Solve the Fraction Equation: Finding the Missing Addend in 2/9 + ? = 2/3

Q: Why can't I just subtract the numerators and denominators separately?

Because denominators represent the size of pieces, not quantities! Think of pizza slices: you can't subtract "eighths" from "thirds" directly. You need pieces of the same size first.

Q: How do I know which denominator to use as the common denominator?

Use the larger denominator when one divides evenly into the other. Here, 9 ÷ 3 = 3, so 9 is our common denominator. For unrelated denominators, find the least common multiple.

Q: What if I get confused about whether to add or subtract?

Look at your equation setup! Since $ \frac{2}{9} + ? = \frac{2}{3} $, you're finding what to add. Rearrange to: $ ? = \frac{2}{3} - \frac{2}{9} $

Q: Can I simplify my answer if it has the same denominator as the other fractions?

Always check if you can simplify! But $ \frac{4}{9} $ is already in lowest terms since 4 and 9 share no common factors except 1.

Q: How do I check my work without doing the whole problem over?

Quick check: Add your answer to the first fraction. $ \frac{2}{9} + \frac{4}{9} = \frac{6}{9} $. Does $ \frac{6}{9} = \frac{2}{3} $? Yes! (6 ÷ 3 = 2, 9 ÷ 3 = 3)

Fraction Addition with Missing Addends

$\frac{2}{9}+?=\frac{2}{3}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the unknown value.

00:07 First, we'll rearrange the equation to isolate the unknown. Ready?

00:20 Next, we need to find the least common denominator. Let's go!

00:26 Let's multiply by three to get a common denominator for both fractions.

00:31 Remember, multiply both the numerator and the denominator by three.

00:38 Now, calculate the products you have.

00:42 Add the fractions together under the common denominator.

00:47 Find the total for the numerator.

00:50 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\frac{2}{9}+?=\frac{2}{3}$

Step-by-step solution

To find the missing fraction in the equation $\frac{2}{9} + ? = \frac{2}{3}$ , we will perform the following steps:

Step 1: Convert the fraction $\frac{2}{3}$ to have the same denominator as $\frac{2}{9}$ .
Step 2: Subtract $\frac{2}{9}$ from the new fraction.

Let's execute these steps:
Step 1: Convert $\frac{2}{3}$ into a fraction with a denominator of 9. To do this, multiply both the numerator and the denominator of $\frac{2}{3}$ by 3 to obtain an equivalent fraction:
$\frac{2}{3} \times \frac{3}{3} = \frac{6}{9}$

Step 2: Subtract $\frac{2}{9}$ from $\frac{6}{9}$ :
$\frac{6}{9} - \frac{2}{9} = \frac{4}{9}$

Thus, the fraction that we need to add to $\frac{2}{9}$ to get $\frac{2}{3}$ is $\frac{4}{9}$ .

The correct answer to the problem is $\frac{4}{9}$ .

Final Answer

$\frac{4}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Convert fractions to same denominator before adding or subtracting
Technique: Rewrite $\frac{2}{3}$ as $\frac{6}{9}$ by multiplying by $\frac{3}{3}$
Check: Verify $\frac{2}{9} + \frac{4}{9} = \frac{6}{9} = \frac{2}{3}$ ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators instead of finding common denominators
Don't try to subtract $\frac{2}{3} - \frac{2}{9}$ by doing 3 - 9 = -6! This creates meaningless fractions like $\frac{0}{-6}$ . Denominators tell you the size of pieces, not quantities to subtract. Always convert to the same denominator first, then subtract only the numerators.

Practice Quiz

Test your knowledge with interactive questions

Complete the following exercise:

$\frac{3}{4}:\frac{5}{6}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just subtract the numerators and denominators separately?

Because denominators represent the size of pieces, not quantities! Think of pizza slices: you can't subtract "eighths" from "thirds" directly. You need pieces of the same size first.

How do I know which denominator to use as the common denominator?

Use the larger denominator when one divides evenly into the other. Here, 9 ÷ 3 = 3, so 9 is our common denominator. For unrelated denominators, find the least common multiple.

What if I get confused about whether to add or subtract?

Look at your equation setup! Since $\frac{2}{9} + ? = \frac{2}{3}$ , you're finding what to add. Rearrange to: $? = \frac{2}{3} - \frac{2}{9}$

Can I simplify my answer if it has the same denominator as the other fractions?

Always check if you can simplify! But $\frac{4}{9}$ is already in lowest terms since 4 and 9 share no common factors except 1.

How do I check my work without doing the whole problem over?

Quick check: Add your answer to the first fraction. $\frac{2}{9} + \frac{4}{9} = \frac{6}{9}$ . Does $\frac{6}{9} = \frac{2}{3}$ ? Yes! (6 ÷ 3 = 2, 9 ÷ 3 = 3)

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Solve the Fraction Equation: Finding the Missing Addend in 2/9 + ? = 2/3

Fraction Addition with Missing Addends

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I just subtract the numerators and denominators separately?

How do I know which denominator to use as the common denominator?

What if I get confused about whether to add or subtract?

Can I simplify my answer if it has the same denominator as the other fractions?

How do I check my work without doing the whole problem over?

🌟 Unlock Your Math Potential

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