Dividing fractions can be a bit tricky, but with a simple step-by-step approach, it becomes straightforward. In this article, we will walk through the process of dividing 1 1/4 by 1 1/3 and provide a clear understanding of the solution.
To start, let's convert the mixed numbers into improper fractions. This step is essential for performing division operations with fractions. The mixed numbers 1 1/4 and 1 1/3 can be converted as follows:
- 1 1/4 = (1*4 + 1)/4 = 5/4
- 1 1/3 = (1*3 + 1)/3 = 4/3
Step-by-Step Solution for 1 1/4 Divided by 1 1/3
Now that we have the improper fractions, we can proceed with the division. To divide fractions, we follow a simple rule: we multiply the first fraction by the reciprocal of the second fraction.
Step 1: Find the Reciprocal of the Second Fraction
The reciprocal of 4/3 is 3/4.
Step 2: Multiply the Fractions
Now, we multiply 5/4 by 3/4:
(5/4) * (3/4) = (5*3)/(4*4) = 15/16
| Operation | Result |
|---|---|
| 1 1/4 ÷ 1 1/3 | 15/16 |
Key Points
- Convert mixed numbers to improper fractions for easier operations.
- To divide fractions, multiply by the reciprocal of the divisor.
- The reciprocal of a fraction is obtained by swapping its numerator and denominator.
- Multiplication of fractions involves multiplying the numerators together and the denominators together.
- The result of 1 1/4 divided by 1 1/3 is 15/16.
Understanding the process of dividing fractions is vital for various mathematical operations and real-world applications. By following these simple steps and practicing with different examples, you'll become more confident in handling fraction division.
Real-World Applications
Fractions are used extensively in cooking, construction, and finance, among other fields. Being able to divide fractions accurately is crucial for making precise calculations and informed decisions.
Example: Cooking
Suppose a recipe requires 1 1/4 cups of flour, and you want to make 1/3 of the recipe. To find out how much flour you need, you would divide 1 1/4 by 3, or equivalently, multiply by 1/3. Using the steps outlined above, you would get 5/4 * 1/3 = 5/12 cups of flour.
What is 1 1/4 as an improper fraction?
+1 1/4 as an improper fraction is 5/4.
How do you find the reciprocal of a fraction?
+To find the reciprocal of a fraction, you swap its numerator and denominator. For example, the reciprocal of 4/3 is 3/4.
What is the result of dividing 1 1/4 by 1 1/3?
+The result of dividing 1 1/4 by 1 1/3 is 15/16.
In conclusion, dividing 1 1⁄4 by 1 1⁄3 involves converting mixed numbers to improper fractions, finding the reciprocal of the divisor, and multiplying the fractions. By mastering this process, you’ll be able to tackle more complex mathematical operations with ease and confidence.