Solve the Fraction Equation: Finding the Denominator in 16ab/? = 8a

Q: Why do I need to write 8a as a fraction?

Writing 8a as $ \frac{8a}{1} $ helps you see the equation structure clearly. Now you have $ \frac{16ab}{?} = \frac{8a}{1} $, making it easy to cross-multiply!

Q: What does cross-multiplication actually do here?

Cross-multiplication gives you 16ab × 1 = 8a × ?. This simplifies to 16ab = 8a × ?, so you can solve for the missing denominator by dividing both sides by 8a.

Q: How do I divide 16ab by 8a step by step?

Break it down: $ \frac{16ab}{8a} = \frac{16}{8} \times \frac{a}{a} \times \frac{b}{1} $. The 16÷8 = 2, the a÷a = 1, and b÷1 = b, giving you 2b.

Q: Can I check my answer a different way?

Yes! Substitute back: $ \frac{16ab}{2b} $. Cancel the b's to get $ \frac{16a}{2} = 8a $. Since this equals the right side, 2b is correct!

Q: What if the variables were different letters?

The same method works! If you had $ \frac{12xy}{?} = 6x $, you'd get 12xy = 6x × ?, so ? = $ \frac{12xy}{6x} = 2y $.

Fraction Equations with Missing Denominators

Complete the corresponding expression for the denominator

$\frac{16ab}{?}=8a$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 First, we need to finish setting up the denominator.

00:11 To make it easier, we'll multiply everything by the denominator to get rid of it.

00:21 Now, let's focus on isolating the denominator step by step.

00:33 Next, we'll simplify everything we can.

00:36 We'll break down sixteen into factors. It becomes eight times two.

00:42 Let's see what else can be simplified.

00:50 And that gives us our final answer! Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the corresponding expression for the denominator

$\frac{16ab}{?}=8a$

Step-by-step solution

Using the formula:

$\frac{x}{y}=\frac{z}{w}\xrightarrow{}x\cdot y=z\cdot y$

We first convert the 8 into a fraction, and multiply

$\frac{16ab}{?}=\frac{8}{1}$

$16ab\times1=8a$

$16ab=8a$

We then divide both sides by 8a:

$\frac{16ab}{8a}=\frac{8a}{8a}$

$2b$

Final Answer

$2b$

Key Points to Remember

Essential concepts to master this topic

Cross-multiply rule: When $\frac{a}{b} = c$ , then a = b × c
Technique: Convert 8a to $\frac{8a}{1}$ then cross-multiply: 16ab = 8a × ?
Check: Substitute back: $\frac{16ab}{2b} = 8a$ ✓

Common Mistakes

Avoid these frequent errors

Trying to solve without converting to equal fractions
Don't just divide 16ab by 8a directly = ignoring the equation structure! This misses the cross-multiplication step and often gives incomplete answers. Always convert the whole number to a fraction first, then cross-multiply.

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 do I need to write 8a as a fraction?

Writing 8a as $\frac{8a}{1}$ helps you see the equation structure clearly. Now you have $\frac{16ab}{?} = \frac{8a}{1}$ , making it easy to cross-multiply!

What does cross-multiplication actually do here?

Cross-multiplication gives you 16ab × 1 = 8a × ?. This simplifies to 16ab = 8a × ?, so you can solve for the missing denominator by dividing both sides by 8a.

How do I divide 16ab by 8a step by step?

Break it down: $\frac{16ab}{8a} = \frac{16}{8} \times \frac{a}{a} \times \frac{b}{1}$ . The 16÷8 = 2, the a÷a = 1, and b÷1 = b, giving you 2b.

Can I check my answer a different way?

Yes! Substitute back: $\frac{16ab}{2b}$ . Cancel the b's to get $\frac{16a}{2} = 8a$ . Since this equals the right side, 2b is correct!

What if the variables were different letters?

The same method works! If you had $\frac{12xy}{?} = 6x$ , you'd get 12xy = 6x × ?, so ? = $\frac{12xy}{6x} = 2y$ .

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