Solve the Fraction Division: 6/7 ÷ 3 Step-by-Step

Q: Why can't I just divide the top number by 3?

While dividing 6 by 3 happens to give the right numerator here, this shortcut doesn't work for all fraction divisions! For example, try $ \frac{5}{8} \div 4 $ - you can't divide 5 by 4 evenly. The reciprocal method always works.

Q: What's the reciprocal of a whole number like 3?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 3 is $ \frac{1}{3} $, of 5 is $ \frac{1}{5} $, and so on!

Q: Do I always need to simplify my final answer?

Yes, always simplify! In this problem, $ \frac{6}{21} $ simplifies to $ \frac{2}{7} $ by dividing both parts by their GCD of 3. Simplified fractions are easier to work with and understand.

Q: How do I find the GCD to simplify fractions?

List the factors of both numbers and find the largest one they share. For 6 and 21: factors of 6 are 1, 2, 3, 6; factors of 21 are 1, 3, 7, 21. The largest common factor is 3!

Q: Can I check my answer by working backwards?

Absolutely! Multiply your answer by the original divisor: $ \frac{2}{7} \times 3 = \frac{6}{7} $. If you get back to the original fraction, your division is correct!

Fraction Division with Whole Number Denominators

Solve the following exercise:

$\frac{6}{7}:3=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Let's solve the problem. Ready?

00:10 First, write the number as a fraction.

00:15 Remember, any number divided by one is just itself.

00:19 Now, be sure to divide the top by the top, and the bottom by the bottom.

00:24 Let's go ahead and find those quotients.

00:27 And that's how we find the solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following exercise:

$\frac{6}{7}:3=\text{?}$

Step-by-step solution

To solve the problem of dividing $\frac{6}{7}$ by 3, we follow these steps:

Step 1: Understand that dividing by a number is the same as multiplying by its reciprocal.
Step 2: Write 3 as a fraction: $3 = \frac{3}{1}$ .
Step 3: Find the reciprocal of $\frac{3}{1}$ , which is $\frac{1}{3}$ .
Step 4: Multiply $\frac{6}{7}$ by $\frac{1}{3}$ .
Step 5: Perform the multiplication: $\frac{6}{7} \times \frac{1}{3} = \frac{6 \times 1}{7 \times 3} = \frac{6}{21}$
Step 6: Simplify $\frac{6}{21}$ by finding the greatest common divisor of 6 and 21, which is 3.
Step 7: Divide both the numerator and the denominator by 3: $\frac{6 \div 3}{21 \div 3} = \frac{2}{7}$

Thus, the result of the division $\frac{6}{7} \div 3$ is $\frac{2}{7}$ .

The correct choice from the provided options is $\frac{2}{7}$ , which matches choice number 4.

Final Answer

$\frac{2}{7}$

Key Points to Remember

Essential concepts to master this topic

Division Rule: Dividing by a whole number means multiplying by its reciprocal
Technique: Convert $\frac{6}{7} \div 3$ to $\frac{6}{7} \times \frac{1}{3}$
Check: Verify $\frac{2}{7} \times 3 = \frac{6}{7}$ matches original dividend ✓

Common Mistakes

Avoid these frequent errors

Dividing numerator by whole number directly
Don't just divide 6 by 3 to get $\frac{2}{7}$ without proper steps = skipping the reciprocal rule! This might work by luck here, but fails with other problems like $\frac{5}{8} \div 4$ . Always convert division to multiplication by the reciprocal first.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{1}{2}:\frac{1}{2}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just divide the top number by 3?

While dividing 6 by 3 happens to give the right numerator here, this shortcut doesn't work for all fraction divisions! For example, try $\frac{5}{8} \div 4$ - you can't divide 5 by 4 evenly. The reciprocal method always works.

What's the reciprocal of a whole number like 3?

The reciprocal of any whole number is 1 over that number. So the reciprocal of 3 is $\frac{1}{3}$ , of 5 is $\frac{1}{5}$ , and so on!

Do I always need to simplify my final answer?

Yes, always simplify! In this problem, $\frac{6}{21}$ simplifies to $\frac{2}{7}$ by dividing both parts by their GCD of 3. Simplified fractions are easier to work with and understand.

How do I find the GCD to simplify fractions?

List the factors of both numbers and find the largest one they share. For 6 and 21: factors of 6 are 1, 2, 3, 6; factors of 21 are 1, 3, 7, 21. The largest common factor is 3!

Can I check my answer by working backwards?

Absolutely! Multiply your answer by the original divisor: $\frac{2}{7} \times 3 = \frac{6}{7}$ . If you get back to the original fraction, your division is correct!

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