Simplify the Fraction 3/10: Step-by-Step Factor Reduction

Q: What does 'simplify by a factor of 1' actually mean?

It means divide both numerator and denominator by 1. Since dividing by 1 doesn't change any number, $ \frac{3}{10} $ stays exactly the same!

Q: Why would a question ask me to simplify by 1 if nothing changes?

This teaches you the identity property - that dividing by 1 is a 'do nothing' operation. It helps you understand that only common factors greater than 1 actually simplify fractions.

Q: How do I know when a fraction can't be simplified further?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. If the GCD is 1, like with 3 and 10, the fraction is already in lowest terms.

Q: Is 3/10 the same as 0.3?

Yes! $ \frac{3}{10} = 0.3 $. Both represent the same value - three-tenths. The fraction form is often more precise for calculations.

Q: What would happen if I tried to simplify 3/10 by a different factor?

You can only simplify by common factors. Since 3 and 10 share no common factors except 1, trying to divide by 2, 3, or 5 won't work for both numerator and denominator.

Fraction Simplification with Identity Factors

Simplify the following fraction by a factor of 1:

$\frac{3}{10}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 1

00:03 Divide the fraction by the given factor

00:06 Make sure to divide both numerator and denominator

00:09 Calculate the quotients (any number divided by 1 equals itself)

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 1:

$\frac{3}{10}=$

Step-by-step solution

We will reduce in the following way, divide the numerator by 1 and the denominator by 1:

$\frac{3:1}{10:1}=\frac{3}{10}$

Final Answer

$\frac{3}{10}$

Key Points to Remember

Essential concepts to master this topic

Identity Rule: Dividing by 1 does not change the value
Technique: Factor of 1 means $\frac{3}{10} \div \frac{1}{1} = \frac{3}{10}$
Check: GCD of 3 and 10 is 1, so fraction is already simplified ✓

Common Mistakes

Avoid these frequent errors

Confusing 'factor of 1' with actual simplification
Don't think dividing by 1 changes the fraction = $\frac{3}{3}$ or $\frac{1}{1}$ ! Dividing by 1 is the identity operation that leaves values unchanged. Always remember that 'simplify by a factor of 1' means the fraction stays exactly the same.

Practice Quiz

Test your knowledge with interactive questions

Simplify the following fraction by a factor of 4:

$\frac{4}{8}=$

FAQ

Everything you need to know about this question

What does 'simplify by a factor of 1' actually mean?

It means divide both numerator and denominator by 1. Since dividing by 1 doesn't change any number, $\frac{3}{10}$ stays exactly the same!

Why would a question ask me to simplify by 1 if nothing changes?

This teaches you the identity property - that dividing by 1 is a 'do nothing' operation. It helps you understand that only common factors greater than 1 actually simplify fractions.

How do I know when a fraction can't be simplified further?

Find the Greatest Common Divisor (GCD) of the numerator and denominator. If the GCD is 1, like with 3 and 10, the fraction is already in lowest terms.

Is 3/10 the same as 0.3?

Yes! $\frac{3}{10} = 0.3$ . Both represent the same value - three-tenths. The fraction form is often more precise for calculations.

What would happen if I tried to simplify 3/10 by a different factor?

You can only simplify by common factors. Since 3 and 10 share no common factors except 1, trying to divide by 2, 3, or 5 won't work for both numerator and denominator.

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