Simplify the Fraction 28/70 Using Factor of 7

Q: Why do I divide both parts by 7?

When simplifying fractions, you must divide both the numerator and denominator by the same number to keep the fraction equivalent. Think of it like cutting a pizza - if you cut both the pieces you have AND the total pieces by the same amount, you still have the same portion!

Q: How do I know 7 is a factor of both numbers?

A number is a factor if it divides evenly with no remainder. Since 28÷7=4 and 70÷7=10 (both whole numbers), 7 is indeed a common factor of both 28 and 70.

Q: Is 4/10 the simplest form?

Not quite! $ \frac{4}{10} $ can be simplified further since both 4 and 10 are divisible by 2. The fully simplified form would be $ \frac{2}{5} $.

Fraction Simplification with Common Factors

Simplify the following fraction by a factor of 7:

$\frac{28}{70}=$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Reduce the fraction by 7

00:03 Divide the fraction by the given factor

00:06 Make sure to divide both numerator and denominator

00:09 Calculate the quotients

00:13 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 7:

$\frac{28}{70}=$

Step-by-step solution

We will reduce in the following way, divide the numerator by 7 and the denominator by 7:

$\frac{28:7}{70:7}=\frac{4}{10}$

Final Answer

$\frac{4}{10}$

Key Points to Remember

Essential concepts to master this topic

Rule: Divide both numerator and denominator by the same factor
Technique: Factor of 7 means 28÷7=4 and 70÷7=10
Check: Verify 4×7=28 and 10×7=70 to confirm correct simplification ✓

Common Mistakes

Avoid these frequent errors

Dividing only the numerator or denominator by the factor
Don't divide just 28 by 7 to get 4/70 = wrong answer! This creates an unequal fraction that's not equivalent to the original. Always divide both the numerator AND denominator by the same factor.

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

Why do I divide both parts by 7?

When simplifying fractions, you must divide both the numerator and denominator by the same number to keep the fraction equivalent. Think of it like cutting a pizza - if you cut both the pieces you have AND the total pieces by the same amount, you still have the same portion!

How do I know 7 is a factor of both numbers?

A number is a factor if it divides evenly with no remainder. Since 28÷7=4 and 70÷7=10 (both whole numbers), 7 is indeed a common factor of both 28 and 70.

Is 4/10 the simplest form?

Not quite! $\frac{4}{10}$ can be simplified further since both 4 and 10 are divisible by 2. The fully simplified form would be $\frac{2}{5}$ .

What if the problem asked for a different factor?

The same process applies! Just make sure the factor you're told to use actually divides evenly into both the numerator and denominator. If it doesn't, the problem might have an error.

Can I simplify by other factors first?

While you could use other common factors, the problem specifically asks you to simplify by a factor of 7. Always follow the instructions given, even if there are multiple ways to simplify!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Simple Fractions questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime