Dividing Fractions: 5/6 ÷ 3/10
In this article, we will explore how to divide two fractions, specifically 5/6 divided by 3/10. Dividing fractions can seem intimidating, but with the right approach, it can be a breeze.
Understanding the Concept of Division
Before we dive into the problem, let's quickly review what division means. Division is the opposite operation of multiplication. When we divide one number by another, we are essentially asking how many times the second number fits into the first number.
The Rule of Dividing Fractions
When dividing fractions, we can use the following rule:
a/b ÷ c/d = ad/bc
In other words, to divide two fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply.
Now, Let's Solve the Problem
We are given the problem:
5/6 ÷ 3/10
To solve this problem, we will apply the rule of dividing fractions.
Step 1: Invert the Second Fraction
We need to invert the second fraction, 3/10. To do this, we will flip the numerator and denominator:
10/3
Step 2: Multiply the Fractions
Now, we will multiply the first fraction, 5/6, by the inverted second fraction, 10/3:
(5/6) × (10/3)
To multiply fractions, we multiply the numerators (5 × 10 = 50) and multiply the denominators (6 × 3 = 18). Then, we write the product as a fraction:
50/18
Step 3: Simplify the Fraction
The resulting fraction, 50/18, can be simplified. We can divide both the numerator and denominator by their greatest common divisor, which is 2:
25/9
And that's it! We have successfully divided 5/6 by 3/10 and obtained the result:
5/6 ÷ 3/10 = 25/9
I hope this explanation has helped you understand how to divide fractions. Remember to invert the second fraction and multiply to get the correct result.
