Simplify the Fraction 3/6 Using Factor of 3: Step-by-Step Solution

Q: What does 'simplify by a factor of 3' mean?

It means divide both the numerator and denominator by 3. Since 3 goes into both 3 and 6 evenly, we can reduce the fraction this way.

Q: Is 1/2 the simplest form of this fraction?

Yes! Since 1 and 2 share no common factors other than 1, $ \frac{1}{2} $ is in lowest terms and cannot be simplified further.

Q: What if I used a different factor instead of 3?

You can only use factors that divide evenly into both the numerator and denominator. For $ \frac{3}{6} $, the only common factors are 1 and 3.

Q: How can I check if my simplified fraction is correct?

Cross-multiply to verify: $ \frac{1}{2} = \frac{3}{6} $ means 1 × 6 should equal 2 × 3. Since 6 = 6, your answer is correct!

Fraction Simplification with Common Factors

Simplify the following fraction by a factor of 3:

$\frac{3}{6}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 3

00:03 Divide the fraction by the given factor

00:06 Make sure to divide both numerator and denominator

00:09 Calculate the quotients

00:12 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

Simplify the following fraction by a factor of 3:

$\frac{3}{6}=$

Step-by-step solution

We will reduce as follows, divide the numerator by 3 and the denominator by 3:

$\frac{3:3}{6:3}=\frac{1}{2}$

Final Answer

$\frac{1}{2}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both numerator and denominator by their greatest common factor
Technique: Find GCF of 3 and 6, which is 3, then divide: 3÷3=1, 6÷3=2
Check: Verify $\frac{1}{2}$ equals $\frac{3}{6}$ by cross-multiplying: 1×6 = 3×2 = 6 ✓

Common Mistakes

Avoid these frequent errors

Dividing only the numerator or only the denominator by the factor
Don't divide just 3 by 3 to get $\frac{1}{6}$ or just 6 by 3 to get $\frac{3}{2}$ ! This changes the value of the fraction completely and gives wrong answers. Always divide both the top and bottom numbers by the same factor to keep the fraction equivalent.

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

What does 'simplify by a factor of 3' mean?

It means divide both the numerator and denominator by 3. Since 3 goes into both 3 and 6 evenly, we can reduce the fraction this way.

How do I know if 3 is the right factor to use?

Check if 3 divides evenly into both numbers: 3 ÷ 3 = 1 and 6 ÷ 3 = 2. Since both give whole numbers, 3 is a valid common factor!

Is 1/2 the simplest form of this fraction?

Yes! Since 1 and 2 share no common factors other than 1, $\frac{1}{2}$ is in lowest terms and cannot be simplified further.

What if I used a different factor instead of 3?

You can only use factors that divide evenly into both the numerator and denominator. For $\frac{3}{6}$ , the only common factors are 1 and 3.

How can I check if my simplified fraction is correct?

Cross-multiply to verify: $\frac{1}{2} = \frac{3}{6}$ means 1 × 6 should equal 2 × 3. Since 6 = 6, your answer is correct!

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