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

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 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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