When dealing with fractions, it's essential to understand the steps involved in solving division problems. In this article, we'll break down the process of solving 2 divided by 5/12, making it easy to understand and follow.
Why Fractions Matter
Fractions are an integral part of mathematics, and understanding how to work with them is crucial in various real-life situations, such as cooking, measurement, and finance. Dividing fractions, in particular, can be a bit tricky, but with the right approach, it can be a breeze.
What Does 2 Divided By 5/12 Mean?
To solve this problem, we need to understand what dividing by a fraction means. In this case, we're dividing 2 by a fraction (5/12). Think of it as "2 divided into groups of 5/12." To make it more manageable, we'll use a simple trick: inverting the fraction and multiplying.
The Invert-and-Multiply Trick
When dividing by a fraction, we can invert the fraction (i.e., flip the numerator and denominator) and then multiply. So, in our case, we'll invert 5/12 to get 12/5 and then multiply 2 by this new fraction.
Multiplying Fractions
To multiply fractions, we simply multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom). So, in our case:
2 × 12/5 = (2 × 12) / (1 × 5) = 24/5
Simplifying the Result
We can simplify our result by dividing both the numerator and denominator by 1:
24/5 = 4.8
Tips and Tricks
Here are some additional tips to keep in mind when working with fractions:
- When multiplying fractions, multiply the numerators and multiply the denominators.
- When dividing fractions, invert the second fraction and multiply.
- Simplify your result by dividing both the numerator and denominator by the greatest common divisor (GCD).
Practical Applications
Dividing fractions has numerous practical applications in various fields, including:
- Cooking: When a recipe calls for a fraction of an ingredient, you may need to divide that fraction to scale the recipe up or down.
- Measurement: Fractions are used in measurement, such as measuring distances or volumes.
- Finance: Fractions are used in finance, such as calculating interest rates or investment returns.
Real-World Examples
Here are some real-world examples of dividing fractions:
- A recipe calls for 3/4 cup of flour. If you want to make half the recipe, you need to divide 3/4 by 2.
- A building is 5/6 of a mile long. If you want to divide it into equal sections of 1/12 mile each, you need to divide 5/6 by 1/12.
Gallery of Fractions
Frequently Asked Questions
What does it mean to divide by a fraction?
+Dividing by a fraction means inverting the fraction and multiplying. For example, dividing by 1/2 is the same as multiplying by 2.
How do I multiply fractions?
+To multiply fractions, multiply the numerators (the numbers on top) and multiply the denominators (the numbers on the bottom).
What is the greatest common divisor (GCD) and how is it used in fractions?
+The GCD is the largest number that divides both the numerator and denominator of a fraction. It's used to simplify fractions by dividing both the numerator and denominator by the GCD.
By following the steps outlined in this article, you should now be able to easily solve 2 divided by 5/12 and understand the concepts behind dividing fractions. Remember to invert and multiply, multiply fractions by multiplying the numerators and denominators, and simplify your results by dividing both the numerator and denominator by the GCD.