Solve for the Missing Fraction: 2/9 + ? + 5/9 = 8/9

Q: Why do I subtract instead of just guessing the missing fraction?

Subtraction gives you the exact answer every time! Guessing might work for simple problems, but subtraction is the reliable method that works for any missing addend problem.

Q: Can I solve this by setting up an equation with x?

Yes! You can write $ \frac{2}{9} + x + \frac{5}{9} = \frac{8}{9} $, then solve for x. Both methods give the same answer: $ \frac{1}{9} $.

Q: What if the fractions had different denominators?

You'd need to find a common denominator first, then follow the same steps. The process is the same - just with an extra step at the beginning.

Q: How do I know my answer makes sense?

Check that your missing fraction is reasonable! Since $ \frac{2}{9} + \frac{5}{9} = \frac{7}{9} $ and we need $ \frac{8}{9} $, the missing piece should be small - just $ \frac{1}{9} $.

Fraction Operations with Missing Addends

Complete the missing fraction

$\frac{2}{9}+_—+\frac{5}{9}=\frac{8}{9}$

What is the missing fraction?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the missing number.

00:11 We know the unknown denominator equals the given denominator.

00:17 Now, let's identify the number that matches our numerators.

00:23 That's the number we need, so we'll use it in our numerator.

00:26 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 missing fraction

$\frac{2}{9}+_—+\frac{5}{9}=\frac{8}{9}$

What is the missing fraction?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Compute the sum of the given fractions $\frac{2}{9}$ and $\frac{5}{9}$ .
Step 2: Subtract the result from the total $\frac{8}{9}$ to find the missing fraction.

First, let's compute the sum of the known fractions:

$\frac{2}{9} + \frac{5}{9} = \frac{2 + 5}{9} = \frac{7}{9}$

Next, subtract this result from the total sum:

$\frac{8}{9} - \frac{7}{9} = \frac{8 - 7}{9} = \frac{1}{9}$

Thus, the missing fraction that completes the equation is $\frac{1}{9}$ .

Therefore, the solution to the problem is $\frac{1}{9}$ .

Final Answer

$\frac{1}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find missing addend by subtracting known parts from total
Technique: Add known fractions first: $\frac{2}{9} + \frac{5}{9} = \frac{7}{9}$
Check: Verify by adding all three fractions: $\frac{2}{9} + \frac{1}{9} + \frac{5}{9} = \frac{8}{9}$ ✓

Common Mistakes

Avoid these frequent errors

Adding all fractions including the unknown
Don't add 2/9 + ? + 5/9 = 8/9 all together without finding the missing piece first = confusion and wrong setup! This creates an equation you can't solve directly. Always find the sum of known fractions first, then subtract from the total.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I subtract instead of just guessing the missing fraction?

Subtraction gives you the exact answer every time! Guessing might work for simple problems, but subtraction is the reliable method that works for any missing addend problem.

Can I solve this by setting up an equation with x?

Yes! You can write $\frac{2}{9} + x + \frac{5}{9} = \frac{8}{9}$ , then solve for x. Both methods give the same answer: $\frac{1}{9}$ .

What if the fractions had different denominators?

You'd need to find a common denominator first, then follow the same steps. The process is the same - just with an extra step at the beginning.

How do I know my answer makes sense?

Check that your missing fraction is reasonable! Since $\frac{2}{9} + \frac{5}{9} = \frac{7}{9}$ and we need $\frac{8}{9}$ , the missing piece should be small - just $\frac{1}{9}$ .

What if I get a negative answer?

A negative answer means the known fractions already add up to more than the total. Double-check your problem setup and arithmetic - there might be an error in the given numbers.

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