Multiply 2/3 by a Factor of 6: Step-by-Step Fraction Scaling

Q: What does 'increase by a factor of 6' actually mean?

It means to scale the fraction so it looks different but has the same value. Think of it like zooming in on a photo - the image looks bigger but shows the same thing!

Q: Why do I multiply both parts instead of just adding 6?

Adding would change the fraction's value completely! Multiplying both numerator and denominator by the same number keeps the fraction equivalent to the original.

Q: How can I tell if my scaled fraction is correct?

Check if both fractions simplify to the same thing! $ \frac{12}{18} $ divides by 6 to give $ \frac{2}{3} $, so they're equivalent.

Q: Is there a difference between scaling and simplifying fractions?

Scaling makes fractions look more complex (bigger numbers), while simplifying makes them look simpler (smaller numbers). Both keep the same value!

Fraction Scaling with Factor Multiplication

Increase the following fraction by a factor of 6:

$\frac{2}{3}=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Expand the fraction by 6

00:03 Multiply the fraction by the given factor

00:06 Make sure to multiply both numerator and denominator

00:12 Calculate the multiplications

00:15 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

Increase the following fraction by a factor of 6:

$\frac{2}{3}=$

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Multiply the numerator by 6.
Step 2: Multiply the denominator by 6.
Step 3: Write down the result as a new fraction.

Now, let's work through each step:
Step 1: The original fraction is $\frac{2}{3}$ . Multiply the numerator 2 by 6, which gives $2 \times 6 = 12$ .
Step 2: Multiply the denominator 3 by 6, which gives $3 \times 6 = 18$ .
Step 3: The resulting fraction after multiplying both numerator and denominator by 6 is $\frac{12}{18}$ .

Therefore, the solution to the problem is $\frac{12}{18}$ .

Final Answer

$\frac{12}{18}$

Key Points to Remember

Essential concepts to master this topic

Rule: Multiply both numerator and denominator by the same factor
Technique: Scale $\frac{2}{3}$ by 6: $\frac{2 \times 6}{3 \times 6} = \frac{12}{18}$
Check: Verify equivalent fractions: $\frac{2}{3} = \frac{12}{18}$ since $12 \div 6 = 2$ and $18 \div 6 = 3$ ✓

Common Mistakes

Avoid these frequent errors

Only multiplying the numerator by the factor
Don't multiply just 2 by 6 to get $\frac{12}{3}$ = 4! This changes the fraction's value completely instead of scaling it. Always multiply both the numerator AND denominator 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 'increase by a factor of 6' actually mean?

It means to scale the fraction so it looks different but has the same value. Think of it like zooming in on a photo - the image looks bigger but shows the same thing!

Why do I multiply both parts instead of just adding 6?

Adding would change the fraction's value completely! Multiplying both numerator and denominator by the same number keeps the fraction equivalent to the original.

How can I tell if my scaled fraction is correct?

Check if both fractions simplify to the same thing! $\frac{12}{18}$ divides by 6 to give $\frac{2}{3}$ , so they're equivalent.

Is there a difference between scaling and simplifying fractions?

Scaling makes fractions look more complex (bigger numbers), while simplifying makes them look simpler (smaller numbers). Both keep the same value!

What if the factor was a fraction instead of 6?

Same process! Multiply both numerator and denominator by that fractional factor. For example, scaling by $\frac{1}{2}$ would give $\frac{2 \times \frac{1}{2}}{3 \times \frac{1}{2}} = \frac{1}{\frac{3}{2}}$ .

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