Solve the Fraction Equation: Finding the Numerator in ?/15a = 5b/15a

Q: Why can I just copy the numerator from the right side?

When two fractions have identical denominators, they can only be equal if their numerators are also identical. Since $ \frac{?}{15a} = \frac{5b}{15a} $, the missing numerator must be exactly 5b.

Q: What if the denominators were different?

If denominators differed, you'd need to find a common denominator first, then compare numerators. But here, both fractions already have $ 15a $ as the denominator!

Q: Do I need to simplify 5b somehow?

No! The expression $ 5b $ is already in its simplest form. Don't try to factor or change it - just write it exactly as shown.

Q: How do I check if 5b is really correct?

Substitute back: $ \frac{5b}{15a} = \frac{5b}{15a} $. Since both sides are exactly the same, your answer is definitely correct!

Q: What if I chose 3ab or 15b instead?

Those would make the fractions unequal! For example: $ \frac{3ab}{15a} \neq \frac{5b}{15a} $ because 3ab ≠ 5b. Only identical numerators work.

Fraction Equality with Same Denominators

Complete the corresponding expression in the numerator

$\frac{?}{15a}=\frac{5b}{15a}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's complete the counter, and find the missing part.

00:16 To focus on the numerator, we multiply both sides by the denominator. Let's get started!

00:29 Now, let's simplify as much as possible.

00:34 And that's the solution to our problem! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Complete the corresponding expression in the numerator

$\frac{?}{15a}=\frac{5b}{15a}$

Step-by-step solution

To solve this problem, we will follow these steps:

Step 1: Note that we are given two fractions $\frac{?}{15a}$ and $\frac{5b}{15a}$ .
Step 2: Observe that both fractions have the same denominator $15a$ .
Step 3: For these fractions to be equal, their numerators must also be equal. Thus, $? = 5b$ .

Now, let's apply these steps:

By equating the numerators of $\frac{?}{15a} = \frac{5b}{15a}$ , we directly find that the missing expression in the numerator, denoted as $?$ , must be $5b$ .

Therefore, the correct answer is $5b$ .

Final Answer

$5b$

Key Points to Remember

Essential concepts to master this topic

Equality Rule: Fractions with identical denominators are equal when numerators match
Technique: Compare numerators directly: $\frac{?}{15a} = \frac{5b}{15a}$ means ? = 5b
Check: Verify $\frac{5b}{15a} = \frac{5b}{15a}$ shows both sides identical ✓

Common Mistakes

Avoid these frequent errors

Trying to cross-multiply or manipulate the denominator
Don't cross-multiply 15a × ? = 5b × 15a when denominators are already the same = unnecessary work and confusion! This wastes time and can introduce errors. Always recognize when denominators match and simply equate the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the corresponding expression for the denominator

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

FAQ

Everything you need to know about this question

Why can I just copy the numerator from the right side?

When two fractions have identical denominators, they can only be equal if their numerators are also identical. Since $\frac{?}{15a} = \frac{5b}{15a}$ , the missing numerator must be exactly 5b.

What if the denominators were different?

If denominators differed, you'd need to find a common denominator first, then compare numerators. But here, both fractions already have $15a$ as the denominator!

Do I need to simplify 5b somehow?

No! The expression $5b$ is already in its simplest form. Don't try to factor or change it - just write it exactly as shown.

How do I check if 5b is really correct?

Substitute back: $\frac{5b}{15a} = \frac{5b}{15a}$ . Since both sides are exactly the same, your answer is definitely correct!

What if I chose 3ab or 15b instead?

Those would make the fractions unequal! For example: $\frac{3ab}{15a} \neq \frac{5b}{15a}$ because 3ab ≠ 5b. Only identical numerators work.

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