Have you ever stumbled upon a math problem that seems straightforward, but then you realize it involves fractions? Don't worry, you're not alone! In this article, we'll tackle a simple yet tricky math problem: solving 4 divided by 2/3. By the end of this article, you'll be a pro at handling fractions in division problems.
Math problems involving fractions can be intimidating, but with the right approach, they can be easily solved. In this case, we're dealing with a division problem that involves a fraction as the divisor. Before we dive into the solution, let's first understand the basics of dividing by a fraction.
Understanding Division by a Fraction
When you divide a number by a fraction, you're essentially asking how many times the fraction fits into the number. In this case, we want to find out how many times 2/3 fits into 4.
The Easy Way to Solve 4 Divided by 2/3
To solve this problem, we can use a simple trick: invert the fraction and multiply. That's right, instead of dividing by a fraction, we'll multiply by its reciprocal. The reciprocal of a fraction is obtained by flipping the numerator and denominator. So, the reciprocal of 2/3 is 3/2.
Now, let's multiply 4 by the reciprocal of 2/3:
4 ÷ 2/3 = 4 × 3/2
To multiply a number by a fraction, we multiply the number by the numerator and then divide by the denominator. In this case:
4 × 3/2 = (4 × 3) / 2
= 12/2
= 6
And there you have it! The solution to 4 divided by 2/3 is 6.
Why This Method Works
So, why does this method work? When you divide by a fraction, you're essentially asking how many times the fraction fits into the number. By inverting the fraction and multiplying, you're asking how many times the reciprocal of the fraction fits into the number. This is equivalent to dividing by the original fraction.
More Examples and Practice
Let's practice this method with a few more examples:
- 6 ÷ 3/4 = 6 × 4/3 = (6 × 4) / 3 = 24/3 = 8
- 8 ÷ 2/5 = 8 × 5/2 = (8 × 5) / 2 = 40/2 = 20
As you can see, this method makes solving division problems involving fractions a breeze.
Tips and Tricks
Here are some additional tips and tricks to keep in mind:
- When dividing by a fraction, always invert the fraction and multiply.
- Make sure to multiply the number by the numerator and then divide by the denominator.
- Practice, practice, practice! The more you practice solving division problems involving fractions, the more comfortable you'll become with the method.
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FAQs
What is the reciprocal of a fraction?
+The reciprocal of a fraction is obtained by flipping the numerator and denominator.
Why do we invert the fraction and multiply when dividing by a fraction?
+We invert the fraction and multiply to find the reciprocal of the fraction, which is equivalent to dividing by the original fraction.
What are some tips for solving division problems involving fractions?
+Make sure to invert the fraction and multiply, multiply the number by the numerator and then divide by the denominator, and practice, practice, practice!
Get Started with Solving Division Problems Involving Fractions Today!
Solving division problems involving fractions may seem daunting at first, but with the right approach, it can be easy and straightforward. Remember to invert the fraction and multiply, multiply the number by the numerator and then divide by the denominator, and practice regularly. With these tips and tricks, you'll become a pro at solving division problems involving fractions in no time!