Reduce the Fraction 6/21 to Its Simplest Form: Step-by-Step Solution

Q: How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. For $ \frac{2}{7} $, since 2 and 7 are both prime numbers, this is fully simplified!

Q: Can I simplify step by step instead of using the HCF?

Yes, but it takes longer! You could divide $ \frac{6}{21} $ by 2 to get $ \frac{3}{10.5} $ - but wait, that gives a decimal! Always divide by factors that work for both numbers.

Q: What if the fraction can't be simplified?

Some fractions like $ \frac{5}{8} $ are already in simplest form because 5 and 8 share no common factors. If the HCF is 1, then your fraction is already simplified!

Fraction Simplification with Common Factors

Reduce the given fraction to its simplest form:

$\frac{6}{21}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction as much as possible

00:03 Divide by the greatest common factor

00:07 Make sure to divide both numerator and denominator

00:11 Calculate the quotients

00:14 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

Reduce the given fraction to its simplest form:

$\frac{6}{21}=$

Step-by-step solution

We need to identify the highest common factor (HCF): The largest number that both the numerator and the denominator can be divided by.

In this case, the number is 3, therefore:

$\frac{6:3}{21:3}=\frac{2}{7}$

Final Answer

$\frac{2}{7}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find the highest common factor of numerator and denominator
Technique: Divide both 6 and 21 by their HCF of 3
Check: Verify $\frac{2}{7}$ cannot be reduced further: 2 and 7 share no common factors ✓

Common Mistakes

Avoid these frequent errors

Dividing by any common factor instead of the highest one
Don't divide 6/21 by 2 to get 3/10.5 = wrong answer with decimals! This doesn't fully simplify the fraction and creates confusion. Always find the highest common factor (HCF) first, then divide both numerator and denominator by that number.

Practice Quiz

Test your knowledge with interactive questions

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$$ 5:6= $$

FAQ

Everything you need to know about this question

How do I find the highest common factor (HCF)?

List the factors of both numbers: 6 has factors 1, 2, 3, 6 and 21 has factors 1, 3, 7, 21. The largest number that appears in both lists is your HCF - in this case, 3!

What if I can't see the HCF right away?

Start with small numbers! Try dividing both the numerator and denominator by 2, then 3, then 5, etc. Keep going until you find the largest number that divides both evenly.

How do I know when a fraction is fully simplified?

A fraction is in simplest form when the numerator and denominator share no common factors except 1. For $\frac{2}{7}$ , since 2 and 7 are both prime numbers, this is fully simplified!

Can I simplify step by step instead of using the HCF?

Yes, but it takes longer! You could divide $\frac{6}{21}$ by 2 to get $\frac{3}{10.5}$ - but wait, that gives a decimal! Always divide by factors that work for both numbers.

What if the fraction can't be simplified?

Some fractions like $\frac{5}{8}$ are already in simplest form because 5 and 8 share no common factors. If the HCF is 1, then your fraction is already simplified!

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