Solve the Fraction Equation: Finding the Missing Term in 5/15 + ? + 3/15 = 13/15

Q: Why don't we add the denominators when they're the same?

Think of fractions like pizza slices! If you have 3 slices of 15-slice pizza plus 5 more slices of the same pizza, you still have slices from one pizza. You just count the slices: 3 + 5 = 8 slices out of 15 total.

Q: What if the denominators were different?

When denominators are different, you'd need to find a common denominator first. But since all fractions here have 15 as the denominator, you can skip that step and work directly with numerators!

Q: How do I solve for the missing numerator?

Set up a simple equation with just the numerators: $ 5 + x + 3 = 13 $. Then solve: $ 8 + x = 13 $, so $ x = 5 $.

Q: Can I simplify the final answer?

Yes! $ \frac{5}{15} $ can be simplified by dividing both numerator and denominator by 5 to get $ \frac{1}{3} $. Both answers are correct!

Q: What's the fastest way to check my work?

Add all three fractions together: $ \frac{5}{15} + \frac{5}{15} + \frac{3}{15} = \frac{5+5+3}{15} = \frac{13}{15} $. If it equals the right side, you're correct!

Fraction Addition with Missing Terms

Complete the missing fraction

$\frac{5}{15}+_—+\frac{3}{15}=\frac{13}{15}$

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the unknown

00:03 According to the calculation, we know that the unknown denominator equals the given denominator

00:08 Let's find the number that completes the numerators to the result numerator

00:18 This is the appropriate number, so we'll substitute it in the unknown numerator

00:21 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

Complete the missing fraction

$\frac{5}{15}+_—+\frac{3}{15}=\frac{13}{15}$

What is the missing fraction?

Step-by-step solution

The goal is to find the missing fraction in the equation $\frac{5}{15} + \_ + \frac{3}{15} = \frac{13}{15}$ .

To find the missing fraction, observe the following:
- Start by focusing only on the numerators because they have the same denominator.

We write the equation for the numerators:

$5 + x + 3 = 13$

Combine the known terms on the left side, $5 + 3$ , which results in 8:

$8 + x = 13$

Now, solve for $x$ by subtracting 8 from both sides:

$x = 13 - 8$
$x = 5$

The missing fraction is $\frac{x}{15} = \frac{5}{15}$ .

Therefore, the missing fraction that completes the equation is $\frac{5}{15}$ .

Final Answer

$\frac{5}{15}$

Key Points to Remember

Essential concepts to master this topic

Like Denominators: When denominators match, add only the numerators
Technique: Work with numerators: 5 + x + 3 = 13
Check: Verify $\frac{5}{15} + \frac{5}{15} + \frac{3}{15} = \frac{13}{15}$ ✓

Common Mistakes

Avoid these frequent errors

Adding denominators together
Don't add denominators when fractions have the same bottom number = $\frac{5+5+3}{15+15+15} = \frac{13}{45}$ ! This creates a completely different fraction. Always keep the denominator the same and add only numerators when denominators match.

Practice Quiz

Test your knowledge with interactive questions

$$ $\frac{4}{5}+\frac{1}{5}=$

FAQ

Everything you need to know about this question

Why don't we add the denominators when they're the same?

Think of fractions like pizza slices! If you have 3 slices of 15-slice pizza plus 5 more slices of the same pizza, you still have slices from one pizza. You just count the slices: 3 + 5 = 8 slices out of 15 total.

What if the denominators were different?

When denominators are different, you'd need to find a common denominator first. But since all fractions here have 15 as the denominator, you can skip that step and work directly with numerators!

How do I solve for the missing numerator?

Set up a simple equation with just the numerators: $5 + x + 3 = 13$ . Then solve: $8 + x = 13$ , so $x = 5$ .

Can I simplify the final answer?

Yes! $\frac{5}{15}$ can be simplified by dividing both numerator and denominator by 5 to get $\frac{1}{3}$ . Both answers are correct!

What's the fastest way to check my work?

Add all three fractions together: $\frac{5}{15} + \frac{5}{15} + \frac{3}{15} = \frac{5+5+3}{15} = \frac{13}{15}$ . If it equals the right side, you're correct!

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