Solve: Division of 4/9 by 6 - Step-by-Step Fraction Problem

Q: Do I always need to simplify my answer?

Yes! Always check if your fraction can be simplified. Find the GCD of the numerator and denominator, then divide both by it. $ \frac{4}{54} $ simplifies to $ \frac{2}{27} $ because GCD(4,54) = 2.

Q: What if I multiply 4 × 6 instead?

That's a common mistake! You'd get $ \frac{24}{9} $ which is wrong. Remember: when dividing fractions, you multiply by the reciprocal, not the original number.

Q: Can I convert the whole number to a fraction first?

Absolutely! Writing 6 as $ \frac{6}{1} $ makes it clearer. Then $ \frac{4}{9} \div \frac{6}{1} = \frac{4}{9} \times \frac{1}{6} $. This helps you see the reciprocal step!

Fraction Division with Whole Numbers

$\frac{4}{9}:6=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Any number divided by 1 equals the number itself

00:10 Convert division to multiplication by reciprocal

00:26 Make sure to multiply numerator by numerator and denominator by denominator

00:30 Calculate the multiplications

00:40 Reduce what's possible

00:49 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{4}{9}:6=$

Step-by-step solution

To solve the problem $\frac{4}{9} : 6$ , we follow these steps:

Convert the whole number $6$ to its reciprocal, which is $\frac{1}{6}$ .
Rewrite the division as multiplication: $\frac{4}{9} \times \frac{1}{6}$ .
Multiply the numerators: $4 \times 1 = 4$ .
Multiply the denominators: $9 \times 6 = 54$ .
Write the result as a fraction: $\frac{4}{54}$ .
Simplify the fraction by finding the greatest common divisor of 4 and 54, which is 2.
Divide both the numerator and the denominator by 2: $\frac{4 \div 2}{54 \div 2} = \frac{2}{27}$ .

Therefore, the solution to the problem is $\frac{2}{27}$ .

Final Answer

$\frac{2}{27}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert division to multiplication using the reciprocal
Technique: $\frac{4}{9} \div 6 = \frac{4}{9} \times \frac{1}{6} = \frac{4}{54}$
Check: Simplify by finding GCD: $\frac{4}{54} = \frac{2}{27}$ ✓

Common Mistakes

Avoid these frequent errors

Dividing by the reciprocal instead of multiplying
Don't divide $\frac{4}{9}$ by $\frac{1}{6}$ = $\frac{24}{9}$ ! This reverses the operation and gives a much larger answer than expected. Always multiply by the reciprocal when dividing fractions.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{2}:3=$ $$ $$ $$

FAQ

Everything you need to know about this question

Why do I flip the 6 to make it 1/6?

When dividing by a whole number, you're actually dividing by $\frac{6}{1}$ . The reciprocal of $\frac{6}{1}$ is $\frac{1}{6}$ . This lets us change division into multiplication!

Do I always need to simplify my answer?

Yes! Always check if your fraction can be simplified. Find the GCD of the numerator and denominator, then divide both by it. $\frac{4}{54}$ simplifies to $\frac{2}{27}$ because GCD(4,54) = 2.

What if I multiply 4 × 6 instead?

That's a common mistake! You'd get $\frac{24}{9}$ which is wrong. Remember: when dividing fractions, you multiply by the reciprocal, not the original number.

How do I find the greatest common divisor?

List the factors of both numbers and find the largest one they share. For 4 and 54:

Factors of 4: 1, 2, 4
Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54
GCD = 2 (largest shared factor)

Can I convert the whole number to a fraction first?

Absolutely! Writing 6 as $\frac{6}{1}$ makes it clearer. Then $\frac{4}{9} \div \frac{6}{1} = \frac{4}{9} \times \frac{1}{6}$ . This helps you see the reciprocal step!

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