Solve Fraction Division: 2/5 ÷ 4/7 Step-by-Step

Fraction Division with Reciprocal Method

Complete the following exercise:

25:47=? \frac{2}{5}:\frac{4}{7}=\text{?}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Instead of division, we'll use multiplication by the reciprocal
00:09 We'll swap the numerator and denominator of the fraction
00:16 Make sure to multiply numerator by numerator and denominator by denominator
00:21 Calculate the multiplications
00:24 Reduce the fraction as much as possible
00:27 Make sure to divide both numerator and denominator
00:32 Calculate the quotients
00:35 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

25:47=? \frac{2}{5}:\frac{4}{7}=\text{?}

2

Step-by-step solution

To solve this problem, we'll employ the division of fractions technique:

  • Step 1: Find the reciprocal of the divisor. Here, the divisor is 47\frac{4}{7}. Its reciprocal is 74\frac{7}{4}.
  • Step 2: Multiply the dividend 25\frac{2}{5} by the reciprocal of the divisor.
  • Step 3: Calculate 25×74\frac{2}{5} \times \frac{7}{4}.
  • Step 4: Simplify the result, if possible.

Now, let's work through these steps:

Step 1: The reciprocal of 47\frac{4}{7} is 74\frac{7}{4}.

Step 2: Multiply the fractions: 25×74=2×75×4=1420\frac{2}{5} \times \frac{7}{4} = \frac{2 \times 7}{5 \times 4} = \frac{14}{20}.

Step 3: Simplify 1420\frac{14}{20}. The greatest common divisor (GCD) of 14 and 20 is 2, so divide both the numerator and the denominator by 2:

1420=14÷220÷2=710\frac{14}{20} = \frac{14 \div 2}{20 \div 2} = \frac{7}{10}.

Therefore, the solution to the problem is 710\frac{7}{10}.

3

Final Answer

710 \frac{7}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Change division to multiplication using the reciprocal
  • Technique: 25÷47=25×74=1420 \frac{2}{5} ÷ \frac{4}{7} = \frac{2}{5} × \frac{7}{4} = \frac{14}{20}
  • Check: Simplify 1420 \frac{14}{20} by dividing by GCD of 2 to get 710 \frac{7}{10}

Common Mistakes

Avoid these frequent errors
  • Multiplying by the divisor instead of its reciprocal
    Don't multiply 25×47=835 \frac{2}{5} × \frac{4}{7} = \frac{8}{35} - this is wrong! Division means multiply by the reciprocal, not the original fraction. Always flip the second fraction first: 47 \frac{4}{7} becomes 74 \frac{7}{4} .

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

\( \frac{1}{4}:\frac{1}{2}=\text{?} \)

FAQ

Everything you need to know about this question

Why do I flip the second fraction?

+

When you divide by a fraction, you're asking 'how many groups' fit into the first fraction. Flipping and multiplying gives the same result as division but is much easier to calculate!

What if I forget to simplify my answer?

+

Your answer is still correct, but not in simplest form. Teachers usually want simplified answers, so always check if you can divide both numerator and denominator by their greatest common divisor (GCD).

How do I find the GCD quickly?

+

List the factors of both numbers and find the largest one they share. For 1420 \frac{14}{20} : factors of 14 are 1, 2, 7, 14 and factors of 20 are 1, 2, 4, 5, 10, 20. The GCD is 2!

Can I cross-multiply instead of using reciprocals?

+

No, cross-multiplication is for solving equations like ab=cd \frac{a}{b} = \frac{c}{d} . For fraction division, you must use the reciprocal method: flip the divisor and multiply.

What's the difference between ÷ and : symbols?

+

They mean exactly the same thing! Both ÷ ÷ and : : represent division. The colon symbol is more common in some countries, but the method is identical.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Operations with Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations