The art of simplifying complex fractions! In this article, we'll break down the problem of 9/10 ÷ 3/5 into manageable steps, making it easy to understand and solve.
Understanding Fractions and Division
Before we dive into the problem, let's quickly review the basics of fractions and division. A fraction represents a part of a whole, with the top number (numerator) telling us how many equal parts we have, and the bottom number (denominator) telling us how many parts the whole is divided into.
Division, on the other hand, is the process of sharing or grouping a certain quantity into equal parts or groups. When dividing fractions, we need to follow a specific set of rules to ensure we get the correct answer.
Step 1: Invert the Second Fraction
When dividing fractions, we need to invert the second fraction (i.e., flip the numerator and denominator). This means that 3/5 becomes 5/3.
Step 2: Multiply the Fractions
Now that we have the inverted second fraction, we can multiply the two fractions together. Multiplying fractions involves multiplying the numerators (9 and 5) and multiplying the denominators (10 and 3).
(9/10) × (5/3) = (9 × 5) / (10 × 3)
Step 3: Simplify the Result
The result of the multiplication is (45/30). However, this fraction can be simplified further. To simplify, we need to find the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 45 and 30 is 15. We can divide both the numerator and denominator by 15 to simplify the fraction:
(45 ÷ 15) / (30 ÷ 15) = 3/2
Step 4: Check for Further Simplification
The fraction 3/2 cannot be simplified further, so our answer is complete.
Step 5: Write the Final Answer
The final answer to the problem 9/10 ÷ 3/5 is 3/2.
Gallery of Fraction Division
What is the purpose of inverting the second fraction in division?
+Inverting the second fraction allows us to multiply the fractions instead of dividing, which makes the calculation simpler.
Why do we need to simplify the result of the multiplication?
+Simplifying the result ensures that the answer is in its simplest form, making it easier to understand and work with.
Can I simplify the fraction further if the numerator and denominator have no common factors?
+No, if the numerator and denominator have no common factors, the fraction is already in its simplest form.
Now that we've completed the problem, you can see that dividing fractions is not as daunting as it seems. By following these simple steps and understanding the basics of fractions and division, you'll be well on your way to solving even the most complex fraction division problems!