Solve the Fraction Equation: 2/3 minus 2/9

Q: Why can't I just subtract 2-2=0 and 3-9=-6?

Because fractions represent parts of a whole! You can't subtract different-sized pieces directly. Think of it like 2 thirds minus 2 ninths - you need equal-sized pieces first.

Q: How do I know 9 is the LCD of 3 and 9?

The LCD is the smallest number both denominators divide into evenly. Since 9 ÷ 3 = 3 and 9 ÷ 9 = 1, both work perfectly! Always check if the larger number is already a multiple of the smaller.

Q: What if I get a different common denominator?

You could use 18, 27, or any multiple of 9, but it makes more work! Using the least common denominator keeps numbers smaller and easier to work with.

Q: Do I need to simplify my answer?

Always check if you can simplify! For $ \frac{4}{9} $, since 4 and 9 share no common factors, it's already in lowest terms.

Q: Can I convert both fractions to decimals instead?

You could, but fractions are often more accurate! Converting $ \frac{2}{3} $ gives 0.666... (repeating), which can lead to rounding errors in your final answer.

Fraction Subtraction with Different Denominators

Solve the following exercise:

$\frac{2}{3}-\frac{2}{9}=\text{?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Multiply by 3 to find the common denominator

00:07 Make sure to multiply both numerator and denominator

00:15 Calculate the products

00:21 Subtract with the common denominator

00:26 Calculate the numerator

00:31 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

Solve the following exercise:

$\frac{2}{3}-\frac{2}{9}=\text{?}$

Step-by-step solution

To solve the subtraction of fractions $\frac{2}{3} - \frac{2}{9}$ , we will follow a step-by-step approach:

Step 1: Identify the denominators of the fractions, which are 3 and 9.
Step 2: Find the least common denominator (LCD) of 3 and 9. Since 9 is a multiple of 3, $\text{LCD} = 9$ .
Step 3: Convert each fraction to an equivalent fraction with this denominator.

The fraction $\frac{2}{3}$ is converted to $\frac{6}{9}$ because $2 \times 3 = 6$ and $3 \times 3 = 9$ .
The fraction $\frac{2}{9}$ remains $\frac{2}{9}$ because it already has the denominator 9.

Step 4: Subtract the numerators: $6 - 2 = 4$ .
Step 5: Place the result over the common denominator: $\frac{4}{9}$ .

Thus, the result of the subtraction $\frac{2}{3} - \frac{2}{9}$ is $\frac{4}{9}$ .

Therefore, the solution to the problem is $\frac{4}{9}$ .

Final Answer

$\frac{4}{9}$

Key Points to Remember

Essential concepts to master this topic

Rule: Find LCD before subtracting fractions with different denominators
Technique: Convert $\frac{2}{3}$ to $\frac{6}{9}$ by multiplying by 3
Check: Verify $\frac{6}{9} - \frac{2}{9} = \frac{4}{9}$ by adding back ✓

Common Mistakes

Avoid these frequent errors

Subtracting denominators along with numerators
Don't subtract 3 - 9 = -6 in the denominator! This creates a meaningless fraction like $\frac{0}{-6}$ . The denominators show what size pieces you're working with - you only subtract the numerators. Always keep the common denominator unchanged.

Practice Quiz

Test your knowledge with interactive questions

Solve the following exercise:

$\frac{8}{5}-\frac{4}{5}=\text{?}$

FAQ

Everything you need to know about this question

Why can't I just subtract 2-2=0 and 3-9=-6?

Because fractions represent parts of a whole! You can't subtract different-sized pieces directly. Think of it like 2 thirds minus 2 ninths - you need equal-sized pieces first.

How do I know 9 is the LCD of 3 and 9?

The LCD is the smallest number both denominators divide into evenly. Since 9 ÷ 3 = 3 and 9 ÷ 9 = 1, both work perfectly! Always check if the larger number is already a multiple of the smaller.

What if I get a different common denominator?

You could use 18, 27, or any multiple of 9, but it makes more work! Using the least common denominator keeps numbers smaller and easier to work with.

Do I need to simplify my answer?

Always check if you can simplify! For $\frac{4}{9}$ , since 4 and 9 share no common factors, it's already in lowest terms.

Can I convert both fractions to decimals instead?

You could, but fractions are often more accurate! Converting $\frac{2}{3}$ gives 0.666... (repeating), which can lead to rounding errors in your final answer.

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