Solve for the Denominator: Finding ? in 12ab/? = 1

Q: Why can't I just use 12 as the denominator?

Because $ \frac{12ab}{12} = ab $, not 1! You need the entire numerator in the denominator to get the result of 1.

Q: What if the numerator had different variables like 5xy?

The same rule applies! $ \frac{5xy}{?} = 1 $ means the denominator must be 5xy - the complete expression from the numerator.

Q: Does this work with negative numbers too?

Yes! $ \frac{-8ab}{-8ab} = 1 $ because any number (positive or negative) divided by itself equals 1.

Q: How is this different from simplifying fractions?

In simplification, you reduce fractions like $ \frac{6}{9} = \frac{2}{3} $. Here, you're finding what makes the fraction equal exactly 1, which requires identical numerator and denominator.

Q: What if there are multiple terms in the numerator?

Include everything! For $ \frac{3x + 2y}{?} = 1 $, the denominator must be the entire expression: 3x + 2y.

Fraction Equations with Self-Division Property

Complete the corresponding expression for the denominator

$\frac{12ab}{?}=1$

❤️ 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

00:06 First, let's complete the correct denominator.

00:11 To isolate the denominator, we will multiply both sides by it.

00:22 Remember, any number times one equals itself.

00:29 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the corresponding expression for the denominator

$\frac{12ab}{?}=1$

Step-by-step solution

Let's examine the problem:

$\frac{12ab}{?}=1$ Now let's think logically, and remember the known fact that dividing any number by itself always yields the result 1,

Therefore, in order to get the result 1 from dividing two numbers, the only way is to divide the number by itself, meaning-

The missing expression in the denominator of the fraction on the left side is the complete expression that appears in the numerator of the same fraction:

$12ab$ .

Therefore- the correct answer is answer D.

Final Answer

$12ab$

Key Points to Remember

Essential concepts to master this topic

Rule: Any number divided by itself always equals 1
Technique: Set denominator equal to numerator: $\frac{12ab}{12ab} = 1$
Check: Verify by calculating: 12ab ÷ 12ab = 1 ✓

Common Mistakes

Avoid these frequent errors

Using only part of the numerator in the denominator
Don't put just 12a or ab in the denominator = wrong result! You get fractions like 12ab/12a = b instead of 1. Always use the complete numerator expression 12ab as the denominator.

Practice Quiz

Test your knowledge with interactive questions

Determine if the simplification shown below is correct:

$\frac{7}{7\cdot8}=8$

FAQ

Everything you need to know about this question

Why can't I just use 12 as the denominator?

Because $\frac{12ab}{12} = ab$ , not 1! You need the entire numerator in the denominator to get the result of 1.

What if the numerator had different variables like 5xy?

The same rule applies! $\frac{5xy}{?} = 1$ means the denominator must be 5xy - the complete expression from the numerator.

Does this work with negative numbers too?

Yes! $\frac{-8ab}{-8ab} = 1$ because any number (positive or negative) divided by itself equals 1.

How is this different from simplifying fractions?

In simplification, you reduce fractions like $\frac{6}{9} = \frac{2}{3}$ . Here, you're finding what makes the fraction equal exactly 1, which requires identical numerator and denominator.

What if there are multiple terms in the numerator?

Include everything! For $\frac{3x + 2y}{?} = 1$ , the denominator must be the entire expression: 3x + 2y.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Factorization 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