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

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 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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