Find the Common Factor of 22abc - 11ab/c: Algebraic Expression Analysis

Q: How do I factor out from a fraction like 11ab/c?

Think of it as $ \frac{11ab}{c} = 11ab \cdot \frac{1}{c} $. The 11ab is still there - it's just being divided by c. You can factor it out just like from any other term!

Q: Why is the answer 11ab(2c - 1/c) and not something simpler?

After factoring out 11ab, what remains inside the parentheses is $ 2c - \frac{1}{c} $. These terms cannot be combined because one has c in the numerator and the other has c in the denominator.

Q: Can I combine 2c and 1/c somehow?

No! You cannot directly add or subtract terms with different denominators. $ 2c - \frac{1}{c} $ is already in its simplest form unless you want to create a compound fraction.

Q: How do I check if my factoring is correct?

Distribute your answer back: $ 11ab(2c - \frac{1}{c}) = 11ab \cdot 2c - 11ab \cdot \frac{1}{c} = 22abc - \frac{11ab}{c} $. It should match the original expression exactly!

Q: What if I factored out something different like 11a?

You could factor out 11a, but then you'd have leftover b terms that could be factored further. Always factor out the greatest common factor to get the most simplified form!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Take out common factor

00:06 Factor 22 into factors 2 and 11

00:13 Mark the common factors

00:23 Take out the common factors from the parentheses

00:47 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Find the common factor:

$22abc-\frac{11ab}{c}$

2

Step-by-step solution

To find the common factor for the expression $22abc - \frac{11ab}{c}$ , we will follow these steps:

Step 1: Determine the common factors in terms of coefficients and variables.
Step 2: Factor these common elements out of the expression.
Step 3: Simplify the expression after factoring.

Now, let's proceed with the solution:

Step 1: Identify the common factors.
The expression is $22abc - \frac{11ab}{c}$ . We can see that both terms have the factors $11ab$ . 11 is a common numerical factor in 22 and 11. Ab is also present in both terms.

Step 2: Factor out the common factors.
Factor out $11ab$ from each term in the expression:

22abc - \frac{11ab}{c} = 11ab \left( \frac{22abc}{11ab} - \frac{\left(\frac{11ab}{c}\right)}{11ab} \right)

Step 3: Simplify the terms inside the parenthesis.

Simplify the first term: $\frac{22abc}{11ab} = 2c$
Simplify the second term: $\frac{\frac{11ab}{c}}{11ab} = \frac{1}{c}$

Thus, we get the factored form:

11ab\left(2c - \frac{1}{c}\right)

Therefore, the common factor form of $22abc - \frac{11ab}{c}$ is $11ab(2c - \frac{1}{c})$ .

3

Final Answer

$11ab(2c-\frac{1}{c})$

Key Points to Remember

Essential concepts to master this topic

Common Factor Rule: Find the greatest common factor of all terms first
Technique: Factor out $11ab$ from both $22abc$ and $\frac{11ab}{c}$
Check: Expand your factored form to verify it equals the original expression ✓

Common Mistakes

Avoid these frequent errors

Forgetting to factor from fractional terms
Don't ignore the fraction $\frac{11ab}{c}$ when finding common factors = missing the complete factorization! The common factor 11ab exists in both the whole term and the fractional term. Always examine every term including fractions for common factors.

Practice Quiz

Test your knowledge with interactive questions

Break down the expression into basic terms:

$$ 4x^2 + 6x $$

FAQ

Everything you need to know about this question

How do I factor out from a fraction like 11ab/c?

+

Think of it as $\frac{11ab}{c} = 11ab \cdot \frac{1}{c}$ . The 11ab is still there - it's just being divided by c. You can factor it out just like from any other term!

Why is the answer 11ab(2c - 1/c) and not something simpler?

+

After factoring out 11ab, what remains inside the parentheses is $2c - \frac{1}{c}$ . These terms cannot be combined because one has c in the numerator and the other has c in the denominator.

Can I combine 2c and 1/c somehow?

+

No! You cannot directly add or subtract terms with different denominators. $2c - \frac{1}{c}$ is already in its simplest form unless you want to create a compound fraction.

How do I check if my factoring is correct?

+

Distribute your answer back: $11ab(2c - \frac{1}{c}) = 11ab \cdot 2c - 11ab \cdot \frac{1}{c} = 22abc - \frac{11ab}{c}$ . It should match the original expression exactly!

What if I factored out something different like 11a?

+

You could factor out 11a, but then you'd have leftover b terms that could be factored further. Always factor out the greatest common factor to get the most simplified form!

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