Solve the Fraction Equation: Finding the Missing Addend in 4/7 + _ = 6/7

Q: Why does the denominator stay the same?

When fractions have identical denominators, you're working with the same-sized pieces! Think of it like pizza slices - if you have 4 sevenths and add some more sevenths, you're still counting sevenths.

Q: What if the denominators were different?

If denominators were different (like $ \frac{4}{7} + \frac{x}{5} $), you'd need to find a common denominator first. But here, both fractions already have 7 as the denominator!

Q: How do I remember which number to subtract?

Think: What + 4 = 6? Since $ \frac{4}{7} + \text{missing} = \frac{6}{7} $, the missing numerator is 6 - 4 = 2.

Q: Can I check my answer a different way?

Yes! Try adding your answer: $ \frac{4}{7} + \frac{2}{7} = \frac{4+2}{7} = \frac{6}{7} $. If it matches the given sum, you're correct!

Q: What if my answer was a bigger fraction than the sum?

That's impossible! The missing addend must be smaller than the total sum. If you get $ \frac{8}{7} $ or larger, double-check your subtraction.

Fraction Addition with Missing Addends

Complete the missing fraction

$\frac{4}{7}+_—=\frac{6}{7}$

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

00:04 According to the calculation, we know that the denominator of the unknown equals the given denominator

00:07 Let's find the number that completes the numerator to match the result's numerator

00:14 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

$\frac{4}{7}+_—=\frac{6}{7}$

What is the missing fraction?

Step-by-step solution

To determine the missing fraction in the equation $\frac{4}{7} + \_\_\_ = \frac{6}{7}$ , we follow these steps:

Step 1: Assume the missing fraction is $\frac{x}{7}$ .
Step 2: Our equation becomes $\frac{4}{7} + \frac{x}{7} = \frac{6}{7}$ .
Step 3: Since the denominators are the same, we equate the numerators: $4 + x = 6$ .
Step 4: Solve for $x$ by subtracting $4$ from both sides: $x = 6 - 4$ .
Step 5: We find $x = 2$ .
Step 6: Substitute $x$ back into the fraction $\frac{x}{7}$ , giving us the missing fraction $\frac{2}{7}$ .

Thus, the missing fraction is $\frac{2}{7}$ .

Final Answer

$\frac{2}{7}$

Key Points to Remember

Essential concepts to master this topic

Same Denominators: Add numerators when denominators are identical
Missing Addend: Subtract known numerator from sum: 6 - 4 = 2
Verification: Check by adding: $\frac{4}{7} + \frac{2}{7} = \frac{6}{7}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators or changing the denominator
Don't subtract 7 - 7 = 0 or change the denominator to something else! The denominator stays the same when fractions have identical denominators. Always keep the denominator as 7 and only work with the numerators: 6 - 4 = 2.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why does the denominator stay the same?

When fractions have identical denominators, you're working with the same-sized pieces! Think of it like pizza slices - if you have 4 sevenths and add some more sevenths, you're still counting sevenths.

What if the denominators were different?

If denominators were different (like $\frac{4}{7} + \frac{x}{5}$ ), you'd need to find a common denominator first. But here, both fractions already have 7 as the denominator!

How do I remember which number to subtract?

Think: What + 4 = 6? Since $\frac{4}{7} + \text{missing} = \frac{6}{7}$ , the missing numerator is 6 - 4 = 2.

Can I check my answer a different way?

Yes! Try adding your answer: $\frac{4}{7} + \frac{2}{7} = \frac{4+2}{7} = \frac{6}{7}$ . If it matches the given sum, you're correct!

What if my answer was a bigger fraction than the sum?

That's impossible! The missing addend must be smaller than the total sum. If you get $\frac{8}{7}$ or larger, double-check your subtraction.

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