2 cups, we need to first convert the mixed number to an improper fraction.
1 1⁄2 cups can be converted to an improper fraction as follows: 1 1⁄2 = (1 * 2) + 1 = 3⁄2 cups
Now, to find half of 3⁄2 cups, we multiply 3⁄2 by 1⁄2: (3⁄2) * (1⁄2) = 3⁄4 cups
So, half of 1 1⁄2 cups is 3⁄4 cups.
Converting Mixed Numbers to Improper Fractions
When working with mixed numbers, it’s often helpful to convert them to improper fractions. This can be done by multiplying the whole number part by the denominator, then adding the numerator.
The formula for converting a mixed number to an improper fraction is: (a * b) + c = (ad + c)/d, where a is the whole number part, b is the denominator, c is the numerator, and d is the denominator.
For example, to convert 2 3⁄4 to an improper fraction: (2 * 4) + 3 = 8 + 3 = 11⁄4
Understanding Fractions and Mixed Numbers
Fractions and mixed numbers are used to represent parts of a whole. A fraction consists of a numerator (the top number) and a denominator (the bottom number), and represents a proportion of a whole. A mixed number, on the other hand, combines a whole number with a fraction.For instance, 3 1/2 can be thought of as 3 whole units and 1/2 of another unit.
Key Points
- To find half of a mixed number, convert it to an improper fraction first.
- Multiply the numerator by the reciprocal of the fraction to find half.
- Converting mixed numbers to improper fractions can simplify calculations.
- Fractions and mixed numbers represent parts of a whole.
- Understanding the relationship between fractions and mixed numbers is essential for working with proportions and ratios.
| Mixed Number | Improper Fraction |
|---|---|
| 1 1/2 | 3/2 |
| 2 3/4 | 11/4 |
| 3 1/2 | 7/2 |
What is the difference between a fraction and a mixed number?
+A fraction represents a part of a whole, while a mixed number combines a whole number with a fraction.
How do I convert a mixed number to an improper fraction?
+Multiply the whole number part by the denominator, then add the numerator. The result is the new numerator, and the denominator remains the same.
What is half of 3/4 cups?
+To find half of 3/4 cups, multiply 3/4 by 1/2. The result is 3/8 cups.
In conclusion, finding half of 1 1⁄2 cups involves converting the mixed number to an improper fraction and then multiplying by 1⁄2. Understanding fractions and mixed numbers is essential for working with proportions and ratios in cooking and other applications.