Solve Fraction Division: Calculate 3/4 ÷ 5/6 Step-by-Step

Fraction Division with Reciprocal Multiplication

Complete the following exercise:

34:56=? \frac{3}{4}:\frac{5}{6}=\text{?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this math problem together.
00:08 Instead of dividing, multiply by the reciprocal.
00:13 Flip the fraction by swapping the numerator and denominator.
00:21 Now, multiply the numerators together and the denominators together.
00:27 Calculate these multiplications.
00:30 Next, simplify the fraction as much as possible.
00:34 Divide the numerator and denominator by the greatest common factor.
00:39 Calculate the results of these divisions.
00:43 And there you have it! That's the solution to the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

34:56=? \frac{3}{4}:\frac{5}{6}=\text{?}

2

Step-by-step solution

To solve the problem of dividing two fractions, we apply the method of multiplication by the reciprocal:

  • Step 1: The given problem is 34÷56 \frac{3}{4} \div \frac{5}{6} .
  • Step 2: Find the reciprocal of the divisor 56 \frac{5}{6} , which is 65 \frac{6}{5} .
  • Step 3: Multiply the dividend 34 \frac{3}{4} by the reciprocal of the divisor: 34×65 \frac{3}{4} \times \frac{6}{5}
  • Step 4: Perform the multiplication: 3×64×5=1820 \frac{3 \times 6}{4 \times 5} = \frac{18}{20}
  • Step 5: Simplify the resulting fraction 1820 \frac{18}{20} : 18÷220÷2=910 \frac{18 \div 2}{20 \div 2} = \frac{9}{10}

Therefore, the correct result of the division 34÷56 \frac{3}{4} \div \frac{5}{6} is 910\frac{9}{10}.

3

Final Answer

910 \frac{9}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Division by a fraction means multiply by its reciprocal
  • Technique: Change 34÷56 \frac{3}{4} ÷ \frac{5}{6} to 34×65 \frac{3}{4} × \frac{6}{5}
  • Check: Simplify 1820 \frac{18}{20} by dividing both by GCD of 2 ✓

Common Mistakes

Avoid these frequent errors
  • Adding or subtracting fractions instead of dividing
    Don't try to add denominators like 4 + 6 = 10 or subtract numerators = wrong operation entirely! Division requires the reciprocal method, not addition or subtraction rules. Always flip the second fraction and multiply.

Practice Quiz

Test your knowledge with interactive questions

\( \frac{1}{3}+\frac{1}{4}= \)

FAQ

Everything you need to know about this question

Why do I flip the second fraction instead of the first one?

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You flip the divisor (the fraction after the division sign). In 34÷56 \frac{3}{4} ÷ \frac{5}{6} , flip 56 \frac{5}{6} to get 65 \frac{6}{5} . The first fraction stays the same!

What if I forget to simplify my final answer?

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Your answer is still correct, but not in simplest form. Always check if the numerator and denominator share common factors. 1820 \frac{18}{20} and 910 \frac{9}{10} are equal, but 910 \frac{9}{10} is preferred.

How do I remember which operation to change to?

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Think: "Division becomes multiplication by the reciprocal." The ÷ symbol changes to ×, and you flip the fraction after the division sign. Practice with simple examples first!

What if my answer is larger than 1?

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That's totally normal! When you divide by a fraction less than 1 (like 56 \frac{5}{6} ), your answer can be larger than the original number. Check your work by substitution.

Can I cross-multiply instead of using reciprocals?

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Cross-multiplication works for equations like ab=cd \frac{a}{b} = \frac{c}{d} , but for division problems, you must use the reciprocal method. They're different types of problems!

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